Design and Implementation of a Thomson Parabola for Fluence Dependent Energy-Loss Measurements at the Neutralized Drift Compression eXperiment
(abstract)
The interaction of ion beams with matter includes the investigation of the basic principles of ion stopping in heated materials. An unsolved question is the effect of different, especially higher, ion beam fluences on ion stopping in solid targets. This is relevant in applications such as in fusion sciences. To address this question, a Thomson parabola was built for the Neutralized Drift Compression eXperiment (NDCX-II) for ion energy-loss measurements at different ion beam fluences. The linear induction accelerator NDCX-II delivers 2 ns short, intense ion pulses, up to several tens of nC/pulse, or 1010-1011 ions, with a peak kinetic energy of ∼1.1 MeV and a minimal spot size of 2 mm FWHM. For this particular accelerator, the energy determination with conventional beam diagnostics, for example, time of flight measurements, is imprecise due to the non-trivial longitudinal phase space of the beam. In contrast, a Thomson parabola is well suited to reliably determine the beam energy distribution. The Thomson parabola differentiates charged particles by energy and charge-to-mass ratio, through deflection of charged particles by electric and magnetic fields. During first proof-of-principle experiments, we achieved to reproduce the average initial helium beam energy as predicted by computer simulations with a deviation of only 1.4%. Successful energy-loss measurements with 1 μm thick silicon nitride foils show the suitability of the accelerator for such experiments. The initial ion energy was determined during a primary measurement without a target, while a second measurement, incorporating the target, was used to determine the transmitted energy. The energy-loss was then determined as the difference between the two energies.
Onset of magnetic reconnection in a
collisionless, high-beta plasma
Andrew Alt & Matthew W. Kunz, submitted
#s879, Wednesday, 25 Sep 2019, 12:00am
Analytical nonlinear collisional dynamics of near-threshold eigenmodes
V. N. Duarte & N. N. Gorelenkov, submitted (2018)
#s855, Tuesday, 17 Sep 2019, 11:00am, T169
A Kinetic Multiscale Method Using Equation-Free Projective Integration
B. Sturdevant, S. Parker et al., submitted (2018)
#s844, Saturday, 14 Sep 2019, 11:00am, T169
3D Magnetohydrodynamic modeling of fast thermal quenches due to impurities in tokamaks
N. M. Ferraro et al., submitted (2018)
#s845, Saturday, 14 Sep 2019, 11:00am, T169
Moment Preserving Constrained Resampling with Applications to Particle-in-Cell
Methods
D. Faghihi et al., J. Comput. Phys., submitted (2018)
#s846, Saturday, 14 Sep 2019, 11:00am, T169
Shadowing effects in simulated Alcator C-Mod gas puff imaging data
Daren Stotler, submitted (2018)
#s797, Friday, 12 Jul 2019, 11:00am, T169
Recent Experiments At Ndcx-II: Irradiation Of Materials Using Short, Intense Ion Beams
P. A. Seidl, Q. Ji, et al., submitted (2018)
#s749, Friday, 14 Jun 2019, 11:00am, T169
Irradiation of Materials with Short, Intense Ion pulses at NDCX-II
P.A. Seidl, Q. Ji, et al., submitted (2018)
#s752, Friday, 14 Jun 2019, 11:00am, T169
A magnetic field augmented single frequency capacitively coupled plasma device
Sarveshwar Sharma, Igor Kaganovich, et al., submitted (2018)
#s753, Friday, 14 Jun 2019, 11:00am, T169
Root-Growth of Boron Nitride Nanotubes: Experiments and Ab Initio Simulations
Biswajit Santra, Hsin-Yu Ko et al., submitted (2018)
#s755, Friday, 14 Jun 2019, 11:00am, T169
Analytical model of three regimes of cold cathode breakdown in helium
Liang Xu, Alexander V. Khrabrov et al., submitted (2018)
#s756, Friday, 14 Jun 2019, 11:00am, T169
Evolution of the electron cyclotron drift instability in two-dimensions
Salomon Janhunen, Andrei Smolyakov et al., submitted (2018)
#s758, Friday, 14 Jun 2019, 11:00am, T169
Short-Pulse, Compressed Ion Beams at the Neutralized Drift Compression Experiment
Peter A Seidl, John J Barnard et al., submitted (2018)
#s760, Friday, 14 Jun 2019, 11:00am, T169
Short intense ion pulses for materials and warm dense matter research
Peter A. Seidl, Wayne G. Greenway et al., submitted (2018)
#s761, Friday, 14 Jun 2019, 11:00am, T169
Structure of Velocity Distribution of Sheath-Accelerated Secondary Electrons in Asymmetric RF-DC Discharge
Alexander V. Khrabrov, Igor D. Kaganovich et al., submitted (2018)
#s762, Friday, 14 Jun 2019, 11:00am, T169
Generation of anomalously energetic suprathermal electrons by an electron beam interacting with a nonuniform plasma
D. Sydorenko, I. D. Kaganovich et al., submitted (2018)
#s763, Friday, 14 Jun 2019, 11:00am, T169
Ion sound instability driven by ion beam
O. Koshkarov, A. I. Smolyakov et al., submitted (2018)
#s764, Friday, 14 Jun 2019, 11:00am, T169
Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence
Chuanfei Dong, Liang Wang, submitted (2018)
#s767, Thursday, 13 Jun 2019, 11:00am, T169
Time-domain global similarity method for automatic data cleaning for multi-channel measurement systems in magnetic confinement fusion devices
(abstract)
To guarantee the availability and reliability of data source in Magnetic Confinement Fusion (MCF) devices, incorrect diagnostic data, which cannot reflect real physical properties of measured objects, should be sorted out before further analysis and study. Traditional data sorting cannot meet the growing demand of MCF research because of the low-efficiency, time-delay, and lack of objective criteria. In this paper, a Time-Domain Global Similarity (TDGS) method based on machine learning technologies is proposed for the automatic data cleaning of MCF devices. The aim of traditional data sorting is to classify original diagnostic data sequences. The lengths and evolution properties of the data sequences vary shot by shot. Hence the classification criteria are affected by many discharge parameters and are different in various discharges. The focus of the TDGS method is turned to the physical similarity between data sequences from different channels, which are more independent of discharge parameters. The complexity arisen from real discharge parameters during data cleaning is avoided in the TDGS method by transforming the general data sorting problem into a binary classification problem about the physical similarity between data sequences. As a demonstration of its application to multi-channel measurement systems, the TDGS method is applied to the EAST POlarimeter–INTerferometer (POINT) system. The optimal performance of the method evaluated by 24-fold cross-validation has reached 0.9871 ± 0.0385.
Full-f gyrokinetic simulation of turbulence in a helical open-field-line plasma
(abstract)
Eric L. Shi, Gregory W. Hammett et al., submitted Oct 2018
#s912, Thursday, 31 Jan 2019, 12:00am
Plasma q-plate for generation and manipulation of intense optical vortices
(abstract)
K. Qu, Q. Jia, & N. J. Fisch, submitted (2017)
#s545, Tuesday, 01 Jan 2019, 12:00am
Abstract.
Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER
(abstract)
C.S. Chang, S. Ku et al., submitted (2017)
#s353, 5418, Tuesday, 01 Jan 2019, 12:00am
A model of solar equilibrium: the hydrodynamic limit
(abstract)
L. M. Gunderson & A. Bhattacharjee, Astro. J. submitted (2018)
#s618, Tuesday, 01 Jan 2019, 12:00am
Helioseismology has revealed the internal density and rotation profile of the Sun. Yet, knowledge of its magnetic fields and
meridional circulation is confined much closer to the surface, and mean entropy gradients at the surface are below detectable
limits. Numerical simulations can offer insight into the interior dynamics, and help identify which ingredients are necessary
to produce particular features. However, several gross features of the Sun can be understood analytically from an equilibrium
perspective, for example the 1-D density profile arising from steady-state energy transport from the core to the surface, or the
tilting of isorotation contours in the convection zone due to baroclinic forcing. To help answer the question of which features can
be qualitatively explained by equilibrium, we propose analyzing stationary axisymmetric ideal MHD flows in the solar regime.
By choosing an appropriate latitudinal entropy profile, we recover a rotation profile that reasonably matches observations in the
bulk of the convection zone. Furthermore, we include the effects of poloidal flow, developing a feature reminiscent of the near
surface shear layer. No tachocline-like feature is seen in hydrodynamic equilibrium, suggesting the importance of either dynamics
or magnetic fields in any description.
Nonlocal transport in toroidal plasma devices.
(abstract)
Gianluca Spizzo & Roscoe White, submitted (2018)
#s640, Tuesday, 01 Jan 2019, 12:00am
Collisional particle transport is examined in ITER in the presence of tearing mode perturbations
typical of modes leading up to a disruption. The onset of subdiffusive transport for electrons and
ions is found to occur at very low amplitudes and to also exist for ions of high energy. Orbit reso-
nances produce long time correlations and traps for particle trajectories at perturbation amplitudes
much too small for the orbits to be represented as uniformly chaotic.
Bound state energies using Phase integral methods
(abstract)
R.B. White & A. Kutlin, Ad. Theoret. Math. Phys. submitted (2017)
#s407, 5318, Tuesday, 01 Jan 2019, 12:00am
The study of asymptotic properties of solutions to differential equations has a long and arduous
history, with the most significant advances having been made in the development of quantum
mechanics. A very powerful method of analysis is that of Phase Integrals, described by Heading.
Key to this analysis are the Stokes constants and the rules for analytic continuation of an asymptotic
solution through the complex plane. These constants are easily determined for isolated singular
points, by analytically continuing around them and, in the case of analytic functions, requiring
the asymptotic solution to be single valued. However, most interesting problems of mathematical
physics involve several singular points. By examination of analytically tractable problems and
more complex bound state problems involving multiple singular points, we show that the method
of Phase Integrals can greatly improve the determination of bound state energy over the simple
WKB values. We also find from these examples that in the limit of large separation the Stokes
constant for a first order singular point approaches the isolated singular point value.
Wave kinetic equation in a nonstationary and inhomogeneous medium with a weak quadratic nonlinearity
D. E. Ruiz, M. E. Glinsky & I. Y. Dodin, Phys. Rev. A, submitted (2018)
#s673, Tuesday, 01 Jan 2019, 12:00am
Density perturbation mode structure of high frequency compressional and global Alfvén eigenmodes in the National Spherical Torus Experiment using a novel reflectometer analysis technique
(abstract)
N. Crocker, E.V. Belova et al., Plasma Phys. Control. Fusion, submitted (2017)
#s451, Tuesday, 01 Jan 2019, 12:00am
Reflectometry measurements of compressional (CAE) and global (GAE) Alfvén eigenmodes are analyzed to obtain the amplitude and spatial structure of the density perturbations associated with the modes. A novel analysis technique developed for this purpose is presented. The analysis also naturally yields the amplitude and spatial structure of the density contour radial displacement, which is found to be 2–4 times larger than the value estimated directly from the reflectometer measurements using the much simpler 'mirror approximation'. The modes were driven by beam ions in a high power (6 MW) neutral beam heated H-mode discharge (#141398) in the National Spherical Torus Experiment. The results of the analysis are used to assess the contribution of the modes to core energy transport and ion heating. The total displacement amplitude of the modes, which is shown to be larger than previously estimated (Crocker et al 2013 Nucl. Fusion 53 43017), is compared to the predicted threshold (Gorelenkov et al 2010 Nucl. Fusion 50 84012) for the anomalously high heat diffusion inferred from transport modeling in similar NSTX discharges. The results of the analysis also have strong implications for the energy transport via coupling of CAEs to kinetic Alfvén waves seen in simulations with the Hybrid MHD code (Belova et al 2015 Phys. Rev. Lett. 115 15001). Finally, the amplitudes of the observed CAEs fall well below the threshold for causing significant ion heating by stochastic velocity space diffusion (Gates et al 2001 Phys. Rev. Lett. 87 205003)
Characterization of Intrinsic Impurity Sources and Edge Transport in NSTX Discharges with Lithium Wall Conditioning
(abstract)
Filippo Scotti, V. A. Soukhanovskii et al., Nucl. Fusion, submitted (2017)
#s476, Tuesday, 01 Jan 2019, 12:00am
.
Scrape-Off Layer Turbulence in Tokamaks Simulated with a Continuum Gyrokinetic Code
(abstract)
We are developing a new continuum gyrokinetic code, Gkeyll, for use in edge plasma simulations, and here present initial simulations of turbulence on open field lines with model sheath boundary conditions.
The code implements an energy conserving discontinuous Galerkin scheme, applicable to a general class of Hamiltonian equations. Several applications to test problems have been done, including a calculation of the parallel heat-flux on divertor plates resulting from an ELM crash in JET, for a $1x/1v$ SOL scenario explored previously, where the ELM is modeled as a time-dependent intense upstream source.
Here we present initial simulations of turbulence on open field lines in the LAPD linear plasma device.
We have also done simulations in a helical open-field-line geometry.
While various simplifications have been made at present, this still includes some of the key physics of SOL turbulence, such as bad-curvature drive for instabilities and rapid parallel losses with sheath boundary conditions.
This is useful for demonstrating the overall feasibility of this approach and for initial physics studies of SOL turbulence.
We developed a novel version of DG that uses Maxwellian-weighted basis functions while still preserving exact particle and energy conservation.
The Maxwellian-weighted DG method achieves the same error with 4 times less computational cost in $1v$, or 16 times lower cost in the 2 velocity dimensions of gyrokinetics (assuming memory bandwidth is the limiting factor).
Magnetohydrodynamical equilibria with DC current singularities and continuous rotational transform
Yao Zhou, submitted
#s891, Monday, 31 Dec 2018, 11:00am
Kelvin-Helmholtz instability is the result of parity-time symmetry breaking
Hong Qin, Ruili Zhang et al., submitted
#s892, Monday, 31 Dec 2018, 11:00am
Antenna-plasma coupling calculations for the ITER low-field side reflectometer
(abstract)
The antenna-plasma coupling for the ITER low-field side reflectometer system (LFSR) was studied using the hybrid 3D reflectometer simulation code FWR3D, in which full-wave, paraxial, and free-space solvers are used for speed and accuracy. Reflections from equilibrium profiles were simulated to study and optimize the power that is coupled the receiving antenna. At the optimal coupling, the effects of density fluctuations were also calculated, showing that the density fluctuations decrease the average coupling by as much as 6 dB. This study indicates that after some minor changes to the location of the proposed antennas, the antenna-plasma coupling of the ITER LFSR provides a sufficient basis from which to design and build a reflectometer system that meets the specifications requested by ITER.
First experimental measurements of a new fast ion driven micro-burst instability in a field-reversed configuration plasma
(abstract)
In modern field-reversed configuration (FRC) experiments (Binderbauer et al 2015 Phys. Plasmas 22 056110) at TAE Technologies, classical FRC instabilities are suppressed by advanced neutral beam injection and edge biasing methods, leading to high plasma confinement and fast ion pressure built-up which is comparable to the bulk plasma pressure. In some of these high performance FRC plasmas, a new macroscopically non-destructive fast ion driven micro-burst instability is observed as periodic small amplitude bursts with frequency down chirping in the diamagnetic drift frequency range, repeating about every 0.1 to 0.5 ms. The occurrence of these micro-bursts and burst-free operation can be controlled by changing the injected neutral beam energy. Major observed characteristics of this new instability are presented. Possible explanation of the phenomenon is suggested.
Comments on “Revision of the Coulomb logarithm in the ideal plasma”
J. A. Krommes, Phys. Plasmas 21, 042103 (2014) submitted
#s646, Monday, 31 Dec 2018, 12:00am
Strategies for Advantageous Differential Transport of Ions in Magnetic Fusion Devices
Elijah Kolmes, Ian Ochs, and Nathaniel Fisch, submitted
#s647, Monday, 31 Dec 2018, 12:00am
Statistical methods and zonal flows
J. A. Krommes and J. B. Parker, submitted
#s648, Monday, 31 Dec 2018, 12:00am
Past
Benchmark of gyrokinetic, kinetic MHD and gyrofluid codes for the linear calculation of fast particle driven TAE dynamics
Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model.
Benchmarking and validation of global model code for negative hydrogen ion sources
Benchmarking and validation are prerequisites for using simulation codes as predictive tools. In this work, we have developed a Global Model for Negative Hydrogen Ion Source (GMNHIS) and performed benchmarking of the GMNHIS against another independently developed code, Global Enhanced Vibrational Kinetic Model (GEVKM). This is the first study to present a quite comprehensive benchmarking test of this kind for models of negative hydrogen ion sources (NHIS), and excellent agreements have been achieved for collisional energy loss per electron-ion pair created, electron number density, electron temperature, densities of H+3 and H+2 ions, and densities of H(n = 1–3) atoms. Very small discrepancies in number densities of H− ions and H+ ions, as well as the vibrational distribution function of hydrogen molecules, can be attributed to the differences in the chemical reactions datasets. The GEVKM includes additional chemical reactions that are more important at high pressures. In addition, we validated the GMNHIS against experimental data obtained in an electron cyclotron resonance discharge used for H− production. The model qualitatively (and even quantitatively for certain conditions) reproduces the experimental H− number density. The H− number density as a function of pressure first increases at pressures below 1.6 Pa and then saturates for higher pressures. This dependence was analyzed by evaluating contributions from different reaction pathways to the creation and loss of the H− ions. The developed codes can be used for predicting the H− production, improving the performance of NHIS, and ultimately optimizing the parameters of negative ion beams for fusion reactors.
Suppression of Tearing Modes by RF Current Condensation
Currents driven by rf (radio frequency) waves in the interior of magnetic islands can stabilize deleterious tearing modes in tokamaks. Present analyses of stabilization assume that the local electron acceleration is unaffected by the presence of the island. However, the power deposition and electron acceleration are sensitive to the perturbation of the temperature. The nonlinear feedback on the power deposition in the island increases the temperature perturbation, and can lead to a bifurcation of the solution to the steady-state heat diffusion equation. The combination of the nonlinearly enhanced temperature perturbation with the rf current drive sensitivity to the temperature leads to an rf current condensation effect, which can increase the efficiency of rf current drive stabilization and reduce its sensitivity to radial misalignment of the ray trajectories. The threshold for the effect is in a regime that has been encountered in experiments, and will likely be encountered in ITER.
Direct observation of nonlinear coupling between pedestal modes leading to the onset of edge localized modes
Ahmed Diallo, Julien Dominski, et al., Phys. Rev. Lett, accepted , abstract
[#s913,
30 Nov 2018]
Prior to eruptive events such as edge localized modes (ELMs), quasi-coherent fluctuations, referred to as pedestal modes, are observed in the edge of fusion devices. We report on the investigations of nonlinear coupling between these modes { during quasi-stationary inter-ELM phases} leading to the ELM onset. Three dominant modes, with density and magnetic signatures, are identified as the key players { in the triggering mechanism of certain { class} of ELMs}. { We demonstrate that one of these mode is generated by the two others through three waves interactions. The generated mode is radially shifted relative to the other two modes towards the last-closed flux surface as the ELM event approaches.} { Our results suggest that nonlinear coupling of pedestal modes, associated with radial distortions pushing out of the pedestal, is a possible mechanism for the triggering low frequency ELMs relevant for future fusion devices.
Structure-preserving geometric particle-in-cell methods for Vlasov-Maxwell systems
Simulations of the heat flux on plasma facing components from exhausting core plasma are reported for two possible Fusion Nuclear Science Facility (FNSF) divertor configurations. One configuration utilizes divertor plates strongly inclined with respect to the poloidal magnetic flux surfaces like that planned for ITER and results in a partially detached divertor-plasma. The second configuration has divertor plates orthogonal to the flux surfaces, which leads to a fully detached divertor-plasma if the width of the divertor region is sufficient. Both configurations use scrape-off layer impurity seeding to yield an acceptable peak heat flux of ∼10 MW/m2 or smaller on the divertor plates and chamber walls. The roles of recycled hydrogenic atoms and molecules are investigated and distribution of sputtering tungsten throughout the edge region modeled. The simulations are performed with the UEDGE 2D transport code to model both plasma and neutral components with supplementary neutral modeling performed with the DEGAS 2 Monte Carlo code.
An automatic data cleaning procedure for electron cyclotron emission imaging on EAST tokamak using machine learning algorithm
A new data cleaning procedure for the electron cyclotron emission imaging (ECEI) of the EAST tokamak is developed. Machine learning techniques, including support vector machine (SVM) and Decision Trees, are applied to the identification of saturated, zero, and weak signals of the ECEI raw data. As a result, the burden of data analysis is reduced, and the classification accuracy is improved. Proper training sets are sampled using the massive raw ECEI data from the EAST tokamak. The optimal window size of temporal signals, the kernel function, and other model parameters are obtained by the model training. Five-fold cross-validation (CV) is applied during modeling and an external testing set is employed to validate the prediction performance of models. The average recall rates on CV sets of saturated, zero, and weak signals are 95.9%, 96.72%, and 100%, respectively, which prove the accuracy of this procedure. Random Forest, as a comparative method, is also employed to deal with the same data sets. The average recall rates on CV sets of saturated, zero, and weak signals performed by Random Forest are 95.9%, 96.72%, and 95.88%. Our method has been proved to outperform Random Forest with small data sets.
Relativistic Magnetic Reconnection in the Laboratory
Magnetic reconnection is a fundamental process occurring in many plasma systems. Magnetic field lines break and reconfigure into a lower energy state, converting released magnetic field energy into plasma kinetic energy. Around some of the universe's most energetic objects, such as
γ
-ray burst or active galactic nuclei, where the magnetic field energy exceeds the plasma rest mass energy, the most extreme magnetic reconnection in the relativistic regime is theorized. The presented experiments and three-dimensional particle-in-cell modeling recreate in the laboratory the scaled plasma conditions necessary to access the relativistic electron regime and therefore approach conditions around these distant, inaccessible objects. High-power, ultrashort laser pulses focused to high intensity (
I
>
2.5
×
10
18
Wcm
−
2
) on solid targets produces relativistic temperature electrons within the focal volume. The hot electrons are largely confined to the target surface and form a radial surface current that generates a huge, expanding azimuthal magnetic field. Focusing two laser pulses in close proximity on the target surface leads to oppositely directed magnetic fields being driven together. The fast electron motion due to the magnetic reconnection is inferred using an experimental x-ray imaging technique. The x-ray images enable the measurement of the reconnection layer dimensions and temporal duration. The reconnection rates implied from the aspect ratio of the reconnection layer,
δ
/
L
≈
0.3
, was found to be consistent over a range of experimental pulse durations (
40
fs
–
20
ps
) and agreed with the modeling. Further experimental evidence for magnetic reconnection is the formation of a nonthermal electron population shown by the modeling to be accelerated in the reconnection layer.
Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence
The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At a sufficiently large magnetic Reynolds number (
R
m
=
10
6
), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The disruption of current sheet structures facilitates the energy cascade towards small scales, leading to the breaking and steepening of the energy spectrum. In the plasmoid-mediated regime, the energy spectrum displays a scaling that is close to the spectral index
−
2.2
as proposed by recent analytic theories. We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25.
quasi-analytical model was developed to map out the low-pressure (left-hand) branch of the Paschen curve at very high voltage when electrons are in the runaway regime and charge exchange/ionization avalanche sustained by ions and fast neutral atoms becomes important. The model was applied to helium gas between parallel-plate electrodes, at potentials ranging in magnitude between 10 and 1000 kV. The respective value of reduced electric field E/n varied in the range of 50−6000 kTd (1 kTd = 10−18 Vm2), with reduced density nd (where n is the gas density and d is the inter-electrode distance) on the order of 1020 m−2. Three regimes of the breakdown have been identified according to the relative share of impact ionization by electrons, by ions, and by fast neutrals. The analytically derived Paschen curve is compared to those obtained with a detailed particle-in-cell/Monte Carlo simulation, and also through experimental measurements (L Xu, A V Khrabrov, I D Kaganovich and T J Sommerer 2017 Phys. Plasmas 24 093511). The model provides accurate predictions for E/n up to ~103 kTd, constrained by availability and quality of required input data.
Reducing Noise for PIC Simulations Using Kernel Density Estimation Algorithm
Noise is a major concern for Particle-In-Cell (PIC) simulations. We propose a new theoretical and algorithmic framework to evaluate and reduce the noise level for PIC simulations based on the Kernel Density Estimation (KDE) theory, which has been widely adopted in machine learning and big data science. According to this framework, the error on particle density estimation for PIC simulations can be characterized by the Mean Integrated Square Error (MISE), which consists of two parts, systematic error and noise. A careful analysis shows that in the standard PIC methods noise is the dominate error, and the noise level can be reduced if we select different shape functions that are capable of balancing the systematic error and the noise. To improve performance, we use the von Mises distribution as the shape function and seek an optimal particle width that minimizes the MISE, represented by a Cross-Validation (CV) function. This procedure significantly reduces both the noise and the MISE for PIC simulations. A particle-wise width adjustment algorithm and a width update algorithm are further developed to reduce the MISE. Simulations using the examples of Langmuir wave and Landau Damping demonstrate that the KDE algorithm developed in the present study reduces the noise level on density estimation by 98%, and gives a much more accurate result on the linear damping rate compared to the standard PIC methods. Meanwhile, it is computational efficient that can save 40% time to achieve the same accuracy.
Kinetic simulation of magnetic field generation and collisionless shock formation in expanding laboratory plasmas
Recent laboratory experiments with laser-produced plasmas have observed and studied a number of fundamental physical processes relevant to magnetized astrophysical plasmas, including magnetic reconnection, collisionless shocks, and magnetic field generation by Weibel instability, opening up new experimental platforms for laboratory astrophysics. We develop a fully kinetic simulation model for first-principles simulation of these systems including the dynamics of magnetic fields---magnetic field generation by the Biermann battery effect or Weibel instability; advection by the ion flow, Hall effect, and Nernst effect; and destruction of the field by dissipative mechanisms. Key dimensionless parameters describing the system are derived for scaling between kinetic simulation, recent experiments, and astrophysical plasmas. First, simulations are presented which model Biermann battery magnetic field generation in plasmas expanding from a thin target. Ablation of two neighboring plumes leads to the formation of a current sheet as the opposing Biermann-generated fields collide, modeling recent laser-driven magnetic reconnection experiments. Second, we simulate recent experiments on collisionless magnetized shock generation, by expanding a piston plasma into a pre-magnetized ambient plasma. For parameters considered, the Biermann effect generates additional magnetic fields in the curved shock front and thereby increases shock particle reflection. Both cases show the importance of kinetic processes in the interaction of plasmas with magnetic fields, and open opportunities to benchmark these important processes through comparison of theory and experiments.
Resonances between high energy particles and ideal magnetohydrodynamic modes in tokamaks
Particle trajectory surfaces in an ideal magnetohydrodynamic high energy particle resonance are studied using kinetic Poincaré plots and through a calculation by perturbing near the resonance and finding canonical variables in the resonance, allowing the study of the distortion of the structure from that of a simple pendulum and to assist in the construction of models for the modification of particle distributions due to the modes. It is found that the narrow structure of an ideal mode eigenfunction can lead to a significant decrease in the resonance width compared to a case in which the eigenfunction does not vary within the resonant island.
Non-planar elasticae as optimal curves for the magnetic axis of stellarators
The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed integrated torsion. The obvious translational and rotational symmetries are exploited to express solutions in a preferred cylindrical coordinate system in terms of elliptic Jacobi functions. These solution curves, which, up to similarity transformations, depend on three dimensionless parameters, do not necessarily close. Two closure conditions are obtained for the vertical and toroidal displacement (the radial coordinate being trivially periodic) to yield a countably infinite set of one-parameter families of closed non-planar curves. The behaviour of the integrated torsion (Twist of the Frenet frame), the Linking of the Frenet frame, and the Writhe of the solution curves are studied in light of the Călugăreanu theorem. A refreshed interpretation of Mercier's formula for the on-axis rotational transform of stellarator magnetic field-lines is proposed.
Nano-size effects in graphite/graphene structure exposed to cesium vapor
A thermionic energy converter with a nickel collector and cesium vapor as a working gas was studied, and an abnormally low value of the surface work function of ≈1 eV was obtained if the collector was covered by a thin carbon layer. Scanning electron microscopy x-ray microanalysis data of the elemental composition of the collector's surface after its long exposure to plasma indicate that the carbon structure was intercalated with cesium atoms, and this change to surface structure can be a reason for the anomalously low work function ∼1 eV. The thermionic energy converter with such a collector demonstrated high heat-to-electric power conversion efficiency up to ∼20%.
This tutorial describes mechanisms for separating ions in a plasma device with respect to their atomic or molecular mass for practical applications. The focus here is not on separating isotopes of a single atomic species but rather on systems with a much lower mass resolution and a higher throughput. These separation mechanisms include ion gyro-orbit separation, drift-orbit separation, vacuum arc centrifugation, steady-state rotating plasmas, and several other geometries. Generic physics issues are discussed such as the ion charge state, neutrals and molecules, collisions, radiation loss, and electric fields and fluctuations. Generic technology issues are also discussed such as plasma sources and ion heating, and suggestions are made for future research.
Differentiating the shape of stellarator coils with respect to the plasma boundary
The task of designing the geometry of a set of current-carrying coils that produce the magnetic field required to confine a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably defined error expressed as a surface integral, which is recognized as the quadratic-flux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-flux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow efficient coil-design algorithms to be implemented, and also enable efficient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given.
Non-planar elasticae as optimal curves for the magnetic axis of stellarators
The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed.
Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their
bending energy while yielding fixed integrated torsion. The obvious translational and rotational
symmetries are exploited to express solutions in a preferred cylindrical coordinate system in terms
of elliptic Jacobi functions. These solution curves, which, up to similarity transformations, depend
on three dimensionless parameters, do not necessarily close. Two closure conditions are obtained
for the vertical and toroidal displacement (the radial coordinate being trivially periodic) to yield a countably infinite set of one-parameter families of closed non-planar curves. The behaviour of the
integrated torsion (Twist of the Frenet frame), the Linking of the Frenet frame, and the Writhe of
the solution curves are studied in light of the Calugareanu theorem. A refreshed interpretation
of Mercier’s formula for the on-axis rotational transform of stellarator magnetic field-lines is
proposed.
Role of electron inertia and electron/ion finite Larmor radius effects
in low-beta, magneto-Rayleigh-Taylor instability
The magneto-Rayleigh-Taylor (MRT) instability has been investigated in great detail in previous work using magnetohydrodynamic and kinetic models for low-beta plasmas. The work presented here extends previous studies of this instability to regimes where finite-Larmor-Radius (FLR) effects may be important. Comparisons of the MRT instability are made using a 5-moment and a 10-moment two-fluid model, the two fluids being ions and electrons. The 5-moment model includes Hall stabilization, whereas the 10-moment model includes Hall and FLR stabilization. Results are presented for these two models using different electron mass to understand the role of electron inertia in the late-time nonlinear evolution of the MRT instability. For the 5-moment model, the late-time nonlinear MRT evolution does not significantly depend on the electron inertia. However, when FLR stabilization is important, the 10-moment results show that a lower ion-to-electron mass ratio (i.e., larger electron inertia) under-predicts the energy in high-wavenumber modes due to larger FLR stabilization.
This tutorial describes mechanisms for separating ions in a plasma device with respect to their
atomic or molecular mass for practical applications. The focus here is not on separating isotopes of
a single atomic species but rather on systems with a much lower mass resolution and a higher
throughput. These separation mechanisms include ion gyro-orbit separation, drift-orbit separation,
vacuum arc centrifugation, steady-state rotating plasmas, and several other geometries. Generic
physics issues are discussed such as the ion charge state, neutrals and molecules, collisions, radiation
loss, and electric fields and fluctuations. Generic technology issues are also discussed such as plasma
sources and ion heating, and suggestions are made for future research.
Regimes of magnetic reconnection in colliding laser-produced magnetized plasma bubbles
We conduct a multiparametric study of driven magnetic reconnection relevant to recent
experiments on colliding magnetized laser-produced plasmas using particle-in-cell simulations.
Varying the background plasma density, plasma resistivity, and plasma bubble geometry, the 2D
simulations demonstrate a rich variety of reconnection behaviors and show the coupling between
magnetic reconnection and the global hydrodynamical evolution of the system. We consider both
the collision between two radially expanding bubbles where reconnection is seeded by the preexisting
X-point and the collision between two flows in a quasi-1D geometry with initially antiparallel
fields where reconnection must be initiated by the tearing instability. At a baseline case of
low-collisionality and low background density, the current sheet is strongly compressed to below
scale of the ion-skin-depth scale, and rapid, multi-plasmoid reconnection results. Increasing the
plasma resistivity, we observe a collisional slow-down of reconnection and stabilization of plasmoid
instability for Lundquist numbers less than approximately $S \sim 10^3$. Second, increasing the
background plasma density modifies the compressibility of the plasma and can also slow down or
even prevent reconnection, even in completely collisionless regimes, by preventing the current
sheet from thinning down to the scale of the ion-skin depth. These results have implications for
understanding recent and future experiments, and signatures for these processes for protonradiography
diagnostics of these experiments are discussed.
On the Rayleigh-Kuo criterion for the tertiary instability of zonal flows
Whistler wave generation near the magnetospheric separatrix during reconnection at the dayside magnetopause is studied with data from the Magnetospheric Multiscale mission. The dispersion relation of the whistler mode is measured for the first time near the reconnection region in space, which shows that whistler waves propagate nearly parallel to the magnetic field line. A linear analysis indicates that the whistler waves are generated by temperature anisotropy in the electron tail population. This is caused by loss of electrons with a high velocity parallel to the magnetic field to the exhaust region. There is a positive correlation between activities of whistler waves and the lower hybrid drift instability both in laboratory and space, indicating the enhanced transport by lower hybrid drift instability may be responsible for the loss of electrons with a high parallel velocity.
Biermann-Battery-Mediated Magnetic Reconnection in 3D Colliding Plasmas
Recent experiments have demonstrated magnetic reconnection between colliding plasma plumes, where the reconnecting magnetic fields were self-generated in the plasma by the Biermann-battery effect. Using fully kinetic 3D simulations, we show the full evolution of the magnetic fields and plasma in these experiments, including self-consistent magnetic field generation about the expanding plume. The collision of the two plasmas drives the formation of a current sheet, where reconnection occurs in a strongly time- and space-dependent manner, demonstrating a new 3D reconnection mechanism. Specifically, we observe a fast, vertically localized Biermann-mediated reconnection, an inherently 3D process where the temperature profile in the current sheet coupled with the out-of-plane ablation density profile conspires to break inflowing field lines, reconnecting the field downstream. Fast reconnection is sustained by both the Biermann effect and the traceless electron pressure tensor, where the development of plasmoids appears to modulate the contribution of the latter. We present a simple and general formulation to consider the relevance of Biermann-mediated reconnection in general astrophysical scenarios.
On the Rayleigh-Kuo criterion for the tertiary instability of zonal flows
This paper reports the stability conditions for intense zonal flows (ZFs) and the growth rate $\gamma_{\tau I}$ of the corresponding “tertiary” instability (TI) within the generalized Hasegawa–Mima plasma model.
The analytical calculation extends and revises Kuo's analysis of the mathematically similar barotropic vorticity equation for incompressible neutral fluids on a rotating sphere [H.-L. Kuo, J. Meteor. 6, 105 (1949)]; then, the results are applied to the plasma case.
An error in Kuo's original result is pointed out.
An explicit analytical formula for $\gamma_{\tau I}$ is derived and compared with numerical calculations.
It is shown that, within the generalized Hasegawa–Mima model, a sinusoidal ZF is TI-unstable if and only if it satisfies the Rayleigh–Kuo criterion (known from geophysics) and that the ZF wave number exceeds the inverse ion sound radius.
For non-sinusoidal ZFs, the results are qualitatively similar.
As a corollary, there is no TI in the geometrical-optics limit, i.e., when the perturbation wavelength is small compared to the ZF scale.
This also means that the traditional wave kinetic equation, which is derived under the geometrical-optics assumption, cannot adequately describe the ZF stability.
Using the maximum entropy distribution to describe electrons in reconnecting current sheets
Particle distributions in weakly collisional environments such as the magnetosphere have been
observed to show deviations from the Maxwellian distribution. These can often be reproduced in
kinetic simulations, but fluid models, which are used in global simulations of the magnetosphere,
do not necessarily capture any of this. We apply the maximum entropy fluid closure of Levermore,
which leads to well posed moment equations, to reconstruct particle distributions from a kinetic
simulation in a reconnection region. Our results show that without information other than the
moments, the model can reproduce the general structure of the distributions but not all of the finer
details. The advantages of the closure over the traditional Grad closure are also discussed.
Nonlinear simulations of thermo-resistive tearing mode formalism of the density limit
This work is an extension of the previous semi-analytical work (Teng et al 2016 Nucl. Fusion 56 106001), explaining the density limit with a thermo-resistive tearing mode model. The thermo-resistive island growth is calculated with a 3D MHD code M3D-C-1 (Jardin et al 2012 Comput. Sci. Discovery 5 014002). It is shown with nonlinear 3D MHD simulations that impurity radiation stimulates large magnetic islands at the density limit. The impact of thermal perturbations inside and outside of the island is explored. Inside the island, net cooling enhances the island growth and net heating suppresses its growth. Outside the island, thermal perturbations have a much smaller impact on the island growth. When the plasma density is increased towards the density limit, the island changes from being heated to being cooled and grows to a much larger island width. The convergence test of the simulations over the temporal and spatial grid is performed. The numerical model and the semi-analytical model are compared by calculating the Delta' terms, which are defined in the modified Rutherford equation, and good agreement is observed.
Fluctuation Dynamo in a Collisionless, Weakly Magnetized Plasma
Results from a numerical study of fluctuation dynamo in a collisionless, weakly magnetized plasma are presented.
The key difference between this dynamo and its magnetohydrodynamic (MHD) counterpart is the adiabatic production of magnetic-field-aligned pressure anisotropy by the amplification of a weak seed field.
This, in turn, drives kinetic instabilities on the ion-Larmor scale-namely, firehose and mirror-which sever the adiabatic link between the thermal and magnetic pressures, thereby allowing the dynamo to proceed.
After an initial phase of rapid growth driven by these instabilities, the magnetic energy grows exponentially and exhibits a $k^{3/2}$ spectrum that peaks near the resistive scale, similar to the large-magnetic-Prandtl-number ($P_m >> 1$) MHD dynamo.
The magnetic field self-organizes into a folded-sheet topology, with direction reversals at the resistive scale and field lines curved at the parallel scale of the flow. The effective $P_m$ is determined by whether the ion-Larmor scale is above or below the field-reversing scale: in the former case, particles undergo Bohm-like diffusion; in the latter case, particles scatter primarily off of firehose fluctuations residing at the ends of the magnetic folds, and the viscosity becomes anisotropic. The magnetic field ultimately saturates at dynamical strengths, with its spectral peak migrating toward larger scales. This feature, along with an anti-correlation of magnetic-field strength and field-line curvature and a gradual thinning of magnetic sheets into ribbons, resembles the saturated state of the large-$P_m$ dynamo, the primary differences manifesting in firehose/mirror-unstable regions. These results have implications for magnetic-field growth in the weakly collisional intracluster medium of galaxy clusters.
Main ion and impurity edge profile evolution across the L- to H-mode transition on DIII-D
Detailed measurements of the main ion ($D^+$) and impurity ion ($C^{6+}$) evolution during the development of the H-mode pedestal across an L-H transition show significant differences in toroidal rotation, density, and temperature profiles in the pedestal region on DIII-D. While both species experience a slow toroidal spin up at constant input neutral beam injected torque, the $C^{6+}$ toroidal rotation develops a non monotonic notch feature and lower toroidal rotation near the plasma edge immediately following the L-H transition. This feature is not present in the main ion rotation that instead, depending on plasma parameters, can show a flat or peaked rotation near the separatrix. The $D^+$ and $C^{6+}$ temperature profiles show a similar evolution; however, the $D^+$ temperature is lower than the $C^{6+}$ temperature at the separatrix in both L and H-mode which may be due to cooling of $D^+$ via charge exchange with cold edge deuterium neutrals. Local neoclassical predictions of the main ion toroidal rotation based on the impurity properties show good agreement with direct measurements at the pedestal top for a lower power, higher collisionality case but can diverge significantly in the steep gradient region for the two shots studied here. These observations highlight the importance of directly measuring the properties of the main ion species at the plasma edge.
Spatial symmetry breaking in single-frequency CCP discharge with transverse magnetic field
An independent control of the flux and energy of ions impacting on an object immersed in a plasma
is often desirable for many industrial processes such as microelectronics manufacturing. We
demonstrate that a simultaneous control of these quantities is possible by a suitable choice of a static
magnetic field applied parallel to the plane electrodes in a standard single frequency capacitively
coupled plasma device. Our particle-in-cell simulations show a 60% reduction in the sheath width
(that improves control of ion energy) and a fourfold increase in the ion flux at the electrode as a
consequence of the altered ion and electron dynamics due to the ambient magnetic field. A detailed
analysis of the particle dynamics is presented, and the optimized operating parameters of the device
are discussed. The present technique offers a simple and attractive alternative to conventional dual
frequency based devices that often suffer from undesirable limitations arising from frequency
coupling and electromagnetic effects.
Linear analyses of peeling-ballooning modes in high beta pedestal plasmas
We present the linear simulations of edge plasma instabilities using the 3-field peeling-ballooning
model and gyro-Landau-fluid model under the BOUT++ framework. A series of realistic equilibria
of shifted circular geometry are generated by a global equilibrium solver CORSICA, where the
Shafranov shift, elongation effects, and bootstrap current are included. The linear growth rate spectrum
of the peeling-ballooning modes is shown in a wide range of pressure gradient and parallel
current density in the pedestal region. The results show that the bootstrap current stabilizes high
beta ballooning modes. The simulations with different fractions of bootstrap current indicate a
trend for the existence of the high beta peeling-ballooning mode stability region. Taking the kinetic
effects into account, the linear simulations of kinetic peeling-ballooning mode using the gyroLandau-fluid
model show that this region can be accessed.
Conservative magnetic moment of runaway
electrons and collisionless pitch-angle scattering
Recently, the validity of the guiding-center approach to model relativistic runaway electrons in tokamaks has been challenged by full-orbit simulations that demonstrate the breakdown of the standard magnetic moment conservation.
In this paper, we derive a new expression for the magnetic moment of relativistic runaway electrons with p(||) >> p, which is conserved significantly better than the standard one. The new result includes one of the second-order corrections in the standard guiding-center theory which, in case of runaway electrons with $p_\parallel << p_\perp$, can peculiarly be of the same order as the lowest-order term. The better conservation of the new magnetic moment also explains the collisionless pitch-angle-scattering effect observed in full-orbit simulations since it allows momentum transfer between the perpendicular and parallel directions when the runaway electron is accelerated by an electric field. While the derivation of the second-order correction to the magnetic moment in general case would require the full extent of the relativistic second-order guiding-center theory, we exploit the Lie-perturbation method at the limit $p_\parallel >> p_\perp$ which simplifies the computations significantly. Consequently, we present the corresponding guiding-center equations applicable to runaway electrons.
A tight-coupling scheme sharing minimum information across a spatial interface between gyrokinetic turbulence codes
A new scheme that tightly couples kinetic turbulence codes across a spatial interface is introduced.
This scheme evolves from considerations of competing strategies and down-selection. It is found
that the use of a composite kinetic distribution function and fields with global boundary conditions
as if the coupled code were one makes the coupling problem tractable. In contrast, coupling the
two solutions from each code across the overlap region is found to be more difficult due to numerical
dephasing of the turbulent solutions between two solvers. Another advantage of the new scheme
is that the data movement can be limited to the 3D fluid quantities, instead of higher dimensional
kinetic information, which is computationally more efficient for large scale simulations on leadership
class computers.
Effects of a Solar Flare on the Martian Hot O Corona and Photochemical Escape
We examine for the first time the flare-induced effects on the Martian hot O corona. The rapid ionospheric response to the increase in the soft X-ray flux (~800%) facilitates more hot O production at altitudes below the main ionospheric peak, but almost all of these atoms are thermalized before escape. In response to the increase in the extreme ultraviolet (EUV) flux (~170%), the overall upper ionospheric and thermospheric densities are enhanced, and the peak thermospheric responses are found ~1.5 hr later. The photochemical escape rate is predicted to increase by ~20% with the increases in the soft X-ray and EUV fluxes but decrease rapidly by ~13% about 2.5 hr later before recovering the preflare level. Since escaping hot O atoms are mostly produced at high altitudes where ionization by the EUV flux is the greatest, the main contributor to the 20% increase in escape rate is the enhancement in the EUV flux.
Analysis of equilibrium and turbulent fluxes across the separatrix in a gyrokinetic simulation
The SOL width is a parameter of paramount importance in modern tokamaks as it controls the
power density deposited at the divertor plates, critical for plasma-facing material survivability. An
understanding of the parameters controlling it has consequently long been sought [Connor et al.
Nucl. Fusion 39(2), 169 (1999)].
Prior to Chang et al. [Nucl. Fusion 57(11), 116023 (2017)], studies
of the tokamak edge have been mostly confined to reduced fluid models and simplified geometries,
leaving out important pieces of physics. Here, we analyze the results of a DIII-D simulation
performed with the full-f gyrokinetic code XGC1 which includes both turbulence and neoclassical
effects in realistic divertor geometry. More specifically, we calculate the particle and heat ${\bf E}\times{\bf B}$ fluxes along the separatrix, discriminating between equilibrium and turbulent contributions. We
find that the density SOL width is impacted almost exclusively by the turbulent electron flux. In
this simulation, the level of edge turbulence is regulated by a mechanism that we are only beginning
to understand: $\nabla B$-drifts and ion X-point losses at the top and bottom of the machine, along
with ion banana orbits at the low field side, result in a complex poloidal potential structure at
the separatrix which is the cause of the ${\bf E}\times{\bf B}$ drift pattern that we observe. Turbulence is being
suppressed by the shear flows that this potential generates. At the same time, turbulence, along
with increased edge collisionality and electron inertia, can influence the shape of the potential
structure by making the electrons non-adiabatic. Moreover, being the only means through which
the electrons can lose confinement, it needs to be in a balance with the original direct ion orbit
losses to maintain charge neutrality
On the structure of the drifton phase space and its relation to the Rayleigh--Kuo criterion of the zonal-flow stability
The phase space of driftons (drift-wave quanta) is studied within the generalized Hasegawa–Mima
collisionless-plasma model in the presence of zonal flows. This phase space is made intricate by
the corrections to the drifton ray equations that were recently proposed by Parker [J. Plasma Phys.
82, 595820602 (2016)] and Ruiz et al. [Phys. Plasmas 23, 122304 (2016)]. Contrary to the traditional
geometrical-optics (GO) model of the drifton dynamics, it is found that driftons can not only
be trapped or passing but also accumulate spatially while experiencing indefinite growth of their
momenta. In particular, it is found that the Rayleigh–Kuo threshold known from geophysics corresponds
to the regime when such “runaway” trajectories are the only ones possible. On one hand,
this analysis helps to visualize the development of the zonostrophic instability, particularly its nonlinear
stage, which is studied here both analytically and through wave-kinetic simulations. On the
other hand, the GO theory predicts that zonal flows above the Rayleigh–Kuo threshold can only
grow; hence, the deterioration of intense zonal flows cannot be captured within a GO model. In particular,
this means that the so-called tertiary instability of intense zonal flows cannot be adequately
described within the quasilinear wave kinetic equation, contrary to some previous studies.
Differentiating stellarator coils with respect to the target boundary
The task of designing the geometry of a set of current-carrying coils that produce the magnetic ﬁeld required to conﬁne a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably deﬁned error expressed as a surface integral, which is recognized as the quadratic-ﬂux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-ﬂux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow eﬃcient coil-design algorithms to be implemented, and also enable eﬃcient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given.
The effects of kinetic instabilities on the electron cyclotron emission from runaway electrons
In this paper we show that the kinetic instabilities associated with runaway electron beams
play an essential role for the production of high-level non-thermal electron–cyclotronemission
(ECE) radiation. Most of the non-thermal ECE comes from runaway electrons in the
low-energy regime with large pitch angle, which are strongly scattered by the excited whistler
waves. The power of ECE from runaway electrons is obtained using a synthetic diagnostic
model based on the reciprocity method. The electron distribution function is calculated using a
kinetic simulation model including the whistler wave instabilities and the quasilinear diffusion
effects. Simulations based on DIII-D low-density discharge reproduces the rapid growth of
the ECE signals observed in DIII-D experiments. Unlike the thermal ECE where radiation for
a certain frequency is strongly localized inside the resonance region, the non-thermal ECE
radiation from runaway electrons is nonlocal, and the emission-absorption ratio is higher than
that of thermal electrons. The runaway electron tail is more significant for ECE with higher
frequencies, and the ECE spectrum becomes flatter as RE population grows. The nonlinear
behavior of the kinetic instabilities is illustrated in the oscillations of the ECE waves. The
good agreement with the DIII-D experimental observations after including the kinetic
instabilities clearly illustrate the significance of the scattering effects from wave-particle
interactions, which can also be important for runaway electrons produced in disruptions.
Scaling of Spoke Rotation Frequency within a Penning Discharge
A rotating plasma spoke is shown to develop in two-dimensional full-sized kinetic simulations of a
Penning discharge cross-section.
Electron cross-field transport within the discharge is highly anomalous and correlates strongly with the spoke phase. Similarity between collisional and collisionless simulations demonstrates that ionization is not necessary for spoke formation.
Parameter scans with discharge current $I_d$, applied magnetic field strength $B$, and ion mass $m_i$ show that the spoke
frequency scales with $\sqrt{e E_r L_n / m_i}$, where $E_r$ is the radial electric field, $L_n$ is the gradient length
scale, and $e$ is the fundamental charge.
This scaling suggests that the spoke may develop as a nonlinear
phase of the collisionless Simon-Hoh instability
Sawtooth mixing of alphas, knock-on D, and T ions, and its influence on NPA spectra in ITER plasma
Sawtooth mixing of fast ions is considered in ITER for plasma parameters close to the
inductive 15 MA scenario. New mixing formula is presented for a drift trajectory averaged
distribution function (DF) of fast passing and trapped ions. This formula generalizes
Kadomtsev’s model for the case of non-circular magnetic surfaces, arbitrary aspect ratio, and
significant deviations of charged particle drift trajectories from the magnetic flux surfaces, and
can be applicable to a wide class of instabilities. Generalized formulae are implemented in the
Fokker–Planck package three-dimensional (FPP-3D) code. FPP-3D is applied for calculation
of the fast alpha-particle ($He^4$), deuterium (D), and tritium (T) DFs. Simulations take into
account D and T nuclear elastic scattering (NES or knock-on) by fast $He^4$.
Changes in the
radial profile of $He^4$ power deposition to the thermal plasma in the presence of plasma mixing
are estimated.
An effective tool for fast ion studies in ITER will be a system of neutral particle analyzers
(NPA) since it allows direct measurements of the fast hydrogen ions’ DF inside the plasma.
The main NPA goal on ITER is to measure the D/T fuel isotope ratio in the plasma core
with the use of D and T atom spectra in the MeV range. The spectra and their sensitivity
to sawtooth mixing are calculated. It was found that ITER NPA allows us to detect those
oscillations. Simulations show the possibility of determining the D/T ratio with NPA
regardless of whether sawtooth oscillations exist.
Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects
We formulate the problem of tokamak plasma equilibrium including the toroidal flow and
fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW)
effects. The problem is formulated via the standard Grad–Shafranov equation (GShE)
amended by the solvability condition which imposes physical constraints on allowed spacial
dependencies of the anisotropic pressure.
The GShE problem employs the pressure coupling scheme and includes the dominant
diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic
tensor elements are obtained via the distribution function represented in the factorized form
via the constants of motion. Considered effects on the plasma equilibrium are estimated
analytically, if possible, to understand their importance for GShE tokamak plasma problem.
The novelty of the proposed approach is in the way FOW is included into the GShE via the
non-diagonal pressure tensor, factorized distribution function of the fast ions representation
and in the prescription of the spacial dependence of P⊥ given the spacial dependence of P.
Projection-operator methods for classical transport in magnetised plasmas. I. Linear response, the Braginskii equations, and fluctuating hydrodynamics
An introduction to the use of projection-operator methods for the derivation of classical fluid transport equations for weakly coupled, magnetised, multispecies plasmas is given. In the present work, linear response (small perturbations from an absolute Maxwellian) is addressed. In the Schrödinger representation, projection onto the hydrodynamic subspace leads to the conventional linearized Braginskii fluid equations when one restricts attention to fluxes of first order in the gradients, while the orthogonal projection leads to an alternative derivation of the Braginskii correction equations for the non-hydrodynamic part of the one-particle distribution function. The projection-operator approach provides an appealingly intuitive way of discussing the derivation of transport equations and interpreting the significance of the various parts of the perturbed distribution function; it is also technically more concise. A special case of the Weinhold metric is used to provide a covariant representation of the formalism; this allows a succinct demonstration of the Onsager symmetries for classical transport. The Heisenberg representation is used to derive a generalized Langevin system whose mean recovers the linearized Braginskii equations but that also includes fluctuating forces. Transport coefficients are simply related to the two-time correlation functions of those forces, and physical pictures of the various transport processes are naturally couched in terms of them. A number of appendices review the traditional Chapman–Enskog procedure; record some properties of the linearized Landau collision operator; discuss the covariant representation of the hydrodynamic projection; provide an example of the calculation of some transport effects; describe the decomposition of the stress tensor for magnetised plasma; introduce the linear eigenmodes of the Braginskii equations; and, with the aid of several examples, mention some caveats for the use of projection operators.
Global Alfvén eigenmode scaling and suppression: experiment and theory
The spherical tokamak NSTX has been upgraded to include a second neutral beam line, with three independent beam sources, and to be capable of higher toroidal fields and longer duration plasmas (Ono et al 2015 Nucl. Fusion 55 073007). In this paper we describe some of the initial observations of the affect that the higher field and the modified fast-ion distributions have had on the nature of the global Alfven eigenmodes (GAE). We also report that the GAE excited through a Doppler-shifted ion cyclotron resonance (DCR) were suppressed in a large number of shots with the injection of a small amount of high pitch ($V_{parallel} / V$) fast ions, consistent with the predictions of an analytic theory (Gorelenkov et al 2003 Nucl. Fusion 43 228). We show that the experimental scaling of the GAE frequency and toroidal mode numbers with toroidal field is qualitatively consistent with the predictions of the analytic theory, providing validation for the DCR model. The observed suppression of GAE has also been reproduced in simulations with the hybrid ideal stability code HYM (Belova et al 2017 Phys. Plasmas 24 042505).
Destabilization of counter-propagating Alfvénic instabilities by tangential, co-current neutral beam injection
Injection of high-energy neutrals is a common tool to heat the plasma and drive current non-inductively in fusion devices. Once neutrals ionize, the resulting energetic particles can drive instabilities that are detrimental for the performance and the predictability of plasma discharges. A broad deposition profile of neutrals from neutral beam injection, e.g. by aiming the beam tangentially on the outboard midplane (i.e. off-axis), is often assumed to limit those undesired effects by reducing the radial gradient of the EP density, thus reducing the drive for instabilities. However, this work presents new evidence that tangential neutral beam injection, including off-axis injection near the plasma mid-radius, can also lead to undesired effects such as the destabilization of Alfvénic instabilities. Time-dependent analysis with the TRANSP code indicates that instabilities are driven by a combination of radial and energy gradients in the distribution function of the energetic particles. The mechanisms for wave-particle interaction revealed by the energetic particle phase space resolved analysis are the basis to identify strategies to mitigate or suppress the observed instabilities.
Resonance broadened quasi-linear (RBQ) model for fast ion distribution relaxation due to Alfvénic eigenmodes
The burning plasma performance is limited by the confinement of the super-alfvénic fusion
products such as alpha particles and the auxiliary heating ions capable of exciting the
Alfvénic eigenmodes (AEs) (Gorelenkov et al 2014 Nucl. Fusion 54 125001). In this work
the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized
for this problem recently (Duarte 2017 PhD Thesis University of São Paulo, Brazil). The
generalization involves the resonance line broadened interaction of energetic particles (EP)
with AEs supplemented by the diffusion coefficients depending on EP position in the velocity
space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing
for EP diffusion in radial direction is built and presented in details. In RBQ1D applications
we reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic
energy is nearly constant. The diffusion equation for EP distribution evolution is then solved
simultaneously for all particles along the angular momentum direction.
We make initial applications of the RBQ1D to a DIII-D plasma with elevated q-profile
where the beam ions show stiff transport properties (Collins et al (The DIII-D Team) 2016
Phys. Rev. Lett. 116 095001). AE driven fast ion profile relaxation is studied for validations of
the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.
Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfvénic eigenmode
We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening width $\Delta\Omega$ on the nonlinear particle trapping frequency $\omega_b$ of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 [Collins et al., Phys. Rev. Lett. 116 095001 (2016)].
When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency $\Delta\Omega/\omega_b$ equals 4, as predicted by theory.
It is found that as the mode amplitude increases, the coefficient $a=\Delta\Omega/\omega_b$ becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.
Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability
The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a `hole' and `clump'.
Here, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto microturbulence via canonical toroidal momentum scattering, affecting hole and clump formation. The profile of a single bursting event in mode amplitude is shown to be stochastic, with small changes in initial conditions affecting the lifetime of a hole and clump. As an extension to the work of Lang and Fu, we find that an intermediate regime exists where noise serves to decrease the effective collisionality, where microturbulence works against pitch-angle scattering.
Study of the likelihood of Alfvénic mode bifurcation in NSTX and predictions for ITER baseline scenarios
Rare Alfvénic wave transitions between fixed-frequency and chirping phases are identified in NSTX, where Alfvénic waves are normally observed to exhibit either chirping or avalanching responses.
For those transitions, we apply a criterion [Duarte et al,
Nucl. Fusion 57, 054001 (2017)] to predict the nature of fast ion redistribution in tokamaks to be in the convective or diffusive nonlinear regimes.
For NSTX discharges in which the transition is not accompanied by changes in the beam deposited power or modifications in the injected radiofrequency power, it has been found that the anomalous fast ion transport is a likely mediator of the bifurcation between the fixed-frequency mode behavior and rapid chirping.
For a quantitative assessment, global gyrokinetic simulations of the effects of electrostatic ion temperature gradient turbulence and trapped electron mode turbulence on chirping were pursued using the GTS code.
The investigation is extended by means of predictive studies of the probable spectral behavior of Alfvénic eigenmodes for baseline ITER cases consisting of elmy, advanced and hybrid scenarios.
It has been observed that most modes are found to be borderline between the steady and the chirping phases.
Role of kinetic instability in runaway electron avalanche and elevated critical electric fields
The effects of kinetic whistler wave instabilities on the runaway-electron (RE) avalanche is investigated. With parameters from experiments at the DIII-D National Fusion Facility, we show that RE scattering from excited whistler waves can explain several poorly understood experimental results. We find an enhancement of the RE avalanche for low density and high electric field, but for high density and low electric field the scattering can suppress the avalanche and raise the threshold electric field, bringing the present model much closer to observations. The excitation of kinetic instabilities and the scattering of resonant electrons are calculated self-consistently using a quasilinear model and local approximation. We also explain the observed fast growth of electron cyclotron emission signals and excitation of very low-frequency whistler modes observed in the quiescent RE experiments at DIII-D tokamak. Simulations using ITER parameters show that by controlling the background thermal plasma density and temperature, the plasma waves can also be excited spontaneously in tokamak disruptions and the avalanche generation of runaway electrons may be suppressed.
Electron Distributions in Kinetic Scale Field Line Resonances: A Comparison of Simulations and Observations
Observations in kinetic scale ﬁeld line resonances, or eigenmodes of the geomagnetic ﬁeld, reveal highly ﬁeld-aligned plateaued electron distributions.
By combining observations from the Van Allen Probes and Cluster spacecraft with a hybrid kinetic gyroﬂuid simulation we show how these distributions arise from the nonlocal self-consistent interaction of electrons with the wavefield.
This interaction is manifested as electron trapping in the standing wave potential.
The process operates along most of the fieldline and qualitatively accounts for electron observations near the equatorial plane and at higher latitudes.
In conjunction with the highly field-aligned plateaus, loss cone features are also evident, which result fromt he action of the upward- directed wave parallel electric ﬁeld on the untrapped electron populations.
Cross-verification of the global gyrokinetic codes GENE and XGC
A detailed cross-verification between two global gyrokinetic codes, the core continuum code
GENE and the edge particle-in-cell code XGC, for the linear and nonlinear simulations of ion-temperature-gradient
modes is carried out. With the recent developments in the edge gyrokinetics, it
may be feasible someday to describe the whole tokamak plasma on turbulence timescales using a
coupled gyrokinetic simulation model. Before pursuing this, the core code (GENE) and the edge
code (XGC) must be carefully benchmarked with each other. The present verification provides a
solid basis for future code coupling research. Also included in the benchmarking is the global particle-in-cell
code ORB5, to raise the confidence in the quality of the obtained results. An excellent
agreement between all three codes is obtained. Furthermore, in order to facilitate a benchmark
framework for other codes, we make a specific effort to provide all the relevant input parameters
and precise details for each code.
Nonlinear structures of lower-hybrid waves driven by the ion beam
The lower-hybrid waves can be driven unstable by the transverse ion beam in a partially magnetized
plasma of a finite length. This instability mechanism, which relies on the presence of fixed
potential boundary conditions, is of particular relevance to axially propagating modes in a Hall
effect thruster. The linear and nonlinear regimes of this instability are studied here with numerical
simulations. In the linear regime, our results agree with analytical and numerical eigenvalue analysis
conducted by Kapulkin and Behar [IEEE Trans. Plasma Sci. 43, 64 (2015)]. It is shown that in
nonlinear regimes, the mode saturation results in coherent nonlinear structures. For the aperiodic
instability [with $Re(\omega)=0$—odd Pierce zones], the unstable eigen-function saturates into new stationary
nonlinear equilibrium. In the case of oscillatory instability [$Re(\omega)=0$—even Pierce
zones], the instability results in the nonlinear oscillating standing wave. It is also shown that finite
Larmor radius effects stabilize instability for parameters corresponding to a large number of Pierce
zones, and therefore, only few first zones remain relevant.
A fluid-kinetic framework for self-consistent runaway-electron simulations
The problem of self-consistently coupling kinetic runaway-electron physics to the macroscopic
evolution of the plasma is addressed by dividing the electron population into a bulk and a tail. A
probabilistic closure is adopted to determine the coupling between the bulk and the tail populations,
preserving them both as genuine, non-negative distribution functions. Macroscopic one-fluid
equations and the kinetic equation for the runaway-electron population are then derived, now
displaying sink and source terms due to transfer of electrons between the bulk and the tail.
Effects of axial boundary conductivity on a free Stewartson-Shercliff layer
The effects of axial boundary conductivity on the formation and stability of a magnetized free StewartsonShercliff
layer (SSL) in a short Taylor-Couette device are reported. As the axial field increases with insulating
endcaps, hydrodynamic Kelvin-Helmholtz-type instabilities set in at the SSLs of the conducting fluid, resulting
in a much reduced flow shear. With conducting endcaps, SSLs respond to an axial field weaker by the square root
of the conductivity ratio of endcaps to fluid. Flow shear continuously builds up as the axial field increases despite
the local violation of the Rayleigh criterion, leading to a large number of hydrodynamically unstable modes.
Numerical simulations of both the mean flow and the instabilities are in agreement with the experimental results.
The effect of magnetic equilibrium on auxiliary heating schemes and fast particle confinement in Wendelstein 7-X
The performance of the auxiliary heating systems ion cyclotron resonance heating and neutral beam injection is calculated in three different magnetic mirror configurations foreseen to be used in future experiments in the Wendelstein 7-X stellarator: low, standard and high mirror.
This numerical work is implemented with the SCENIC code package, which is designed to model three-dimensional magnetic equilibria whilst retaining effects such as anisotropy and the influence of including a finite orbit width of the particles.
The ability to simulate NBI deposition in three-dimensional equilibria, the implementation of the realistic beam injector geometry, and the modification of the SCENIC package to permit the investigation of the 3-ion species heating scheme, are recent developments.
Using these modifications, an assessment of the advantages and disadvantages of these two fast-ion producing auxiliary heating systems is made in the three different magnetic mirror equilibria. For NBI heating, the high mirror configuration displays the best global confinement properties, resulting in a larger collisional power transfer to the background plasma.
The standard mirror has the best particle confinement in the core region, but the worst towards the edge of the plasma.
The low mirror has the largest lost power and thus the lowest total collisional power.
For ICRH, the displacement of the RF-resonant surface significantly impacts the heating performance.
Due to the large toroidal magnetic mirror in the high mirror equilibrium, resonant particles easily become trapped and cannot remain in resonance, generating only small energetic particle populations.
Despite this, global confinement is still the strongest in this equilibrium.
The low mirror is the only equilibrium to produce peaked on-axis collisional power deposition, with associated peaked on-axis fast ion pressure profiles. A highly energetic particle population is then produced but this results in larger lost power as this equilibrium is not sufficiently
optimised for fast ion confinement.
A comparison between the two heating methods concludes that NBI produces a smaller fraction of lost to input power, and a reduced sensitivity of the
performance to variations of the toroidal magnetic mirror. The main limit of NBI which does not apply to ICRH is the production of highly energetic particle populations, with predictions of energetic particles of E ∼ 0.45 MeV.
Cumulative displacement induced by a magnetosonic soliton bouncing in a bounded plasma slab
The passage of a magnetosonic (MS) soliton in a cold plasma leads to the displacement of charged
particles in the direction of a compressive pulse and in the opposite direction of a rarefaction pulse.
In the overdense plasma limit, the displacement induced by a weakly nonlinear MS soliton is
derived analytically. This result is then used to derive an asymptotic expansion for the
displacement resulting from the bouncing motion of a MS soliton reflected back and forth in a
vacuum-bounded cold plasma slab. Particles’ displacement after the pulse energy has been lost to
the vacuum region is shown to scale as the ratio of light speed to Alfvén velocity. Results for the
displacement after a few MS soliton reflections are corroborated by particle-in-cell simulations.
Grassy-ELM regime with edge resonant magnetic perturbations in fully noninductive plasmas in the DIII-D tokamak
Resonant magnetic perturbations (n = 3 RMPs) are used to suppress large amplitude ELMs and mitigate naturally occurring 'grassy'-ELMs in DIII-D plasmas relevant to the ITER steady-state mission. Fully non-inductive discharges in the ITER shape and pedestal collisionality (nu(e)* approximate to 0.05-0.15) are routinely achieved in DIII-D with RMP suppression of the Type-I ELMs. The residual grassy-ELMs deliver a low peak heat flux to the divertor as low as 1.2 x the inter-ELM heat flux in plasmas with sustained high H-factor (H-98y2 approximate to 1.2). The operating window for the RMP grassy-ELM regime is q(95) = 5.3-7.1 and external torque in the range 9-0.7 Nm in the co-Ip direction, which is in the range required for a steady-state tokamak reactor. The RMP grassy-ELM regime is associated with a two-step pedestal, with strong flattening of the density around the zero crossing in the E x B shear. The edge magnetic response of the plasma to the n = 3 RMP is found to be approximate to 2-3x larger than for comparable ITER baseline plasmas (beta(N) approximate to 1.8, q(95) approximate to 3.1). The amplification of the RMP is consistent with the weak magnetic perturbation level (delta B/B approximate to 1. x 10(-4)) required for effective Type-I ELM suppression. Cyclic variations in the pedestal pressure, width, and toroidal rotation are observed in these plasmas, correlated with cyclic variations in the strength and frequency of the grassy-ELMs. Extended MHD analysis and magnetic measurements indicate that these pedestal pulsations are driven by cyclic variations in the resonant field strength at the top of the pedestal. These pedestal pulsations reveal that the grassy-ELMs is correlated with the proximity of the pedestal to the low-n peeling-ballooning mode stability boundary. The use of low amplitude magnetic fields to access grassy-ELM conditions free of Type-I ELMs in high beta poloidal plasmas (beta(p) approximate to 1.5-2.0) opens the possibility for the further optimization of the steady-state tokamak by use of edge resonant magnetic perturbations.
Energy spectrum of tearing mode turbulence in sheared background field
The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied
in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale
modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The
spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on
the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence
mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause
an effective damping during the energy cascade. The other is the scale-independent anisotropy
induced by the large-scale modes tilting the sheared background field, as opposed to the scaledependent
anisotropy frequently encountered in traditional critically balanced turbulence theories.
Due to these two differences, the energy spectrum deviates from a simple power law and takes
the form of a power law multiplied by an exponential falloff. Numerical simulations are carried
out using visco-resistive MHD equations to verify our theoretical predictions, and a reasonable
agreement is found between the numerical results and our model.
Validation of the kinetic-turbulent-neoclassical theory for edge intrinsic rotation in DIII-D
In a recent kinetic model of edge main-ion (deuterium) toroidal velocity, intrinsic rotation results from neoclassical orbits in an inhomogeneous turbulent field [T. Stoltzfus-Dueck, Phys. Rev. Lett. 108, 065002 (2012)].
This model predicts a value for the toroidal velocity that is co-current for a typical inboard X-point plasma at the core-edge boundary ($\rho \sim 0.9$).
Using this model, the velocity prediction is tested on the DIII-D tokamak for a database of L-mode and H-mode plasmas with nominally low neutral beam torque, including both signs of plasma current.
Values for the flux-surface-averaged main-ion rotation velocity in the database are obtained from the impurity carbon rotation by analytically calculating the main-ion-impurity neoclassical offset. The deuterium rotation obtained in this manner has been validated by direct main-ion measurements for a limited number of cases.
Key theoretical parameters of ion temperature and turbulent scale length are varied across a wide range in an experimental database of discharges. Using a characteristic electron temperature scale length as a proxy for a turbulent scale length, the predicted main-ion rotation velocity has a general agreement with the experimental measurements for neutral beam injection (NBI) powers in the range $P_{NBI} < 4MW$.
At higher NBI power, the experimental rotation is observed to saturate and even degrade compared to theory.
TRANSP-NUBEAM simulations performed for the database show that for discharges with nominally balanced-but high powered NBI, the net injected torque through the edge can exceed 1 Nm in the counter-current direction.
The theory model has been extended to compute the rotation degradation from this counter-current NBI torque by solving a reduced momentum evolution equation for the edge and found the revised velocity prediction to be in agreement with experiment.
Using the theory modeled-and now tested-velocity to predict the bulk plasma rotation opens up a path to more confidently projecting the confinement and stability in ITER.
Full-f version of GENE for turbulence in open-field-line systems
Unique properties of plasmas in the tokamak edge, such as large amplitude fluctuations and
plasma–wall interactions in the open-field-line regions, require major modifications of existing
gyrokinetic codes originally designed for simulating core turbulence. To this end, the global version
of the 3D2V gyrokinetic code GENE, so far employing a df-splitting technique, is extended to
simulate electrostatic turbulence in straight open-field-line systems. The major extensions are the
inclusion of the velocity-space nonlinearity, the development of a conducting-sheath boundary, and
the implementation of the Lenard–Bernstein collision operator. With these developments, the code
can be run as a full-f code and can handle particle loss to and reflection from the wall. The extended
code is applied to modeling turbulence in the Large Plasma Device (LAPD), with a reduced mass
ratio and a much lower collisionality. Similar to turbulence in a tokamak scrape-off layer, LAPD turbulence
involves collisions, parallel streaming, cross-field turbulent transport with steep profiles, and
particle loss at the parallel boundary.
Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation
Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact.
This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale.
Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conventional quantum particles.
This causes unusual phase-space dynamics that is typically not captured by the WKE.
We demonstrate how to correctly model this dynamics with the WME instead.
Specifically, we report full-wave phase-space simulations of the zonal-flow formation (zonostrophic instability), deterioration (tertiary instability), and the so-called predator-prey oscillations.
We also show how the WME facilitates analysis of these phenomena, namely, (i) we show that full-wave effects critically affect the zonostrophic instability, particularly its nonlinear stage and saturation; (ii) we derive the tertiary-instability growth rate; and (iii)
we demonstrate that, with full-wave effects retained, the predator-prey oscillations do not require zonal-flow collisional damping, contrary to previous studies.
We also show how the famous Rayleigh-Kuo criterion, which has been missing in wave-kinetic theories of drift-wave turbulence, emerges from the WME.
Amplification due to two-stream instability of self-electric and magnetic fields of an ion beam propagating in background plasma
Propagation of charged particle beams in background plasma as a method of space charge
neutralization has been shown to achieve a high degree of charge and current neutralization and
therefore enables nearly ballistic propagation and focusing of charged particle beams.
Correspondingly, the use of plasmas for propagation of charged particle beams has important
applications for transport and focusing of intense particle beams in inertial fusion and high energy
density laboratory plasma physics. However, the streaming of beam ions through a background
plasma can lead to the development of two-stream instability between the beam ions and the
plasma electrons. The beam electric and magnetic fields enhanced by the two-stream instability can
lead to defocusing of the ion beam. Using particle-in-cell simulations, we study the scaling of the
instability-driven self-electromagnetic fields and consequent defocusing forces with the background
plasma density and beam ion mass. We identify plasma parameters where the defocusing
forces can be reduced.
Electromagnetic fluctuations during guide field reconnection in a laboratory plasma
Electromagnetic fluctuations are studied during magnetic reconnection in a laboratory plasma for a range of guide magnetic fields from nearly zero up to normalized guide fields $B_g / B_{up} = 1.2$.
The predominant fluctuations are identified as right-hand polarized whistler modes, which become increasingly organized and less intermittent, and obtain larger amplitude with the increasing guide field.
The fluctuation amplitude also increases with the reconnecting magnetic field, implying a relatively constant conversion of upstream magnetic energy to turbulent fluctuations of 1% across guide field strengths.
Modeling Martian Atmospheric Losses over Time: Implications for Exoplanetary Climate Evolution and Habitability
In this Letter, we make use of sophisticated 3D numerical simulations to assess the extent of atmospheric ion
and photochemical losses from Mars over time. We demonstrate that the atmospheric ion escape rates
were significantly higher (by more than two orders of magnitude) in the past at ∼4 Ga compared to the present-day
value owing to the stronger solar wind and higher ultraviolet fluxes from the young Sun. We found that the
photochemical loss of atomic hot oxygen dominates over the total ion loss at the current epoch, while the
atmospheric ion loss is likely much more important at ancient times. We briefly discuss the ensuing implications of
high atmospheric ion escape rates in the context of ancient Mars, and exoplanets with similar atmospheric
compositions around young solar-type stars and M-dwarfs.
TSC simulation of transient CHI in new electrode
configuration on QUEST
In QUEST, transient Coaxial Helicity Injection (CHI) has now been implemented using a new electrode
configuration in which the CHI insulator is not part of the vacuum boundary. In this paper, for the first time,
suitable conditions for generation of the CHI-produced toroidal current in the QUEST vessel configuration were
investigated using the Tokamak Simulation Code (TSC). The simulation results show that the configuration in
which the biased electrode is located farther away from the injector flux coil requires higher currents in the
injector coil to generate the required injector flux. Additionally, energizing a lower inboard poloidal field coil
and possibly lowering the electrode plate closer to the injector flux coil may be necessary to improve injector flux
shaping to permit a configuration that is more favorable for inducing flux closure.
Comparison of Global Martian Plasma Models in the Context of MAVEN Observations
Global models of the interaction of the solar wind with the Martian upper atmosphere haveproved to be valuable tools for investigating both the escape to space of the Martian atmosphere andthe physical processes controlling this complex interac tion.
The many models currently in use employ different physical assumptions, but it can be diﬃcult to directly compare the eﬀectiveness of the models since they are rarely run for the same input conditions.
Here we present the results of a model comparison activity, where ﬁve global models (single-ﬂuid MHD, multifluid MHD, multifluid electron pressure MHD,and two hybrid models) were run for identical conditions corresponding to a single orbit of observations from the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft.
We ﬁnd that low-altitude ion densities are very similar across all models and are comparable to MAVEN ion density measurements from periapsis.
Plasma boundaries appear generally symmetric in all models and vary only slightly in extent.Despite these similarities there are clear morphological diﬀerences in ion behavior in other regions such as the tail and southern hemisphere.
These diﬀerences are observable in ion escape loss maps and are necessary to understand in order to accurately use models in aiding our understanding of the Martian plasma environment.
Geometric field theory and weak Euler-Lagrange equation for classical relativistic particle-field systems
A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is developed. The connection between the space-time symmetry and energy-momentum conservation laws of the system is established geometrically without splitting the space and time coordinates; i.e., space-time is treated as one entity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that the particles and the field reside on different manifolds. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of the electromagnetic fields and also a functional of the particles’ world lines. The other difficulty associated with the geometric setting results from the mass-shell constraint. The standard Euler–Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell constraint is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for the field and the geometric weak EL equation for particles, the symmetries and conservation laws can be established geometrically. A geometric expression for the particle energy-momentum tensor is derived for the first time, which recovers the non-geometric form in the literature for a chosen coordinate system.
Gyroaveraging operations using adaptive matrix operators
A new adaptive scheme to be used in particle-in-cell codes for carrying out gyroaveraging operations with matrices is presented. This new scheme uses an intermediate velocity grid whose resolution is adapted to the local thermal Larmor radius.
The charge density is computed by projecting marker weights in a field-line following manner while preserving the adiabatic magnetic moment $\mu$.
These choices permit to improve the accuracy of the gyroaveraging operations performed with matrices even when strong spatial variation of temperature and magnetic field is present. Accuracy of the scheme in different geometries from simple 2D slab geometry to realistic 3D toroidal equilibrium has been studied. A successful implementation in the gyrokinetic code XGC is presented in the delta-f limit.
Response to "Comment on 'Equilibrium potential well due to finite Larmor radius effects at the tokamak edge'" [Phys. Plasmas 25, 054701 (2018)]
We perform gyrokinetic simulations to study the effects of a stationary magnetic island on neoclassical flow and micro-instability in a realistic KSTAR plasma condition.
Through the simulations, we aim to analyze a recent KSTAR experiment, which was to measure the details of poloidal flow and fluctuation around a stationary (2, 1) magnetic island [M. J. Choi et al., Nucl. Fusion 57, 126058 (2017)].
From the simulations, it is found that the magnetic island can significantly enhance the equilibrium $E \times B$ flow.
The corresponding flow shearing is strong enough to suppress a substantial portion of ambient micro-instabilities, particularly $\nabla T_e$-driven trapped electron modes.
This implies that the enhanced $E \times B$ flow can sustain a quasi-internal transport barrier for $T_e$ in an inner region neighboring the magnetic island.
The enhanced $E \times B$ flow has a (2, 1) mode structure with a finite phase shift from the mode structure of the magnetic island.
It is shown that the flow shear and the fluctuation suppression patterns implied from the simulations are consistent with the observations on the KSTAR experiment.
Simulations of relativistic quantum plasmas using real-time lattice scalar QED
Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales.
As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry.
he lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action.
To demonstrate the capability of our numerical scheme, we apply it to two example problems.
The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum.
The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.
Synthesis of nanoparticles in carbon arc: measurements and modeling
This work presents a study of the region of nanoparticle growth in an atmospheric pressure carbon arc. The nanoparticles are detected using
the planar laser-induced incandescence technique. The measurements revealed large clouds of nanoparticles in the arc periphery bordering
the region with a high density of diatomic carbon molecules. Two-dimensional computational fluid dynamic simulations of the arc combined
with thermodynamic modeling show that this is due to the interplay of the condensation of carbon molecular species and the convection flow
pattern. These results show that the nanoparticles are formed in the colder, peripheral regions of the arc and describe the parameters
necessary for coagulation.
Predict-first experimental analysis using automated and integrated magnetohydrodynamic modeling
An integrated-modeling workflow has been developed for the purpose of performing predict-first analysis of transient-stability experiments.
Starting from an existing equilibrium reconstruction from a past experiment, the workflow couples together the EFIT Grad-Shafranov solver
[L. Lao et al., Fusion Sci. Technol. 48, 968 (2005)],
the EPED model for the pedestal structure
[P. B. Snyder et al., Phys. Plasmas 16, 056118 (2009)],
and the NEO drift-kinetic-equation solver
[E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]
(for bootstrap current calculations) in order to generate equilibria with self-consistent pedestal structures as the plasma shape and various scalar parameters (e.g., normalized $\beta$, pedestal density, and edge safety factor [$q_{95}$]) are changed.
These equilibria are then analyzed using automated M3D-C1 extended-magnetohydrodynamic modeling [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to compute the plasma response to three-dimensional magnetic perturbations.
This workflow was created in conjunction with a DIII-D experiment examining the effect of triangularity on the 3D plasma response.
Several versions of the workflow were developed, and the initial ones were used to help guide experimental planning (e.g., determining the plasma current necessary to maintain the constant edge safety factor in various shapes).
Subsequent validation with the experimental results was then used to revise the workflow, ultimately resulting in the complete model presented here.
We show that quantitative agreement was achieved between the M3D-C1 plasma response calculated for equilibria generated by the final workflow and equilibria reconstructed from experimental data.
A comparison of results from earlier workflows is used to show the importance of properly matching certain experimental parameters in the generated equilibria, including the normalized $\beta$, pedestal density, and $q_{95}$.
On the other hand, the details of the pedestal current did not significantly impact the plasma response in these equilibria.
A comparison to the experimentally measured plasma response shows mixed agreement, indicating that while the equilibria are predicted well, additional analysis tools may be needed.
Finally, we note the implications that these results have for the success of future predict-first studies, particularly the need for scans of uncertain parameters
and for close collaboration between experimentalists and theorists.
Degenerate variational integrators for magnetic field line flow and guiding center trajectories
Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets.
Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates.
New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character.
This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem “degenerate variational integration.”
Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations.
We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure.
Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.
Impact of bootstrap current and Landau-fluid closure on ELM crashes and transport
Results presented here are from 6-field Landau-Fluid simulations using shifted circular cross-section
tokamak equilibria on BOUT++ framework. Linear benchmark results imply that the collisional and
collisionless Landau resonance closures make a little difference on linear growth rate spectra which
are quite close to the results with the flux limited Spitzer-Härm parallel flux. Both linear and nonlinear
simulations show that the plasma current profile plays dual roles on the peeling-ballooning modes
that it can drive the low-n peeling modes and stabilize the high-n ballooning modes. For fixed total
pressure and current, as the pedestal current decreases due to the bootstrap current which becomes
smaller when the density (collisionality) increases, the operational point is shifted downwards vertically
in the Jped – a diagram, resulting in threshold changes of different modes. The bootstrap current
can slightly increase radial turbulence spreading range and enhance the energy and particle transports
by increasing the perturbed amplitude and broadening cross-phase frequency distribution.
Opportunities for plasma separation techniques in rare earth elements recycling
Rare earth elements recycling has been proposed to alleviate supply risks and market volatility. In this context, the potential of a new recycling pathway, namely plasma mass separation, is uncovered through the example of nedodymium - iron - boron magnets recycling. Plasma mass separation is shown to address some of the shortcomings of existing rare earth elements recycling pathways, in particular detrimental environmental effects. A simplified mass separation model suggests that plasma separation performances could compare favourably with existing recycling options. In addition, simple energetic considerations of plasma processing suggest that the cost of these techniques may not be prohibitive, particularly considering that energy costs from solar may become significantly cheaper. Further investigation and experimental demonstration of plasma separation techniques should permit asserting the potential of these techniques against other recycling techniques currently under development.
Energetic-particle-modified global Alfvén eigenmodes
Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfven eigenmodes (GAEs) in low-aspect ratio, NSTX-like conditions.
Key parameters defining the fast ion distribution function-the normalized injection velocity $\nu_0/\nu_A$ and central pitch-are varied in order to study their influence on the characteristics of the excited modes.
It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on $\nu_0/\nu_A$.
This unexpected result is present for both counter-propagating GAEs, which are routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in the mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE.
Additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.
The Morphology of the Solar Wind Magnetic Field Drapingon the Dayside of Mars and Its Variability
The magnetic ﬁeld draping pattern in the magnetosheath of Mars is of interest for what it tells us about both the solar wind interaction with the Mars obstacle and the use of the ﬁeld measured there as a proxy for the upstream interplanetary magnetic ﬁeld (IMF) clock angle.
We apply a time-dependent, global magnetohydrodynamic model toward quantifying the spatial and temporal variations of the magnetic ﬁeld draping direction on the Martian dayside above 500-km altitude.
The magnetic ﬁeld and plasma are self-consistently solved over one Mars rotation period, with the dynamics of the ﬁeld morphology considered as the result of the rotation of the crustal ﬁeld orientation.
Our results show how the magnetic ﬁeld direction on the plane perpendicular to the solar wind ﬂow direction gradually departs from the IMF as the solar wind penetrates toward the obstacle and into the tail region.
This clock angle departure occurs mainly inside the magnetic pileup region and tailward of the terminator plane, exhibiting signiﬁcant dawn-dusk and north-south asymmetries.
Inside the dayside sheath region, the ﬁeld direction has the greatest departure from the IMF-perpendicular component direction downstream of the quasi-parallel bow shock, which for the nominal Parker spiral is over the dawn quadrant.
Thus, the best region to obtain an IMF clock angle proxy is within the dayside magnetosheath at suﬃciently high altitudes, particularly over subsolar and dusk sectors.
Our results illustrate that the crustal ﬁeld has only a mild inﬂuence on the magnetic ﬁeld draping direction within the magnetosheath region.
The Sawtooth Oscillation Effect on Fast-Ion Energy Spectra in ITER Plasma and Neutral Particle Analyzer Measurements
ITER plasma with parameters close to those with the inductive scenario is considered.
The distribution functions of fast ions of deuterium D and tritium T are calculated while taking into account the elastic nuclear collisions with alpha particles 4He using the code FPP-3D.
The D and T energy spectra detected by the neutral-particle analyzer (NPA) are determined.
The plasma mixing effect on these spectra during sawtooth oscillations is studied.
It is shown that the NPA makes it possible to detect sawtooth plasma oscillations in ITER and determine the percentage composition of the D‒T mixture in it both with the presence of instabilities and without them.
A conclusion is drawn on the prospects of using NPA data in automatic controllers of thermonuclear fuel isotopic composition control and plasma oscillation regulation in ITER.
Bulk hydrodynamic stability and turbulent saturation in compressing hot spots
For hot spots compressed at constant velocity, we give a hydrodynamic stability criterion that describes the expected energy behavior of non-radial hydrodynamic motion for different classes of trajectories (in $\rho R - T$ space).
For a given compression velocity, this criterion depends on $\rho R$, $T$, and $dT/d(\rho R)$ (the trajectory slope) and applies point-wise so that the expected behavior can be determined instantaneously along the trajectory.
Among the classes of trajectories are those where the hydromotion is guaranteed to decrease and those where the hydromotion is bounded by a saturated value. We calculate this saturated value and find the compression velocities for which hydromotion may be a substantial fraction of hot-spot energy at burn time.
The Lindl [Phys. Plasmas 2, 3933 (1995)] “attractor” trajectory is shown to experience non-radial hydrodynamic energy that grows towards this saturated state.
Comparing the saturation value with the available detailed 3D simulation results, we find that the fluctuating velocities in these simulations reach substantial fractions of the saturated value
The Twisted Configuration of the Martian Magnetotail: MAVEN Observations
Measurements provided by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft are analyzed to investigate the Martian magnetotail configuration as a function of interplanetary magnetic field (IMF) B-Y. We find that the magnetotail lobes exhibit a similar to 45 degrees twist, either clockwise or counterclockwise from the ecliptic plane, up to a few Mars radii downstream. Moreover, the associated cross-tail current sheet is rotated away from the expected location for a Venus-like induced magnetotail based on nominal IMF draping. Data-model comparisons using magnetohydrodynamic simulations are in good agreement with the observed tail twist. Model field line tracings indicate that a majority of the twisted tail lobes are composed of open field lines, surrounded by draped IMF. We infer that dayside magnetic reconnection between the crustal fields and draped IMF creates these open fields and may be responsible for the twisted tail configuration, similar to what is observed at Earth.
Helical variation of density profiles and fluctuations in the tokamak pedestal with applied 3D fields and implications for confinement
Small 3D perturbations to the magnetic field in DIII-D ($\delta B / B \sim 2×10^{−4}$) result in large modulations of density fluctuation amplitudes in the pedestal, which are shown using Doppler backscattering measurements to vary by a factor of 2.
Helical perturbations of equilibrium density within flux surfaces have previously been observed in the pedestal of DIII-D plasmas when 3D fields are applied and were correlated with density fluctuation asymmetries in the pedestal.
These intra-surface density and pressure variations are shown through two fluid MHD modeling studies using the M3D-C1 code to be due to the misalignment of the density and temperature equilibrium iso-surfaces in the pedestal region.
This modeling demonstrates that the phase shift between the two iso-surfaces corresponds to the diamagnetic direction of the two species, with the mass density surfaces shifted in the ion diamagnetic direction relative to the temperature and magnetic flux iso-surfaces.
The resulting pedestal density, potential, and turbulence asymmetries within flux surfaces near the separatrix may be at least partially responsible for several poorly understood phenomena that occur with the application of 3D fields in tokamaks, including density pump out and the increase in power required to transition from L- to H-mode.
Designing stellarator coils by a modified
Newton method using FOCUS
To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in
existing coil design codes. However, none of these codes have used the information from the
second-order derivatives. In this paper, we present a modified Newton method in the recently
developed code FOCUS. The Hessian matrix is calculated with analytically derived equations.
Its inverse is approximated by a modified Cholesky factorization and applied in the iterative
scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X
modular coils starting from a simple initial guess. Results demonstrate significant advantages.
Validation of the ‘full reconnection model’ of the sawtooth instability in KSTAR
The central safety factor ($q_0$) during sawtooth oscillation has been measured with a great accuracy with the motional Stark effect (MSE) system on KSTAR and the measured value was $\sim 1.0 \pm 0.03$.
However, this measurement alone cannot validate the disputed full and partial reconnection models definitively due to non-trivial off-set error (similar to 0.05). Supplemental experiment of the excited $m = 2$, $m = 3$ modes that are extremely sensitive to the background go and core magnetic shear definitively validates the ‘full reconnection model’.
The radial position of the excited modes right after the crash and time evolution into the $1/1$ kink mode before the crash in a sawtoothing plasma suggests that $q_0 \ge 1.0$ in the MHD quiescent period after the crash and $q_0 < 1.0$ before the crash.
Additional measurement of the long lived $m = 3$, $n = 5$ modes in a non-sawtoothing discharge (presumably $q_0 \ge 1.0$) further validates the ‘full reconnection model’.
A fast low-to-high confinement mode bifurcation dynamics in the boundary-plasma gyrokinetic code XGC1
A fast edge turbulence suppression event has been simulated in the electrostatic version of the gyrokinetic particle-in-cell code XGC1 in a realistic diverted tokamak edge geometry under neutral particle recycling.
The results show that the sequence of turbulent Reynolds stress followed by neoclassical ion orbit-loss driven together conspire to form the sustaining radial electric field shear and to quench turbulent transport just inside the last closed magnetic flux surface.
The main suppression action is located in a thin radial layer around $\psi_N \approx 0.96–0:98$, where $\psi_N$ is the normalized poloidal flux, with the time scale 0.1 ms.
Insights into type-I edge localized modes and edge localized modecontrol from JOREK non-linear magneto-hydrodynamicsimulations
Edge localized modes (ELMs) are repetitive instabilities driven by the large pres-sure gradients and current densities in the edge of H-mode plasmas. Type-I ELMslead to a fast collapse of the H-mode pedestal within several hundred microsec-onds to a few milliseconds. Localized transient heat fluxes to divertor targetsare expected to exceed tolerable limits for ITER, requiring advanced insightsinto ELM physics and applicable mitigation methods. This paper describes hownon-linear magneto-hydrodynamic (MHD) simulations can contribute to this effort.The JOREK code is introduced, which allows the study of large-scale plasma insta-bilities in tokamak X-point plasmas covering the main plasma, the scrape-off layer,and the divertor region with its finite element grid. We review key physics relevantfor type-I ELMs and show to what extent JOREK simulations agree with experimentsand help reveal the underlying mechanisms. Simulations and experimental findingsare compared in many respects for type-I ELMs in ASDEX Upgrade. The role ofplasma flows and non-linear mode coupling for the spatial and temporal structure ofELMs is emphasized, and the loss mechanisms are discussed. An overview of recentELM-related research using JOREK is given, including ELM crashes, ELM-freeregimes, ELM pacing by pellets and magnetic kicks, and mitigation or suppressionby resonant magnetic perturbation coils (RMPs). Simulations of ELMs and ELMcontrol methods agree in many respects with experimental observations from varioustokamak experiments. On this basis, predictive simulations become more and morefeasible. A brief outlook is given, showing the main priorities for further research inthe field of ELM physics and further developments necessary.
Particle-in-cell simulations of anomalous transport in a Penning discharge
Electrostatic particle-in-cell simulations of a Penning discharge are performed in order to investigate azimuthally asymmetric, spoke-like structures previously observed in experiments. Two-dimensional simulations show that for Penning-discharge conditions, a persistent nonlinear spoke-like structure forms readily and rotates in the direction of ${\small {\bf E} \times {\bf B}}$ and electron diamagnetic drifts.
The azimuthal velocity is within about a factor of 2 of the ion acoustic speed. The spoke frequency follows the experimentally observed scaling with ion mass, which indicates the importance of ion inertia in spoke formation. The spoke provides enhanced (anomalous) radial electron transport, and the effective cross-field conductivity is several times larger than the classical (collisional) value. The level of anomalous current obtained in the simulations is in good agreement with the experimental data. The rotating spoke channels most of the radial current, observable by an edge probe as short pulses.
A basal magma ocean dynamo to explain the early lunar magnetic ﬁeld
The source of the ancient lunar magnetic ﬁeld is an unsolved problem in the Moon’s evolution. Theoretical work invoking a core dynamo has been unable to explain the magnitude of the observed ﬁeld, falling instead one to two orders of magnitude below it. Since surface magnetic ﬁeld strength is highly sensitive to the depth and size of the dynamo region, we instead hypothesize that the early lunar dynamo was driven by convection in a basal magma ocean formed from the ﬁnal stages of an early lunar magma ocean; this material is expected to be dense, radioactive, and metalliferous. Here we use numerical convection models to predict the longevity and heat ﬂow of such a basal magma ocean and use scaling laws to estimate the resulting magnetic ﬁeld strength. We show that, if suﬃciently electrically conducting, a magma ocean could have produced an early dynamo with surface ﬁelds consistent with the paleomagnetic observations
High flux femtosecond x-ray emission from the electron-hose instability in laser wakefield accelerators
Bright and ultrashort duration x-ray pulses can be produced by through betatron oscillations of electrons during laser wakefield acceleration (LWFA).
Our experimental measurements using the Hercules laser system demonstrate a dramatic increase in x-ray flux for interaction distances beyond the depletion/dephasing lengths, where the initial electron bunch injected into the first wake bucket catches up with the laser pulse front and the laser pulse depletes.
A transition from an LWFA regime to a beam-driven plasma wakefield acceleration regime consequently occurs.
The drive electron bunch is susceptible to the electron-hose instability and rapidly develops large amplitude oscillations in its tail, which leads to greatly enhanced x-ray radiation emission.
We measure the x-ray flux as a function of acceleration length using a variable length gas cell. 3D particle-in-cell simulations using a Monte Carlo synchrotron x-ray emission algorithm elucidate the time-dependent variations in the radiation emission processes.
In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical simulations as resolving both the bulk and the tail on the same mesh is often challenging. A multi-scale approach, providing evolution equations for the bulk and the tail individually, could offer a resolution in the sense that both populations could be treated on separate meshes or different reduction techniques applied to the bulk and the tail population. In this letter, we propose a multi-scale method which allows us to split a distribution function into a bulk and a tail so that both populations remain genuine, non-negative distribution functions and may carry density, momentum, and energy. The proposed method is based on the observation that the motion of an individual test particle in a plasma obeys a stochastic differential equation, also referred to as a Langevin equation. This allows us to define transition probabilities between the bulk and the tail and to provide evolution equations for both populations separately.
Astrophysical gyrokinetics: Turbulence in pressure-anisotropic plasmas at ion scales and beyond
We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. The turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion-Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (J. Plasma Phys., vol. 81, 2015, 325810501). At scales at and below the ion-Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalization of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvenic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfven waves transition into kinetic Alfven waves. Secondly, we derive and discuss a very general gyrokinetic free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfven waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy, even within the bounds imposed on it by firehose and mirror instabilities, can cause order-of-magnitude variations in the ion-to-electron heating ratio due to the dissipation of Alfvenic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects turbulent fluctuation spectra, the differential heating of particle species and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.
First Direct Observation of Runaway-Electron-Driven Whistler Waves in Tokamaks
DIII-D experiments at low density ($n_e \sim 10^{19} m^{-3}$) have directly measured whistler waves in the 100-200 MHz range excited by multi-MeV runaway electrons. Whistler activity is correlated with runaway intensity (hard x-ray emission level), occurs in novel discrete frequency bands, and exhibits nonlinear limit-cycle-like behavior. The measured frequencies scale with the magnetic field strength and electron density as expected from the whistler dispersion relation. The modes are stabilized with increasing magnetic field, which is consistent with wave-particle resonance mechanisms. The mode amplitudes show intermittent time variations correlated with changes in the electron cyclotron emission that follow predator-prey cycles. These can be interpreted as wave-induced pitch angle scattering of moderate energy runaways. The tokamak runaway-whistler mechanisms have parallels to whistler phenomena in ionospheric plasmas. The observations also open new directions for the modeling and active control of runaway electrons in tokamaks.
A basal magma ocean dynamo to explain the early lunar magnetic field
The source of the ancient lunar magnetic ﬁeld is an unsolved problem in the Moon’s evolution.
Theoretical work invoking a core dynamo has been unable to explain the magnitude of the observed ﬁeld, falling instead one to two orders of magnitude below it.
Since surface magnetic ﬁeld strength is highly sensitive to the depth and size of the dynamo region, we instead hypothesize that the early lunar dynamo was driven by convection in a basal magma ocean formed from the ﬁnal stages of an early lunar magma ocean; this material is expected to be dense, radioactive, and metalliferous.
Here we use numerical convection models to predict the longevity and heat ﬂow of such a basal magma ocean and use scaling laws to estimate the resulting magnetic ﬁeld strength.
We show that, if sufficiently electrically conducting, a magma ocean could have produced an early dynamo with surface ﬁelds consistent with the paleomagnetic observations.
Hessian matrix approach for determining error field sensitivity to coil deviations
The presence of error fields has been shown to degrade plasma confinement and drive instabilities.
Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry.
In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations.
A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field.
The FOCUS code [Zhu et al., Nucl. Fusion 58, 016008 (2018)] is utilized to provide fast and accurate calculations of the Hessian.
The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix.
A proof-of-principle example is given on a CNT-like configuration.
We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.
Modeling of NSTX hot Vertical Displacement Event using M3D-C1
The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3D-C1 are presented.
A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a so-called NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability.
The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations.
The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes.
In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered.
For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE time depends on the choice of halo temperature. The evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed in detail.
The 3D simulations highlight a rich structure of toroidal modes, penetrating inwards from edge to core and cascading from high-n to low-n mode numbers.
The break-up of flux-surfaces results in a progressive stochastisation of field-lines precipitating the thermalisation of the plasma with the wall.
The plasma current then decays rapidly, inducing large currents in the halo region and the wall.
Analysis of normal currents flowing in and out of the divertor plate reveals rich time-varying patterns.
Strategies for advantageous differential transport of ions in magnetic fusion devices
In a variety of magnetized plasma geometries, it has long been known that highly charged impurities tend to accumulate in regions of higher density. This “collisional pinch” is modified in the presence of additional forces, such as those might be found in systems with gravity, fast rotation, or non-negligible space charge. In the case of a rotating, cylindrical plasma, there is a regime in which the radially outermost ion species is intermediate in both mass and charge. This could have implications for fusion devices and plasma mass filters.
Electron Physics in 3-D Two-Fluid Ten-Moment Modeling of Ganymede's Magnetosphere
We studied the role of electron physics in 3‐D two‐fluid 10‐moment simulation of Ganymede's magnetosphere.
The model captures nonideal physics like the Hall effect, electron inertia, and anisotropic, nongyrotropic pressure effects. A series of analyses were carried out: (1) The resulting magnetic field topology and electron and ion convection patterns were investigated.
The magnetic fields were shown to agree reasonably well with in situ measurements by the Galileo satellite.
(2) The physics of collisionless magnetic reconnection were carefully examined in terms of the current sheet formation and decomposition of generalized Ohm's law. The importance of pressure anisotropy and nongyrotropy in supporting the reconnection electric field is confirmed.
(3) We compared surface “brightness” morphology, represented by surface electron and ion pressure contours, with oxygen emission observed by the Hubble Space Telescope.
The correlation between the observed emission morphology and spatial variability in electron/ion pressure was demonstrated. Potential extension to multi‐ion species in the context of Ganymede and other magnetospheric systems is also discussed.
Dual Phase-space Cascades in 3D Hybrid-Vlasov–Maxwell Turbulence
To explain energy dissipation via turbulence in collisionless, magnetized plasmas, the existence of a dual real- and
velocity-space cascade of ion-entropy fluctuations below the ion gyroradius has been proposed. Such a dual
cascade, predicted by the gyrokinetic theory, has previously been observed in gyrokinetic simulations of twodimensional,
electrostatic turbulence. For the first time, we show evidence for a dual phase-space cascade of ionentropy
fluctuations in a three-dimensional simulation of hybrid-kinetic, electromagnetic turbulence. Some of the
scalings observed in the energy spectra are consistent with a generalized theory for the cascade that accounts for
the spectral anisotropy of critically balanced, intermittent, sub-ion-Larmor-scale fluctuations. The observed
velocity-space cascade is also anisotropic with respect to the magnetic-field direction, with linear phase mixing
along magnetic-field lines proceeding mainly at spatial scales above the ion gyroradius and nonlinear phase mixing
across magnetic-field lines proceeding at perpendicular scales below the ion gyroradius. Such phase-space
anisotropy could be sought in heliospheric and magnetospheric data of solar-wind turbulence and has far-reaching
implications for the dissipation of turbulence in weakly collisional astrophysical plasmas.
Resolving runaway electron distributions in space, time, and energy
Areas of agreement and disagreement with present-day models of runaway electron (RE) evolution
are revealed by measuring MeV-level bremsstrahlung radiation from runaway electrons (REs) with
a pinhole camera. Spatially resolved measurements localize the RE beam, reveal energy-dependent
RE transport, and can be used to perform full two-dimensional (energy and pitch-angle) inversions
of the RE phase-space distribution. Energy-resolved measurements find qualitative agreement with
modeling on the role of collisional and synchrotron damping in modifying the RE distribution
shape. Measurements are consistent with predictions of phase-space attractors that accumulate
REs, with non-monotonic features observed in the distribution. Temporally resolved measurements
find qualitative agreement with modeling on the impact of collisional and synchrotron damping in
varying the RE growth and decay rate. Anomalous RE loss is observed and found to be largest at
low energy. Possible roles for kinetic instability or spatial transport to resolve these anomalies are
discussed.
Laser-plasma interactions in magnetized environment
Propagation and scattering of lasers present new phenomena and applications when the plasma medium becomes strongly magnetized. With mega-Gauss magnetic fields, scattering of optical lasers already becomes manifestly anisotropic. Special angles exist where coherent laser scattering is either enhanced or suppressed, as we demonstrate using a cold-fluid model. Consequently, by aiming laser beams at special angles, one may be able to optimize laser-plasma coupling in magnetized implosion experiments. In addition, magnetized scattering can be exploited to improve the performance of plasma-based laser pulse amplifiers. Using the magnetic field as an extra control variable, it is possible to produce optical pulses of higher intensity, as well as compress UV and soft x-ray pulses beyond the reach of other methods. In even stronger giga-Gauss magnetic fields, laser-plasma interaction enters a relativistic-quantum regime. Using quantum electrodynamics, we compute a modified wave dispersion relation, which enables correct interpretation of Faraday rotation measurements of strong magnetic fields.
Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions
Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic
models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we
demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the
ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and
including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the
cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show
excellent agreement with analogous gyrokinetic simulations across a wide range of parameters.
The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work
demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which
are critical aspects of modeling plasma turbulence with full ion dynamics.
On limitations of laser-induced fluorescence diagnostics for xenon ion velocity distribution function measurements in Hall thrusters
Hall thruster operation is characterized by strong breathing oscillations of the discharge current, the
plasma density, the temperature, and the electric field. Probe- and laser-induced fluorescence (LIF)
diagnostics were used to measure temporal variations of plasma parameters and the xenon ion
velocity distribution function (IVDF) in the near-field plasma plume in regimes with moderate
(<18%) external modulations of applied DC discharge voltage at the frequency of the breathing
mode. It was shown that the LIF signal collapses while the ion density at the same location is finite.
The proposed explanation for this surprising result is based on a strong dependence of the excitation
cross-section of metastables on the electron temperature. For large amplitudes of oscillations,
the electron temperature at the minimum enters the region of very low cross-section (for the excitation
of the xenon ions); thus, significantly reducing the production of metastable ions. Because the
residence time of ions in the channel is generally shorter than the time scale of breathing oscillations,
the density of the excited ions outside the thruster is low and they cannot be detected. In the
range of temperature of oscillations, the ionization cross-section of xenon atoms remains suffi-
ciently large to sustain the discharge. This finding suggests that the commonly used LIF diagnostic
of xenon IVDF can be subject to large uncertainties in the regimes with significant oscillations of
the electron temperature, or other plasma parameters.
Scenario development during commissioning operations on the National Spherical Torus Experiment Upgrade
The National Spherical Torus Experiment Upgrade (NSTX-U) will advance the physics basis required for achieving steady-state, high-beta, and high-confinement conditions in a tokamak by accessing high toroidal fields ($1 T$) and plasma currents ($1.0–2.0 MA$) in a low aspect ratio geometry ($A = 1.6–1.8$) with flexible auxiliary heating systems (12 MW NBI, 6 MW HHFW).
This paper describes the progress in the development of L- and H-mode discharge scenarios and the commissioning of operational tools in the first ten weeks of operation that enable the scientific mission of NSTX-U.
Vacuum field calculations completed prior to operations supported the rapid development and optimization of inductive breakdown at different values of ohmic solenoid current.
The toroidal magnetic field ($B_{T0} = 0.65 T$) exceeded the maximum values achieved on NSTX and novel long-pulse L-mode discharges with regular sawtooth
activity exceeded the longest pulses produced on NSTX ($t_{pulse} > 1.8 s$).
The increased flux of the central solenoid facilitated the development of stationary L-mode discharges over a range of density and plasma current ($I_p$).
H-mode discharges achieved similar levels of stored energy, confinement ($H_{98,y2} > 1$) and stability ($\beta_N/\beta_{N-nowall} > 1$) compared to NSTX discharges for
$I_p ⩽ 1 MA$.
High-performance H-mode scenarios require an L–H transition early in the $I_p$ ramp-up phase in order to obtain low internal inductance ($l_i$) throughout the discharge, which is conducive to maintaining vertical stability at high elongation ($\kappa > 2.2$) and achieving long periods of MHD quiescent operations.
The rapid progress in developing L- and H-mode scenarios in support of the scientific program was enabled by advances in real-time plasma control, efficient error field identification and correction, effective conditioning of the graphite wall and excellent diagnostic availability.
The vertical displacement of a tokamak plasma is modelled during its non-linear phase by considering a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell.
The models capture the leading term in a Taylor expansion of the Green’s function for the interaction between the plasma column and the surrounding vacuum vessel.
The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents.
Consequently, the plasma wire oscillates at Alfvenic frequencies about a given force-free position.
In addition to damping oscillations, resistivity in the wall allows for the equilibrium point to drift towards the vessel on the slow timescale of flux penetration.
The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour, that is analytically shown to be algebraic and decelerating.
The acceleration of the plasma column often observed in experiments is thus conjectured to originate from an early sharing of toroidal current between the core, the halo plasma and the wall or from the thermal quench dynamics precipitating loss of plasma current.
Orchestrating TRANSP Simulations for Interpretative and Predictive Tokamak Modeling with OMFIT
TRANSP simulations are being used in the OMFIT workflow manager to enable a machineindependent
means of experimental analysis, postdictive validation, and predictive time-dependent simulations
on the DIII-D, NSTX, JET, and C-MOD tokamaks. The procedures for preparing input data from plasma profile diagnostics and equilibrium reconstruction, as well as processing of the time-dependent heating and current drive
sources and assumptions about the neutral recycling, vary across machines, but are streamlined by using a common workflow manager. Settings for TRANSP simulation fidelity are incorporated into the OMFIT framework, contrasting
between-shot analysis, power balance, and fast-particle simulations. A previously established series of data consistency metrics are computed such as comparison of experimental versus calculated neutron rate, equilibrium
stored energy versus total stored energy from profile and fast-ion pressure, and experimental versus computed surface loop voltage. Discrepancies between data consistency metrics can indicate errors in input quantities such as
electron density profile or $Z_{eff}$, or indicate anomalous fast-particle transport. Measures to assess the sensitivity of
the verification metrics to input quantities are provided by OMFIT, including scans of the input profiles and
standardized postprocessing visualizations. For predictive simulations, TRANSP uses GLF23 or TGLF to predict
core plasma profiles, with user-defined boundary conditions in the outer region of the plasma. International
Tokamak Physics Activity (ITPA) validation metrics are provided in postprocessing to assess the transport model
validity. By using OMFIT to orchestrate the steps for experimental data preparation, selection of operating mode,
submission, postprocessing, and visualization, we have streamlined and standardized the usage of TRANSP.
Stellarator Research Opportunities: A Report of the National Stellarator Coordinating Committee
This document is the product of a stellarator community workshop, organized by the National Stellarator Coordinating Committee and referred to as Stellcon, that was held in Cambridge, Massachusetts in February 2016, hosted by MIT.
The workshop was widely advertised, and was attended by 40 scientists from 12 different institutions including national labs, universities and private industry, as well as a representative from the Department of Energy.
The final section of this document describes areas of community wide consensus that were developed as a result of the discussions held at that workshop.
Areas where further study would be helpful to generate a consensus path forward for the US stellarator program are also discussed.
The program outlined in this document is directly responsive to many of the strategic priorities of FES as articulated in “Fusion Energy Sciences: A Ten-Year Perspective (2015–2025)” [1].
The natural disruption immunity of the stellarator directly addresses “Elimination of transient events that can be deleterious to toroidal fusion plasma confinement devices” an area of critical importance for the US fusion energy sciences enterprise over the next decade.
Another critical area of research “Strengthening our partnerships with international research facilities,” is being significantly advanced on the W7-X stellarator in Germany and serves as a test-bed for development of successful international collaboration on ITER.
This report also outlines how materials science as it relates to plasma and fusion sciences, another critical research area, can be carried out effectively in a stellarator.
Additionally, significant advances along two of the Research Directions outlined in the report; “Burning Plasma Science: Foundations—Next-generation research capabilities”, and “Burning Plasma Science: Long pulse—Sustainment of Long-Pulse Plasma Equilibria” are proposed.
Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. The numerical simulation of relativistic dynamics is often multi-scale and requires accurate long-term numerical simulations. Therefore, explicit symplectic algorithms are much more preferable than non-symplectic methods and implicit symplectic algorithms. In this paper, we employ the proper time and express the Hamiltonian as the sum of exactly solvable terms and product-separable terms in space-time coordinates. Then, we give the explicit symplectic algorithms based on the generating functions of orders 2 and 3 for relativistic dynamics of a charged particle. The methodology is not new, which has been applied to non-relativistic dynamics of charged particles, but the algorithm for relativistic dynamics has much significance in practical simulations, such as the secular simulation of runaway electrons in tokamaks.
Magnetohydrodynamic Turbulence in the Plasmoid-mediated Regime
Magnetohydrodynamic turbulence and magnetic reconnection are ubiquitous in astrophysical environments. In most situations these processes do not occur in isolation but interact with each other. This renders a comprehensive theory of these processes highly challenging. Here we propose a theory of magnetohydrodynamic turbulence driven at a large scale that self-consistently accounts for the mutual interplay with magnetic reconnection occurring at smaller scales. Magnetic reconnection produces plasmoids (flux ropes) that grow from turbulence-generated noise and eventually disrupt the sheet-like structures in which they are born. The disruption of these structures leads to a modification of the turbulent energy cascade, which in turn exerts a feedback effect on the plasmoid formation via the turbulence-generated noise. The energy spectrum in this plasmoid-mediated range steepens relative to the standard inertial range and does not follow a simple power law. As a result of the complex interplay between turbulence and reconnection, we also find that the length scale that marks the beginning of the plasmoid-mediated range and the dissipation length scale do not obey true power laws. The transitional magnetic Reynolds number above which the plasmoid formation becomes statistically significant enough to affect the turbulent cascade is fairly modest, implying that plasmoids are expected to modify the turbulent path to dissipation in many astrophysical systems.
Collisionless kinetic theory of oblique tearing instabilities
The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the
Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at
the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant
surface have a unique angle with respect to the guide field direction. Both kinetic simulations and
numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed
that standard analytic theories vastly overestimate the growth rate of oblique modes. We find that
this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories
miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently
far that the assumption of scale separation between the inner and outer regions of boundarylayer
theory breaks down. The dispersion relation obtained by numerically solving a single second
order differential equation is found to approximately capture the drift stabilization predicted by solutions
of the full integro-differential eigenvalue problem. A simple analytic estimate for the stability
criterion is provided.
Collisionless Magnetic Reconnection in Curved Spacetime and the Effect of Black Hole Rotation
Magnetic reconnection in curved spacetime is studied by adopting a general-relativistic magnetohydrodynamic model that retains collisionless effects for both electron-ion and pair plasmas. A simple generalization of the standard Sweet-Parker model allows us to obtain the first-order effects of the gravitational field of a rotating black hole. It is shown that the black hole rotation acts to increase the length of azimuthal reconnection layers, thus leading to a decrease of the reconnection rate. However, when coupled to collisionless thermal-inertial effects, the net reconnection rate is enhanced with respect to what would happen in a purely collisional plasma due to a broadening of the reconnection layer. These findings identify an underlying interaction between gravity and collisionless magnetic reconnection in the vicinity of compact objects.
Optimizing beam transport in rapidly compressing beams on the neutralized drift compression experiment – II
The current flow in two-fluid plasma is inherently unstable if plasma components (e.g., electrons and ions) are in different collisionality regimes. A typical example is a partially magnetized E×B plasma discharge supported by the energy released from the dissipation of the current in the direction of the applied electric field (perpendicular to the magnetic field). Ions are not magnetized so they respond to the fluctuations of the electric field ballistically on the inertial time scale. In contrast, the electron current in the direction of the applied electric field is dissipatively supported either by classical collisions or anomalous processes. The instability occurs due to a positive feedback between the electron and ion current coupled by the quasi-neutrality condition. The theory of this instability is further developed taking into account the electron inertia, finite Larmor radius and nonlinear effects. It is shown that this instability results in highly nonlinear quasi-coherent structures resembling breathing mode oscillations in Hall thrusters.
Quantitative imaging of carbon dimer precursor for nanomaterial synthesis in the carbon arc
Delineating the dominant processes responsible for nanomaterial synthesis in a plasma environment requires measurements of the precursor species contributing to the growth of nanostructures.
We performed comprehensive measurements of spatial and temporal profiles of carbon dimers ($C_2$) in sub-atmospheric-pressure carbon arc by laser-induced fluorescence.
Measured spatial profiles of C2 coincide with the growth region of carbon nanotubes [Fang et al., Carbon 107, 273 (2016)] and vary depending on the arc operation mode, which is determined by the discharge current and the ablation rate of the graphite anode.
The $C_2$ density profile exhibits large spatial and time variations due to motion of the arc core.
A comparison of the experimental data with the 2D simulation results of selfconsistent arc modeling shows good agreement.
The model predicts well the main processes determining spatial profiles of carbon dimers ($C_2$).
Effect of polarization forces on carbon deposition on a non-spherical nanoparticle. Monte Carlo simulations
Trajectories of a polarizable species (atoms or molecules) in the vicinity of a negatively charged nanoparticle (at a floating potential) are considered. The atoms are pulled into regions of strong electric field by polarization forces. The polarization increases the deposition rate of the atoms and molecules at the nanoparticle. The effect of the non-spherical shape of the nanoparticle is investigated by the Monte Carlo method. The shape of the non-spherical nanoparticle is approximated by an ellipsoid. The total deposition rate and its flux density distribution along the nanoparticle surface are calculated. It is shown that the flux density is not uniform along the surface. It is maximal at the nanoparticle tips.
Centrifugal particle confinement in Mirror Geometry
The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermonuclear fusion.
The device is steady state, there are no disruptions, the loss cone is almost closed, sheared rotation stabilizes magnetohydrodynamic instabilities as well as plasma turbulence, there are no runaway electrons, and the coil configuration is simple.
In this work, we examine the effect of rotation on mirror confinement using a full cyclotron orbit code.
The full cyclotron simulations give a much more complete description of the particle energy distribution and losses than the use of guiding center equations.
Both collisionless loss as a function of rotation and the effect of collisions are investigated.
Although the cross field diffusion is classical, we find that the local rotating Maxwellian is increased to higher energy, increasing the fusion rate and also enhancing the radial diffusion.
We find a loss channel not envisioned with a guiding center treatment, but a design can be chosen that can satisfy the Lawson criterion for ions.
Of course, the rotation has a minimal effect on the alpha particle birth distribution, so there is initially loss through the usual loss cone, just as in a mirror with no rotation.
However after this loss, the alphas slow down on the electrons with little pitch angle scattering until reaching low energy, so over half of the initial alpha energy is transferred to the electrons.
The important problem of energy confinement, with losses primarily through the electron channel, is not addressed in this work.
We also discuss the use of rotating mirror geometry to produce an ion thruster.
Preface to Special Topic: Collective Effects in Particle Beams and Nonneutral Plasmas
Abstract Atmospheric pressure arcs have recently found application in the production of nanoparticles. Distinguishing features of such arcs are small length and hot ablating anode characterized by intensive electron emission and radiation from its surface. We performed one-dimensional modeling of argon arc, which shows that near-electrode effects of thermal and ionization non-equilibrium play important role in operation of a short arc, because the non-equilibrium regions are up to several millimeters long and are comparable with the arc length. The near-anode region is typically longer than the near-cathode region and its length depends more strongly on the current density. The model was extensively verified and validated against previous simulation results and experimental data. Volt-Ampere characteristic (VAC) of the near-anode region depends on the anode cooling mechanism. In case of strong anode cooling when anode is cold, the anode voltage decreases with current density, therefore suggesting the arc constriction near the anode. Without anode cooling, the anode temperature increases significantly with current density, leading to drastic increase in the thermionic emission current from anode. Correspondingly, the anode voltage increases with current density – and the opposite trend in the VAC is observed. The results of simulations were found to be independent of sheath model used: collisional (fluid) or collisionless model gave the same plasma profiles for both near-anode and near-cathode regions.
Investigation of the Short Argon Arc with Hot Anode, Part II: Analytical Model
Short atmospheric pressure argon arc is studied numerically and analytically. In a short arc with inter-electrode gap of several millimeters non-equilibrium effects in plasma play important role in operation of the arc. High anode temperature leads to electron emission and intensive radiation from its surface.
Complete self-consistent analytical model of the whole arc comprising of models for near-electrode
regions, arc column and a model of heat transfer in cylindrical electrodes was developed. The model
predicts width of non-equilibrium layers and arc column, voltages and plasma profiles in these regions,
heat and ion fluxes to the electrodes. Parametric studies of the arc have been performed for a range of
the arc current densities, inter-electrode gap widths and gas pressures. The model was validated against
experimental data and verified by comparison with numerical solution. Good agreement between the
analytical model and simulations and reasonable agreement with experimental data were obtained.
Investigating the radial structure of axisymmetric fluctuations in the TCV tokamak with local and global gyrokinetic GENE simulations
Axisymmetric $(n=0)$ density fluctuations measured in the TCV tokamak are observed to possess a frequency $f_0$ which is either varying (radially dispersive oscillations) or a constant over a large fraction of the plasma minor radius (radially global oscillations) as reported in a companion paper [Z. Huang et al., this issue].
Given that $f_0$ scales with the sound speed and given the poloidal structure of density fluctuations, these oscillations were interpreted as Geodesic Acoustic Modes,
even though $f_0$ is in fact smaller than the local linear GAM frequency $f_{GAM}$. In this work we
employ the Eulerian gyrokinetic code GENE to simulate TCV relevant conditions and investigate
the nature and properties of these oscillations, in particular their relation to the safety factor profile.
Local and global simulations are carried out and a good qualitative agreement is observed between
experiments and simulations. By varying also the plasma temperature and density profiles, we
conclude that a variation of the edge safety factor alone is not sufficient to induce a transition from
global to radially inhomogeneous oscillations, as was initially suggested by experimental results. This
transition appears instead to be the combined result of variations in the different plasma profiles,
collisionality and finite machine size effects. Simulations also show that radially global GAM-like
oscillations can be observed in all fluxes and fluctuation fields, suggesting that they are the result of
a complex nonlinear process involving also finite toroidal mode numbers and not just linear global
GAM eigenmodes.
A Maximum Entropy Principle for inferring the Distribution of 3D Plasmoids
The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced.
The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance.
The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of $−4/3$, $−2$, $−3$, and $−2$, respectively, for small values, whilst all of them display an exponential falloff for large values.
In contrast, the velocity distribution, as a function of $v=|v|$, is shown to be flat for $v→0$, and becomes a power law with an exponent of $−7/3$ for $v\rightarrow\infty$.
Most of these results are nearly independent of the free parameters involved in this specific problem.
A preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed
Identifying microturbulence regimes in a TCV discharge making use
of physical constraints on particle and heat fluxes
Reducing the uncertainty on physical input parameters derived from experimental measurements is
essential towards improving the reliability of gyrokinetic turbulence simulations. This can be
achieved by introducing physical constraints. Amongst them, the zero particle flux condition is
considered here. A first attempt is also made to match as well the experimental ion/electron heat
flux ratio. This procedure is applied to the analysis of a particular Tokamak a Configuration
Variable discharge. A detailed reconstruction of the zero particle flux hyper-surface in the multidimensional
physical parameter space at fixed time of the discharge is presented, including the
effect of carbon as the main impurity. Both collisionless and collisional regimes are considered.
Hyper-surface points within the experimental error bars are found. The analysis is done performing
gyrokinetic simulations with the local version of the GENE code, computing the fluxes with a
Quasi-Linear (QL) model and validating the QL results with non-linear simulations in a subset of
cases.
The Propitious Role of Solar Energetic Particles in the Origin of Life
We carry out 3D numerical simulations to assess the penetration and bombardment effects of solar energetic particles (SEPs), i.e., high-energy particle bursts during large flares and superflares, on ancient and current Mars. We demonstrate that the deposition of SEPs is non-uniform at the planetary surface, and that the corresponding energy flux is lower than other sources postulated to have influenced the origin of life. Nevertheless, SEPs may have been capable of facilitating the synthesis of a wide range of vital organic molecules (e.g., nucleobases and amino acids). Owing to the relatively high efficiency of these pathways, the overall yields might be comparable to (or even exceed) the values predicted for some conventional sources such as electrical discharges and exogenous delivery by meteorites. We also suggest that SEPs could have played a role in enabling the initiation of lightning. A notable corollary of our work is that SEPs may constitute an important mechanism for prebiotic synthesis on exoplanets around M-dwarfs, thereby mitigating the deficiency of biologically active ultraviolet radiation on these planets. Although there are several uncertainties associated with (exo)planetary environments and prebiotic chemical pathways, our study illustrates that SEPs represent a potentially important factor in understanding the origin of life.
Low Mach-number collisionless shocks and associated ion acceleration
The existence and properties of low Mach-number ($M \ge 1$) electrostatic collisionless shocks are investigated
with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in
the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where
the shock is generated by the decay of an initial density discontinuity. Using this semi-analytical model,
we study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum
shock potential and Mach number. We find that even a small amount of impurities can influence the shock
properties significantly, including the reflected light ion fraction, which can change several orders of magnitude.
Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.
Modeling of reduced secondary electron emission yield from a foam or fuzz
surface
Complex structures on a material surface can significantly reduce the total secondary electron emission yield from that surface.
A foam or fuzz is a solid surface above which is placed a layer of isotropically aligned whiskers.
Primary electrons that penetrate into this layer produce secondary electrons that become trapped and do not escape into the bulk plasma.
In this manner the secondary electron yield (SEY) may be reduced.
We developed an analytic model and conducted numerical simulations of secondary electron emission from a foam to determine the extent of SEY reduction.
We find that the relevant condition for SEY minimization is $\bar u \equiv AD/2 >> 1$ while $D<<1$, where $D$ is the volume fill fraction and $A$ is the aspect ratio of the whisker layer, the ratio of the thickness of the layer to the radius of the fibers.
We find that foam can not reduce the SEY from a surface to less than 0.3 of its flat value.
Generation of forerunner electron beam during interaction of ion beam pulse with plasma
The long-time evolution of the two-stream instability of a cold tenuous ion beam pulse propagating through the background plasma with density much higher than the ion beam density is investigated using a large-scale one-dimensional electrostatic kinetic simulation. The three stages of the instability are investigated in detail. After the initial linear growth and saturation by the electron trapping, a portion of the initially trapped electrons becomes detrapped and moves ahead of the ion beam pulse forming a forerunner electron beam, which causes a secondary two-stream instability that preheats the upstream plasma electrons. Consequently, the self-consistent nonlinear-driven turbulent state is set up at the head of the ion beam pulse with the saturated plasma wave sustained by the influx of the cold electrons from upstream of the beam that lasts until the final stage when the beam ions become trapped by the plasma wave. The beam ion trapping leads to the nonlinear heating of the beam ions that eventually extinguishes the instability.
Atmospheric escape from the TRAPPIST-1 planets and implications for habitability
The presence of an atmosphere over sufficiently long timescales
is widely perceived as one of the most prominent criteria associated
with planetary surface habitability. We address the crucial
question of whether the seven Earth-sized planets transiting the
recently discovered ultracool dwarf star TRAPPIST-1 are capable of
retaining their atmospheres. To this effect, we carry out numerical
simulations to characterize the stellar wind of TRAPPIST-1 and the
atmospheric ion escape rates for all of the seven planets. We also
estimate the escape rates analytically and demonstrate that they
are in good agreement with the numerical results. We conclude
that the outer planets of the TRAPPIST-1 system are capable of
retaining their atmospheres over billion-year timescales. The consequences
arising from our results are also explored in the context
of abiogenesis, biodiversity, and searches for future exoplanets.
In light of the many unknowns and assumptions involved, we
recommend that these conclusions must be interpreted with due
caution.
Nonlinear dynamics of the electron-cyclotron instability driven by the electron $\small {\bf E}\times{\bf B}$ current in a
crossed electric and magnetic field is studied. In the nonlinear regime, the instability proceeds by
developing a large amplitude coherent wave driven by the energy input from the fundamental
cyclotron resonance. Further evolution shows the formation of the long wavelength envelope akin
to the modulational instability. Simultaneously, the ion density shows the development of a high-k
content responsible for wave focusing and sharp peaks on the periodic cnoidal wave structure. It is
shown that the anomalous electron transport (along the direction of the applied electric field) is
dominated by the long wavelength part of the turbulent spectrum.
Gyrokinetic nonlinear continuum interaction of Toroidal Alfvén eigenmodes
Energetic particle transport in toroidal magnetic confinement fusion devices can be enhanced by
the particles’ interaction with electromagnetic global modes. This process has been modelled
numerically. The most extensive work has been with reduced models, which may use a simplified
description of the bulk plasma, assuming a perturbative approximation for mode structure
evolution, restrict simulation to the linear phase, or some combination. In this work, nonlinear nonperturbative
simulations are performed using a fully gyrokinetic and reduced models of the bulk
plasma. Previous linear investigation of a simple model tokamak case is extended to show that, at
least under some conditions, dramatic qualitative differences in mode structure and saturated mode
amplitude can exist due to non-perturbative response in the linear and nonlinear phases that
depends upon the bulk plasma physics. This supports analytical work which has shown that the
non-perturbative energetic particle response should depend upon the magnetic geometry and
kinetic physics. It is also shown that energetic particle modes that dominate in the linear phase can
be subdominant to a non-perturbative toroidal Alfven eigenmode-based global structure in the nonlinear
phase.
Gyrokinetic magnetohydrodynamics and the associated equilibria
The gyrokinetic magnetohydrodynamics (MHD) equations, related to the recent paper by W. W. Lee [“Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective,” Phys. Plasmas 23, 070705 (2016)], and their associated equilibria properties are discussed.
This set of equations is consisted of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm’s law, and the gyrokinetic Ampere’s law as well as the equations of state, which are expressed in terms of the electrostatic potential, $\phi$, and the vector potential, ${\bf A}$ and support both spatially varying perpendicular and parallel pressure gradients and the associated currents.
The corresponding gyrokinetic MHD equilibria can be reached when $\phi \rightarrow 0$ and ${\bf A}$ becomes constant in time, which, in turn, gives $\nabla \cdot ( {\bf J}_\parallel + {\bf J}_\perp ) = 0$ and the associated magnetic islands, if they exist.
Examples in simple cylindrical geometry are given.
These gyrokinetic MHD equations look quite different from the conventional MHD equations and their comparisons will be an interesting topic in the future.
Constructing current singularity in a 3D line-tied plasma
We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas, using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, hence arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm-Kulsrud-Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for all system lengths. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.
Excitation of a global plasma mode by an intense electron beam in a dc discharge
Interaction of an intense electron beam with a finite-length, inhomogeneous plasma is investigated numerically. The plasma density profile is maximal in the middle and decays towards the plasma edges. Two regimes of the two-stream instability are observed. In one regime, the frequency of the instability is the plasma frequency at the density maximum and plasma waves are excited in the middle of the plasma. In the other regime, the frequency of the instability matches the local plasma frequency near the edges of the plasma and the intense plasma oscillations occur near plasma boundaries. The latter regime appears sporadically and only for strong electron beam currents. This instability generates copious amount of suprathermal electrons. The energy transfer to suprathermal electrons is the saturation mechanism of the instability.
Generalized parametrization methods for centroid and envelope dynamics of charged particle beams in coupled lattices
For almost 60 years, the well-known Courant-Snyder (CS) theory has been employed as the standard method to describe the uncoupled dynamics of charged particle beams in electromagnetic focusing lattices. Meanwhile, the generalization of the CS theory to coupled dynamics with two or more degrees of freedom has been attempted in numerous directions. The parametrization method developed by Qin and Davidson is particularly noteworthy, because their method enables the treatment of complicated coupled beam dynamics using a remarkably similar mathematical structure to that of the original CS theory. In this paper, we revisit the Qin-Davidson parametrization method and extend it to include beam centroid motions. The linear terms in the quadratic Hamiltonian for the coupled dynamics are handled by introducing a special time-dependent canonical transformation. In this manner, we show that the centroid dynamics is decoupled from the envelope dynamics, even for the cases of coupled lattice, and all formulations of the Qin-Davidson method can be applied in a straightforward manner.
Modeling turbulent energy behavior and sudden viscous dissipation in compressing plasma turbulence
We present a simple model for the turbulent kinetic energy behavior of subsonic plasma turbulence
undergoing isotropic three-dimensional compression, which may exist in various inertial confinement
fusion experiments or astrophysical settings. The plasma viscosity depends on both the temperature
and the ionization state, for which many possible scalings with compression are possible.
For example, in an adiabatic compression the temperature scales as $1/L^2$, with $L$ the linear compression
ratio, but if thermal energy loss mechanisms are accounted for, the temperature scaling
may be weaker. As such, the viscosity has a wide range of net dependencies on the compression.
The model presented here, with no parameter changes, agrees well with numerical simulations for
a range of these dependencies. This model permits the prediction of the partition of injected energy
between thermal and turbulent energy in a compressing plasma..
Mode conversion in cold low-density plasma with a sheared magnetic field
A theory is proposed that describes mutual conversion of two electromagnetic modes in cold low-density plasma, specifically, in the high-frequency limit where the ion response is negligible.
In contrast to the classic (Landau–Zener-type) theory of mode conversion, the region of resonant coupling in low-density plasma is not necessarily narrow, so the coupling matrix cannot be approximated with its first-order Taylor expansion; also, the initial conditions are set up differently.
For the case of strong magnetic shear, a simple method is identified for preparing a two-mode wave such that it transforms into a single-mode wave upon entering high-density plasma.
The theory can be used for reduced modeling of wave-power input in fusion plasmas.
In particular, applications are envisioned in stellarator research, where the mutual conversion of two electromagnetic modes near the plasma edge is a known issue.
Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the ‘parasitic instabilities’ that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.
Current flow instability and nonlinear structures in dissipative two-fluid plasmas
The current flow in two-fluid plasma is inherently unstable if plasma components (e.g., electrons
and ions) are in different collisionality regimes. A typical example is a partially magnetized $\small {\bf E}\times{\bf B}$
plasma discharge supported by the energy released from the dissipation of the current in the direction
of the applied electric field (perpendicular to the magnetic field). Ions are not magnetized so
they respond to the fluctuations of the electric field ballistically on the inertial time scale. In contrast,
the electron current in the direction of the applied electric field is dissipatively supported
either by classical collisions or anomalous processes. The instability occurs due to a positive feedback
between the electron and ion current coupled by the quasi-neutrality condition. The theory of
this instability is further developed taking into account the electron inertia, finite Larmor radius and
nonlinear effects. It is shown that this instability results in highly nonlinear quasi-coherent structures
resembling breathing mode oscillations in Hall thrusters.
The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is generalized to relativistic plasmas in curved spacetime.
The connections between plasma elements, which are established by a covariant connection equation, display a particularly complex structure in curved spacetime.
Nevertheless, it is shown that these connections can be interpreted in terms of magnetic field lines alone by adopting a 3 + 1 foliation of spacetime.
Theory and observation of the onset of nonlinear structures due to eigenmode destabilization by fast ions in tokamaks
Alfvén waves can induce the ejection of fast ions in different forms in tokamaks. In order to develop predictive capabilities to anticipate the nature of fast ion transport, a methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. The proposed method employs numerically calculated eigenstructures and multiple resonance surfaces of a given mode in the presence of energetic ion drag and stochasticity (due to collisions and micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced Alfvén-acoustic eigenmodes are used as examples. Waves measured in experiments are characterized, and compatibility is found between the proposed criterion predictions and the experimental observation or lack of observation of chirping behavior of Alfvénic modes in different tokamaks. It is found that the stochastic diffusion due to micro-turbulence can be the dominant energetic particle detuning mechanism near the resonances in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise. The proposed criterion constitutes a useful predictive tool in assessing whether the nature of the transport for fast ion losses in fusion devices will be dominated by convective or diffusive processes.
Collisionless shocks are ubiquitous in space and astrophysical systems, and the class of
supercritical shocks is of particular importance due to their role in accelerating particles to high
energies. While these shocks have been traditionally studied by spacecraft and remote sensing
observations, laboratory experiments can provide reproducible and multi-dimensional datasets that
provide a complementary understanding of the underlying microphysics. We present experiments
undertaken on the OMEGA and OMEGA EP laser facilities that show the formation and evolution
of high-Mach number collisionless shocks created through the interaction of a laser-driven magnetic
piston and a magnetized ambient plasma. Through time-resolved, 2-D imaging, we observe
large density and magnetic compressions that propagate at super-Alfvenic speeds and that occur
over ion kinetic length scales. The electron density and temperature of the initial ambient plasma
are characterized using optical Thomson scattering. Measurements of the piston laser-plasma are
modeled with 2-D radiation-hydrodynamic simulations, which are used to initialize 2-D particle-incell
simulations of the interaction between the piston and ambient plasmas. The numerical results
show the formation of collisionless shocks, including the separate dynamics of the carbon and
hydrogen ions that constitute the ambient plasma and their effect on the shock structure. The simulations
also show the shock separating from the piston, which we observe in the data at late experimental
times.
The generation of the plasma current resulting from Bremsstrahlung absorption is considered. It is shown that
the electric current is higher than the naive estimates assuming that electrons absorb only the photon momentum
and using the Spitzer conductivity would suggest. The current enhancement is in part because electrons get the
recoil momentum from the Coulomb field of ions during the absorption and in part because the electromagnetic
power is absorbed asymmetrically within the electron velocity distribution space.
The plasmoid instability has revolutionized our understanding of magnetic reconnection in astrophysical
environments. By preventing the formation of highly elongated reconnection layers, it is crucial in enabling the
rapid energy conversion rates that are characteristic of many astrophysical phenomena. Most previous studies have
focused on Sweet–Parker current sheets, which are unattainable in typical astrophysical systems. Here we derive a
general set of scaling laws for the plasmoid instability in resistive and visco-resistive current sheets that evolve
over time. Our method relies on a principle of least time that enables us to determine the properties of the
reconnecting current sheet (aspect ratio and elapsed time) and the plasmoid instability (growth rate, wavenumber,
inner layer width) at the end of the linear phase. After this phase the reconnecting current sheet is disrupted and fast
reconnection can occur. The scaling laws of the plasmoid instability are not simple power laws, and they depend on
the Lundquist number ($S$), the magnetic Prandtl number ($P_m$), the noise of the system ($\psi_0$), the characteristic rate of
current sheet evolution ($1/\tau$), and the thinning process. We also demonstrate that previous scalings are inapplicable
to the vast majority of astrophysical systems. We explore the implications of the new scaling relations in
astrophysical systems such as the solar corona and the interstellar medium. In both of these systems, we show that
our scaling laws yield values for the growth rate, wavenumber, and aspect ratio that are much smaller than the
Sweet–Parker–based scalings.
Physics conditions for robust control of tearing modes in a rotating tokamak plasma
The disruptive collapse of the current sustained equilibrium of a tokamak is perhaps the single most
serious obstacle on the path toward controlled thermonuclear fusion. The current disruption is
generally too fast to be identified early enough and tamed efficiently, and may be associated with a
variety of initial perturbing events. However, a common feature of all disruptive events is that they
proceed through the onset of magnetohydrodynamic instabilities and field reconnection processes
developing magnetic islands, which eventually destroy the magnetic configuration. Therefore the
avoidance and control of magnetic reconnection instabilities is of foremost importance and great
attention is focused on the promising stabilization techniques based on localized rf power absorption
and current drive. Here a short review is proposed of the key aspects of high power rf control
schemes (specifically electron cyclotron heating and current drive) for tearing modes, considering
also some effects of plasma rotation. From first principles physics considerations, new conditions are
presented and discussed to achieve control of the tearing perturbations by means of high power
($P_{EC} \ge R_{ohm}$) in regimes where strong nonlinear instabilities may be driven, such as secondary island
structures, which can blur the detection and limit the control of the instabilities. Here we consider
recent work that has motivated the search for the improvement of some traditional control strategies,
namely the feedback schemes based on strict phase tracking of the propagating magnetic islands.
Effect of electron-to-ion mass ratio on radial electric
field generation in tokamak
Generation of coherent radial electric fields in plasma by drift-wave turbulence driven by plasma inhomogeneities is ab initio studied using gyro-kinetic
particle simulation for conditions of operational tokamaks. In particular, the effect of
the electron-to-ion mass ratio ϵ on the entire evolution of the plasma is considered. It
is found that the electric field can be increased, and the turbulence-induced particle
transport reduced, by making ϵ smaller, in agreement with many existing experimental
observations.
The growth and saturation of magnetic fields due to the Weibel instability (WI) have important
implications for laboratory and astrophysical plasmas, and this has drawn significant interest
recently. Since the WI can generate a large magnetic field from no initial field, the maximum
magnitudes achieved can have significant consequences for a number of applications. Hence, an
understanding of the detailed dynamics driving the nonlinear saturation of the WI is important.
This work considers the nonlinear saturation of the WI when counter-streaming populations of initially
unmagnetized electrons are perturbed by a magnetic field oriented perpendicular to the direction
of streaming. Previous works have found magnetic trapping to be important [Davidson et al.,
Phys. Fluids 15, 317 (1972)] and connected electron skin depth spatial scales to the nonlinear saturation
of the WI [Califano et al., Phys. Rev. E 57, 7048 (1998)]. The results presented in this work
are consistent with these findings for a high-temperature case. However, using a high-order continuum
kinetic simulation tool, this work demonstrates that when the electron populations are colder,
a significant electrostatic potential develops that works with the magnetic field to create potential
wells. The electrostatic field develops due to transverse flows induced by the WI and in some cases
is strengthened by a secondary instability. This field plays a key role in saturation of the WI for
colder populations. The role of the electrostatic potential in Weibel instability saturation has not
been studied in detail previously
A numerical investigation is carried out to understand the equilibrium β-limit in a classical stellarator.
The stepped-pressure equilibrium code [S.R. Hudson et al., Phys. Plasmas, 19 112502, (2012)] is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high β.
Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator.
Despite the fact that relaxation is allowed [J.B. Taylor, Rev. Mod. Phys. 58, 741 (1986)], the former is shown to maintain good flux surfaces up to the equilibrium β-limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms.
The latter, which has no ideal equilibrium β-limit, is shown to develop regions of magnetic islands and chaos at sufficiently high β, thereby providing a ‘non-ideal β-limit’.
Perhaps surprisingly, however, the value of β at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD.
We compare our results to the High-Beta-Stellarator theory of Freidberg [Ideal MHD, 2014, Cambridge University Press] and derive a new prediction for the non-ideal equilibrium β-limit above which chaos emerges.
New method to design stellarator coils without the winding surface
We present a new method using 3D curves to design coils for stellarators. Finding an easy-to-build coils set has been a critical issue for stellarator design for decades. Conventional approaches assume a toroidal “winding” surface. Either a surface current potential on the winding surface is
constructed using a Green’s function; or a discrete set of filamentary coils that lie on the winding surface is employed, with a direct non-linear optimization to determine how the coils “wind” on the surface to provide the required magnetic field and meet the target engineering criteria. We’ll
investigate if the existence of winding surface unnecessarily constrains the optimization and a general representation is presented. Each discrete coil is represented as an arbitrary, closed, one-dimensional curve embedded in three-dimensional space. The target function to be minimized is constructed
with several well-chosen object functions that cover both physical requirements and engineering constraints. And for the first time, the derivatives of the target function are calculated analytically to enable fast optimization algorithms for finding minima. A numerical code, named FOCUS, has
been developed. Illustrations of using the code to design coils for a simple configuration and the W7-X plasma are presented. Numerical experiments show that the code is working efficiently and more attractive coil sets can be obtained by using this method.
Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection
The scaling of plasmoid instability maximum linear growth rate with respect to Lundquist number $S$ in a Sweet-Parker current sheet, $\gamma_{max}\sim S^{1/4}$, indicates that at high $S$, the current sheet will break apart before it approaches the Sweet-Parker width.
Therefore, a proper description for the onset of the plasmoid instability must incorporate the evolving process of the current sheet.
We carry out a series of two-dimensional simulations and develop diagnostics to separate fluctuations from an evolving background.
It is found that the fluctuation amplitude starts to grow only when the linear growth rate is sufficiently large ($\gamma_{max} \tau_A > O(1)$) to overcome convective losses.
The linear growth rate continues to rise until the sizes of plasmoids become comparable to the inner layer width of the tearing mode.
At this point the current sheet is disrupted and the instability enters the early nonlinear regime.
The growth rate suddenly decreases, but the fluctuation amplitude continues to grow until it reaches nonlinear saturation.
We identify important time scales of the instability development, as well as scalings for the linear growth rate, current sheet width, and dominant wavenumber at current sheet disruption.
These scalings depend on not only the Lundquist number, but also the initial noise amplitude.
A phenomenological model that reproduces scalings from simulation results is proposed.
The model incorporates the effect of reconnection outflow, which is crucial for yielding a critical Lundquist number $S_c$ below which disruption does not occur.
The critical Lundquist number $S_c$ is not a constant value but has a weak dependence on the noise amplitude.
The ability to separate large volumes of mixed species based on atomic mass appears desirable
for a variety of emerging applications with high societal impact. One possibility to meet this
objective consists in leveraging mass differential effects in rotating plasmas. Beyond
conventional centrifugation, rotating plasmas offer in principle additional ways to separate
elements based on mass. Single ion orbits show that ion radial mass separation in a uniform
magnetized plasma column can be achieved by applying a tailored electric potential profile
across the column, or by driving a rotating magnetic field within the column. Furthermore,
magnetic pressure and centrifugal effects can be combined in a non-uniform geometry to
separate ions based on mass along the field lines. Practical application of these separation
schemes hinges on the ability to produce the desirable electric and magnetic field configuration
within the plasma column.
Surface currents associated with external kink modes in tokamak plasmas during a major disruption
The surface current on the plasma-vacuum interface during a disruption event involving kink instability can play an important role in driving current into the vacuum vessel. However, there have been disagreements over the nature or even the sign of the surface current in recent theoretical calculations based on idealized step-function background plasma profiles. We revisit such calculations by replacing step-function profiles with more realistic profiles characterized by a strong but finite gradient along the radial direction. It is shown that the resulting surface current is no longer a delta-function current density, but a finite and smooth current density profile with an internal structure, concentrated within the region with a strong plasma pressure gradient. Moreover, this current density profile has peaks of both signs, unlike the delta-function case with a sign opposite to, or the same as the plasma current. We show analytically and numerically that such current density can be separated into two parts, with one of them, called the convective current density, describing the transport of the background plasma density by the displacement, and the other part that remains, called the residual current density. It is argued that consideration of both types of current density is important and can resolve past controversies.
Computational optimization has revolutionized the field of stellarator design. To date, optimizations have focused primarily on optimization of neoclassical confinement and ideal MHD stability, although limited optimization of other parameters has also been performed. The purpose of this paper is to outline a select set of new concepts for stellarator optimization that, when taken as a group, present a significant step forward in the stellarator concept. One of the criticisms that has been leveled at existing methods of design is the complexity of the resultant field coils. Recently, a new coil optimization code—COILOPT++, which uses a spline instead of a Fourier representation of the coils,—was written and included in the STELLOPT suite of codes. The advantage of this method is that it allows the addition of real space constraints on the locations of the coils. The code has been tested by generating coil designs for optimized quasi-axisymmetric stellarator plasma configurations of different aspect ratios. As an initial exercise, a constraint that the windings be vertical was placed on large major radius half of the non-planar coils. Further constraints were also imposed that guaranteed that sector blanket modules could be removed from between the coils, enabling a sector maintenance scheme. Results of this exercise will be presented. New ideas on methods for the optimization of turbulent transport have garnered much attention since these methods have led to design concepts that are calculated to have reduced turbulent heat loss. We have explored possibilities for generating an experimental database to test whether the reduction in transport that is predicted is consistent with experimental observations. To this end, a series of equilibria that can be made in the now latent QUASAR experiment have been identified that will test the predicted transport scalings. Fast particle confinement studies aimed at developing a generalized optimization algorithm are also discussed. A new algorithm developed for the design of the scraper element on W7-X is presented along with ideas for automating the optimization approach.
Toroidal coupling in the kinetic response to edge magnetic perturbations
The magnetic topology of the stochastic edge of a helical reversed-field pinch, with helicity m/n, shows to be deeply influenced by higher harmonics (m ± 1)/n, with the same n, due to toroidal coupling.
As a consequence, by measuring kinetic quantities in a particular $\theta$, $\phi$ location, one can incur in substantial errors or misinterpretations of the kinetic plasma response: only a full 3D coverage of $\theta$, $\phi$ angles can reveal the real topology of the plasma.
This can be a caveat for MP application in tokamaks, because it shows that toroidal and poloidal sidebands, though smaller than the base mode by a factor $\sim \epsilon = a/R$, can have a sizable effect on the kinetic response of the edge plasma, and thus on related issues (for example, ELM stabilization and suppression).
Recent upgrades in H-1 power supplies have enabled the operation of the H-1 experiment at higher
heating powers than previously attainable. A heating power scan in mixed hydrogen/helium plasmas
reveals a change in mode activity with increasing heating power. At low power (<50 kW) modes
with beta-induced Alfvén eigenmode frequency scaling are observed. At higher power modes
consistent with an analysis of nonconventional global Alfvén eigenmodes (GAEs) are observed, the
subject of this work. We have computed the mode continuum, and identified GAE structures using
the ideal MHD solver CKA and the gyrokinetic code EUTERPE. An analytic model for ICRHheated
minority ions is used to estimate the fast ion temperature from the hydrogen species. Linear
growth rate scans using a local flux surface stability calculation, LGRO, are performed. These studies
demonstrate drive from the radial spatial gradient of circulating particles whose speed is significantly
less than the Alfvén speed, and are resonant with the mode through harmonics of the Fourier
decomposition of the strongly shaped heliac magnetic field. They reveal drive is possible with a small
(n n f 0 < 0.2) hot energetic tail of the hydrogen species, for which Tf > 300 eV. Local linear
growth rate scans are also complemented with global calculations from CKA and EUTERPE. These
qualitatively confirm the findings from the LGRO study, and show that the inclusion of finite Larmor
radius effects can reduce the growth rate by a factor of up to ten, and increases the marginal stability
fast ion temperature by a factor of two. Finally, a study of damping of the global mode with the
thermal plasma is conducted, computing continuum damping , and the damping arising from finite
Larmor radius and parallel electric fields (via resistivity). We find that continuum damping is of order
0.1% for the configuration studied. A similar calculation in the cylindrical plasma model produces a
frequency 35% higher and a damping 30% of the three-dimensional result: this confirms the
importance of strong magnetic shaping to the frequency and damping. The inclusion of resistivity
lifts the damping to g w = -0.189. Such large damping is consistent with experimental
observations that in absence of drive the mode decays rapidly (∼0.1 ms).
Improvement of training set structure in fusion data cleaning using Time-Domain Global Similarity method
Traditional data cleaning identifies dirty data by classifying original data sequences, which is a class-imbalanced problem since the proportion of incorrect data is much less than the proportion of correct ones for most diagnostic systems in Magnetic Confinement Fusion (MCF) devices. When using machine learning algorithms to classify diagnostic data based on class-imbalanced training set, most classifiers are biased towards the major class and show very poor classification rates on the minor class. By transforming the direct classification problem about original data sequences into a classification problem about the physical similarity between data sequences, the class-balanced effect of Time-Domain Global Similarity (TDGS) method on training set structure is investigated in this paper. Meanwhile, the impact of improved training set structure on data cleaning performance of TDGS method is demonstrated with an application example in EAST POlarimetry-INTerferometry (POINT) system.
Adaptive time-stepping Monte Carlo integration of Coulomb collisions
We report an accessible and robust tool for evaluating the effects of Coulomb collisions on a test particle in a plasma that obeys Maxwell–Jüttner statistics. The implementation is based on the Beliaev–Budker collision integral which allows both the test particle and the background plasma to be relativistic. The integration method supports adaptive time stepping, which is shown to greatly improve the computational efficiency. The Monte Carlo method is implemented for both the three-dimensional particle momentum space and the five-dimensional guiding center phase space.
Detailed description is provided for both the physics and implementation of the operator. The focus is in adaptive integration of stochastic differential equations, which is an overlooked aspect among existing Monte Carlo implementations of Coulomb collision operators. We verify that our operator converges to known analytical results and demonstrate that careless implementation of the adaptive time step can lead to severely erroneous results.
The operator is provided as a self-contained Fortran 95 module and can be included into existing orbit-following tools that trace either the full Larmor motion or the guiding center dynamics. The adaptive time-stepping algorithm is expected to be useful in situations where the collision frequencies vary greatly over the course of a simulation. Examples include the slowing-down of fusion products or other fast ions, and the Dreicer generation of runaway electrons as well as the generation of fast ions or electrons with ion or electron cyclotron resonance heating.
Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High-β Plasma
Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear “interruption” of standing and
traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure
anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave
amplitudes δB⊥=B0 ≳ β−1=2 (where β is the ratio of thermal to magnetic pressure). We use highly elongated
domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves
above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics
are strongly affected by the excitation of oblique firehose modes, which transition into long-lived parallel
fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more
slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our
results demonstrate that collisionless plasmas cannot support linearly polarized Alfvén waves above
δB⊥=B0 ∼ β−1=2. They also provide a vivid illustration of two key aspects of low-collisionality plasma
dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high β, and
(ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into
thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.
On non-local energy transfer via zonal flow in the Dimits shift
The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states.
This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an ${\bf E}\times{\bf B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius.
The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions.
The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased.
This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.
Discontinuous Galerkin algorithms for fully kinetic plasmas
We present a new algorithm for the discretization of the non-relativistic Vlasov–Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge–Kutta method. Since the Vlasov equation in the Vlasov–Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.
Heavy impurity confinement in hybrid operation scenario plasmas with a rotating 1/1 continuous mode
In future tokamaks like ITER with tungsten walls, it is imperative to control tungsten accumulation in the core of operational plasmas, especially since tungsten accumulation can lead to radiative collapse and disruption. We investigate the behavior of tungsten trace impurities in a JET-like hybrid scenario with both axisymmetric and saturated 1/1 ideal helical core in the presence of strong plasma rotation. For this purpose, we obtain the equilibria from VMEC and use VENUS-LEVIS, a guiding-center orbit-following code, to follow heavy impurity particles. In this work, VENUS-LEVIS has been modified to account for strong plasma flows with associated neoclassical effects arising from such flows. We find that the combination of helical core and plasma rotation augments the standard neoclassical inward pinch compared to axisymmetry, and leads to a strong inward pinch of impurities towards the magnetic axis despite the strong outward diffusion provided by the centrifugal force, as frequently observed in experiments.
Momentum transport and nonlocality in heat-flux-driven magnetic reconnection in high energy density plasmas
Recent theory has demonstrated a novel physics regime for magnetic reconnection in high-energy-density plasmas where the magnetic field is advected by heat flux via the Nernst effect. Here we elucidate the physics of the electron dissipation layer in this regime. Through fully kinetic simulation and a generalized Ohm's law derived from first principles, we show that momentum transport due to a nonlocal effect, the heat-flux-viscosity, provides the dissipation mechanism for magnetic reconnection. Scaling analysis, and simulations show that the reconnection process comprises a magnetic field compression stage and quasisteady reconnection stage, and the characteristic width of the current sheet in this regime is several electron mean-free paths. These results show the important interplay between nonlocal transport effects and generation of anisotropic components to the distribution function.
Metriplectic Integrators for
the Landau Collision Operator
We present a novel framework for addressing the nonlinear Landau collision
integral in terms of finite element and other subspace projection methods. We
employ the underlying metriplectic structure of the Landau collision integral and,
using a finite element discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system.
Temporal discretization is accomplished using the concept of discrete gradients. The
conservation of energy, momentum, and particle densities, as well as the production
of entropy is demonstrated algebraically for the fully discrete system. Due to the
generality of our approach, the conservation properties and the monotonic behaviour
of entropy are guaranteed for finite element discretizations in general, independently
of the mesh configuration.
Comparison of JET AVDE disruption data with M3D simulations and implications for ITER
Nonlinear 3D MHD asymmetric vertical displacement disruptions simulations have been performed using JET equilibrium reconstruction initial data. Several experimentally measured quantities are compared with the simulation. These include vertical displacement, halo current, toroidal current asymmetry, and toroidal rotation. The experimental data and the simulations are in reasonable agreement. Also compared was the correlation of the toroidal variation of the toroidal current and the vertical displacement. The Noll relation between asymmetric wall force and vertical current moment is verified in the simulations. Also verified is toroidal flux asymmetry. Although in many ways JET is a good predictor of ITER disruption behavior, JET and ITER can be in different parameter regimes, and extrapolating from JET data overestimates the ITER wall force.
Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles
In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions, and analyzed mathematically by classifying the gradient-supporting irrational numbers into subsets. Applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.
Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations
A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at q≈1, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C1 code.
In these simulations, the most important mechanism responsible for the flux pumping is that a saturated (m=1,n=1) quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect.
It is shown that sawtoothing is prevented in the simulations if β is sufficiently high to provide the necessary drive for the (m=1,n=1) instability that generates the dynamo loop voltage.
The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.
In magnetized toroidal plasmas, neoclassical effects and turbulent drift waves can induce the geodesic acoustic mode (GAM).
We simulate the GAM using the gyro-kinetic code GTS for typical tokamak parameters and investigate its properties, especially its frequency continuum, evolution of its radial wave number, and propagation characteristics.
The simulation results are compared with those of the relevant theory and experiment. It is found that the radial phase velocity of the GAM is roughly proportional to the ion thermal speed.
Two-Dimensional Turbulence Cross-Correlation Functions in the Edge of NSTX
The 2D radial vs. poloidal cross-correlation functions of edge plasma turbulence were measured
near the outer midplane using a gas puff imaging (GPI) diagnostic on NSTX. These correlation
functions were evaluated at radii r = 0 cm, $\pm$ 3 cm, and $\pm$ 6 cm from the separatrix and poloidal
locations p = 0 cm and $\pm$ 7.5 cm from the GPI poloidal center line for 20 different shots. The ellipticity
$\epsilon$ and tilt angle $\varphi$ of the positive cross-correlation regions and the minimum negative crosscorrelation
“cmin” and total negative over positive values “neg/pos” were evaluated for each of
these cases. The average results over this dataset were $\epsilon = \pm$ 2.2 $\pm$ 0.9, $\varphi = \pm$ 87 $\pm$ 34
(i.e., poloidally oriented), cmin = 0.30 $\pm$ 0.15, and neg/pos = 0.25 $\pm$ 0.24.
Thus, there was a significant variation in these correlation results within this database, with dependences on the location within the image,
the magnetic geometry, and the plasma parameters. Possible causes for this variation are discussed,
including the misalignment of the GPI view with the local B field line, the magnetic shear of field
lines at the edge, the poloidal flow shear of the turbulence, blob-hole correlations, and the neutral
density ’shadowing’ effect in GPI.
Beam cleaning of an incoherent laser via plasma Raman amplification
We show that backward Raman amplification in plasma can efficiently compress a temporally
incoherent pump laser into an intense coherent amplified seed pulse, provided that the correlation
time of the pump is longer than the inverse plasma frequency. An analytical theory for Raman
amplification using pump beams with different correlation functions is developed and compared to
numerical calculations and particle-in-cell simulations. Since incoherence on scales shorter than the
instability growth time suppresses spontaneous noise amplification, we point out a broad regime
where quasi-coherent sources may be used as efficient low-noise Raman amplification pumps. As
the amplified seed is coherent, Raman amplification additionally provides a beam-cleaning mechanism
for removing incoherence. At near-infrared wavelengths, finite coherence times as short as
50 fs allow amplification with only minor losses in efficiency.
Validation of the model for ELM suppression with 3D magnetic fields using low torque ITER baseline scenario discharges in DIII-D
Experiments have been executed in the DIII-D tokamak to extend suppression of Edge Localized
Modes (ELMs) with Resonant Magnetic Perturbations (RMPs) to ITER-relevant levels of beam torque.
The results support the hypothesis for RMP ELM suppression based on transition from an
ideal screened response to a tearing response at a resonant surface that prevents expansion of the
pedestal to an unstable width [Snyder et al., Nucl. Fusion 51, 103016 (2011) and Wade et al., Nucl.
Fusion 55, 023002 (2015)]. In ITER baseline plasmas with I/aB ¼ 1.4 and pedestal 0.15,
ELMs are readily suppressed with co-Ip neutral beam injection. However, reducing the beam torque
from 5 Nm to 3.5 Nm results in loss of ELM suppression and a shift in the zero-crossing of the
electron perpendicular rotation x?e 0 deeper into the plasma. The change in radius of x?e 0 is
due primarily to changes to the electron diamagnetic rotation frequency x
e . Linear plasma response
modeling with the resistive MHD code M3D-c1 indicates that the tearing response location tracks
the inward shift in x?e 0. At pedestal 1, ELM suppression is also lost when the beam torque
is reduced, but the x?e change is dominated by collapse of the toroidal rotation vT. The hypothesis
predicts that it should be possible to obtain ELM suppression at reduced beam torque by also reducing
the height and width of the x
e profile. This prediction has been confirmed experimentally with
RMP ELM suppression at 0 Nm of beam torque and plasma normalized pressure bN 0.7. This
opens the possibility of accessing ELM suppression in low torque ITER baseline plasmas by establishing
suppression at low beta and then increasing beta while relying on the strong RMP-island
coupling to maintain suppression.
TGE: Machine Learning Based Task Graph Embedding for Large-Scale Topology Mapping
Task mapping is an important problem in parallel and distributed computing. The goal in task mapping is to find an optimal layout of the processes of an application (or a task) onto a given network topology. We target this problem in the context of staging applications. A staging application consists of two or more parallel applications (also referred to as staging tasks) which run concurrently and exchange data over the course of computation. Task mapping becomes a more challenging problem in staging applications, because not only data is exchanged between the staging tasks, but also the processes of a staging task may exchange data with each other. We propose a novel method, called Task Graph Embedding (TGE), that harnesses the observable graph structures of parallel applications and network topologies. TGE employs a machine learning based algorithm to find the best representation of a graph, called an embedding, onto a space in which the task-to-processor mapping problem can be solved. We evaluate and demonstrate the effectiveness of TGE experimentally with the communication patterns extracted from runs of XGC, a large-scale fusion simulation code, on Titan.
The Dehydration of Water Worlds via Atmospheric Losses
We present a three-species multi-fluid magnetohydrodynamic model ($H^+$, $H_2O^+$, and $e^−$), endowed with the requisite atmospheric chemistry, that is capable of accurately quantifying the magnitude of water ion losses from exoplanets.
We apply this model to a water world with Earth-like parameters orbiting a Sun-like star for three cases: (i) current normal solar wind conditions, (ii) ancient normal solar wind conditions, and (iii) one extreme "Carrington-type" space weather event.
We demonstrate that the ion escape rate for (ii), with a value of $6.0 × 10^{26} s^{−1}$, is about an order of magnitude higher than the corresponding value of $6.7 × 10^{25} s^{−1}$ for (i).
Studies of ion losses induced by space weather events, where the ion escape rates can reach $~10^{28} s^{−1}$, are crucial for understanding how an active, early solar-type star (e.g., with frequent coronal mass ejections) could have accelerated the depletion of the exoplanet's atmosphere.
We briefly explore the ramifications arising from the loss of water ions, especially for planets orbiting M-dwarfs where such effects are likely to be significant.
Space Weather Storm Responses at Mars: Lessons from A Weakly Magnetized Terrestrial Planet
Much can be learned from terrestrial planets that appear to have had the potential to be habitable, but failed to realize that potential. Mars shows evidence of a once hospitable surface environment. The reasons for its current state, and in particular its thin atmosphere and dry surface, are of great interest for what they can tell us about habitable zone planet outcomes. A main goal of the MAVEN mission is to observe Mars’ atmosphere responses to solar and space weather influences, and in particular atmosphere escape related to space weather ‘storms’ caused by interplanetary coronal mass ejections (ICMEs). Numerical experiments with a data-validated MHD model suggest how the effects of an observed moderately strong ICME compare to what happens during a more extreme event. The results suggest the kinds of solar and space weather conditions that can have evolutionary importance at a planet like Mars.
Electron heating and energy inventory during asymmetric reconnection in a laboratory plasma
Electron heating and the energy inventory during asymmetric reconnection are studied in
the laboratory plasma with a density ratio of about 8 across the current sheet. Features of asymmetric
reconnection such as the large density gradients near the low-density side separatrices, asymmetric in-plane
electric field, and bipolar out-of-plane magnetic field are observed. Unlike the symmetric case, electrons
are also heated near the low-density side separatrices. The measured parallel electric field may explain
the observed electron heating. Although large fluctuations driven by lower hybrid drift instabilities are
also observed near the low-density side separatrices, laboratory measurements and numerical simulations
reported here suggest that they do not play a major role in electron energization. The average electron
temperature increase in the exhaust region is proportional to the incoming magnetic energy per an
electron/ion pair but exceeds scalings of the previous space observations. This discrepancy is explained
by differences in the boundary condition and system size. The profile of electron energy gain from the
electric field shows that there is additional electron energy gain associated with the electron diamagnetic
current besides a large energy gain near the X line. This additional energy gain increases electron enthalpy,
not the electron temperature. Finally, a quantitative analysis of the energy inventory during asymmetric
reconnection is conducted. Unlike the symmetric case where the ion energy gain is about twice
more than the electron energy gain, electrons and ions obtain a similar amount of energy during
asymmetric reconnection.
A compact solar UV burst triggered in a magnetic field with a fan-spine topology
Solar UV bursts are small-scale features that exhibit intermittent brightenings that are thought to be due to magnetic reconnection. They are observed abundantly in the chromosphere and transition region, in particular in active regions. We investigate in detail a UV burst related to a magnetic feature that is advected by the moat flow from a sunspot towards a pore. The moving feature is parasitic in that its magnetic polarity is opposite to that of the spot and the pore. We use UV spectroscopic and slit-jaw observations from the IRIS to identify and study chromospheric and transition region spectral signatures of said UV burst. To investigate the magnetic topology surrounding the UV burst, we use a 2 hrs long time sequence of simultaneous line-of-sight magnetograms from the HMI and perform a data-driven, 3D magnetic field extrapolations by means of a magnetofrictional relaxation technique. We can connect UV burst signatures to the overlying EUV coronal loops observed by the AIA. The UV burst shows a variety of extremely broad line profiles indicating plasma flows in excess of ±200 km s−1 at times. The whole structure is divided into two spatially distinct zones of predominantly up- and downflows. The magnetic field extrapolations show the presence of a persistent fan-spine magnetic topology at the UV burst. The associated 3D magnetic null point exists at a height of about 500 km above the photosphere and evolves co-spatially with the observed UV burst. The EUV emission at the footpoints of coronal loops is correlated with the evolution of the underlying UV burst. The magnetic field around the null point is sheared by photospheric motions, triggering magnetic reconnection that ultimately powers the observed UV burst and energizes the overlying coronal loops. The location of the null point suggests that the burst is triggered low in the solar chromosphere.
Investigation of the Paschen curve for helium in the 100–1000 kV range
The left branch of the Paschen curve for helium gas is studied both experimentally and by means of particle-in-cell/Monte Carlo collision (PIC/MCC) simulations.
The physical model incorporates electron, ion, and fast atom species whose energy-dependent anisotropic scattering on background
neutrals, as well as backscattering at the electrodes, is properly accounted for.
For the range of
breakdown voltage $15 kV \le V_{br} \le 130 kV$, a good agreement is observed between simulations and
available experimental results for the discharge gap $d=1.4 cm$.
The PIC/MCC model is used to
predict the Paschen curve at higher voltages up to 1 MV, based on the availability of input atomic
data. We find that the pd similarity scaling does hold and that above 300 kV, the value of pd at
breakdown begins to increase with increasing voltage. To achieve good agreement between PIC/
MCC predictions and experimental data for the Paschen curve, it is essential to account for impact
ionization by fast atoms (produced in charge exchange) and ions and for anisotropic scattering of
all species on background atoms. With the increase of the applied voltage, energetic fast atoms progressively
dominate in the overall ionization rate. The model makes this clear by predicting that
breakdown would occur even without electron- and ion-induced ionization of the background gas,
due to ionization by fast atoms backscattered at the cathode, and their high production rate in
charge exchange collisions. Multiple fast neutrals per ion are produced when the free path is small
compared to the electrode gap.
Advances in the steady-state hybrid regime in DIII-D – a fully non-inductive, ELM-suppressed scenario for ITER
The hybrid regime with beta, collisionality, safety factor and plasma shape relevant to the ITER steady-state mission has been successfully integrated with ELM suppression by applying an odd parity $n=3$ resonant magnetic perturbation (RMP).
Fully non-inductive hybrids in the DIII-D tokamak with high beta ( $<\beta>≤ 2.8$%) and high confinement ($H_{98y2} ≤ 1.4$) in the ITER similar shape have achieved zero surface loop voltage for up to two current relaxation times using efficient central current drive from ECCD and NBCD. The $n=3$ RMP causes surprisingly little increase in thermal transport during ELM suppression. Poloidal magnetic flux pumping in hybrid plasmas maintains $q$ above 1 without loss of current drive efficiency, except that experiments show that extremely peaked ECCD profiles can create sawteeth.
During ECCD, Alfvén eigenmode (AE) activity is replaced by a more benign fishbone-like mode, reducing anomalous beam ion diffusion by a factor of 2. While the
electron and ion thermal diffusivities substantially increase with higher ECCD power, the loss of confinement can be offset by the decreased fast ion transport resulting from AE suppression.
Extrapolations from DIII-D along a dimensionless parameter scaling path as well as those using self-consistent theory-based modeling show that these ELM-suppressed, fully non-inductive hybrids can achieve the $Q_{fus} = 5$ ITER steady-state mission.
Pedestal and edge electrostatic turbulence characteristics from an XGC1 gyrokinetic simulation
Understanding the multi-scale neoclassical and turbulence physics in the edge region (pedestal + scrape-off layer) is required in order to reliably predict performance in future fusion devices.
We explore turbulent characteristics in the edge region from a multi-scale neoclassical and turbulent XGC1 gyrokinetic simulation in a DIII-D like tokamak geometry, here excluding neutrals and collisions.
For an H-mode type plasma with steep pedestal, it is found that the electron density fluctuations increase towards the separatrix, and stay high well into the SOL, reaching a maximum value of $\delta n_e/\bar n_e \sim 0.18$.
Blobs are observed, born around the magnetic separatrix surface and propagate radially outward with velocities generally less than 1 km/s.
Strong poloidal motion of the blobs is also present, near 20 km/s, consistent with ${\bf E}\times{\bf B}$ rotation.
The electron density fluctuations show a negative skewness in the closed field line pedestal region, consistent with the presence of “holes”, followed by a transition to strong positive skewness across the separatrix and into the SOL. These simulations indicate that not only neoclassical phenomena, but also turbulence, including the blob-generation mechanism, can remain important in the steep H-mode pedestal and SOL. Qualitative comparisons will be made to experimental observations.
Numerical study on wave-induced beam ion prompt losses in DIII-D tokamak
A numerical study is performed on the coherent beam ion prompt losses driven by Alfven
eigenmodes (AEs) in DIII-D plasmas using realistic parameters and beam ion deposition profiles.
The synthetic signal of a fast-ion loss detector (FILD) is calculated for a single AE mode. The first
harmonic of the calculated FILD signal is linearly proportional to the AE amplitude with the same
AE frequency in agreement with the experimental measurement. The calculated second harmonic
is proportional to the square of the first harmonic for typical AE amplitudes. The coefficient of quadratic
scaling is found to be sensitive to the AE mode width. The second part of this work considers
the AE drive due to coherent prompt loss. It is shown that the loss-induced mode drive is much
smaller than the previous estimate and can be ignored for mode stability.
The build-up of energetic electrons triggering electron cyclotron emission bursts due to a magnetohydrodynamic mode at the edge of tokamaks
Intense bursts of electron cyclotron emission (ECE) triggered by magnetohydrodynamic (MHD) instabilities such as edge localized modes have been observed on many tokamaks.
On the DIII-D tokamak, it is found that a MHD mode is necessary in order to trigger the ECE bursts in the low collisionality regime at the plasma edge.
ORBIT-code simulations have shown that energetic electrons build up due to an interaction between barely trapped electrons with a MHD mode (f = 50 kHz for the current case).
The energetic tail of the electron distribution function develops a bump within several microseconds for this collisionless case.
This behavior depends on the competition between the perturbing MHD mode and slowing down and pitch angle scattering due to collisions.
For typical DIII-D parameters, the calculated ECE radiation transport predicted by ORBIT is in excellent agreement with ECE measurements, clarifying the electron dynamics of the ECE bursts for the first time.
Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian
Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.
Astrophysical particle acceleration mechanisms in colliding magnetized laser-produced plasmas
Significant particle energization is observed to occur in numerous astrophysical environments, and in the standard models this acceleration occurs alongside energy conversion processes including collisionless shocks or magnetic reconnection. Recent platforms for laboratory experiments using magnetized laser-produced plasmas have opened opportunities to study these particle acceleration processes in the laboratory. Through fully kinetic particle-in-cell simulations, we investigate acceleration mechanisms in experiments with colliding magnetized laser-produced plasmas, with geometry and parameters matched to recent high-Mach number reconnection experiments with externally-controlled magnetic fields. 2-D simulations demonstrate significant particle acceleration with three phases of energization: first a “direct” Fermi acceleration driven by approaching magnetized plumes; second, x-line acceleration during magnetic reconnection of anti-parallel fields; and finally an additional Fermi energization of particles trapped in contracting and relaxing magnetic islands produced by reconnection. The relative effectiveness of these mechanisms depends on plasma and magnetic field parameters of the experiments.
Hybrid simulation of fishbone instabilities in the EAST tokamak
Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the Experimental Advanced Superconducting Tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfvén eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.
Equilibrium Potential Well due to Finite Larmor Radius Effects at the Tokamak Edge
We present a novel mechanism for producing an equilibrium potential well near the edge of a tokamak.
Briefly, because of the difference in gyroradii between electrons and ions, an equilibrium electrostatic potential is generated in the presence of spatial inhomogeneity of the background plasma, which, in turn, produces a well associated with the radial electric field, Er, as observed at the edge of many tokamak experiments.
We will show that this theoretically predicted Er field, which can be regarded as producing a long radial wavelength zonal flow, agrees well with recent experimental measurements. The relationship between the equilibrium configuration used in this study and that of the Woltjer-Taylor state will be discussed.
Understanding and predicting profile structure and parametric scaling of intrinsic rotation
This paper reports on a recent advance in developing physical understanding and a first-principles based model for predicting intrinsic rotation profiles in magnetic fusion experiments.
It is shown for the first time that turbulent fluctuation-driven residual stress (a non-diffusive component of momentum flux) along with diffusive momentum flux can account for both the shape and magnitude of the observed intrinsic toroidal rotation profile.
Both the turbulence intensity gradient and zonal flow ${\bf E}\times{\bf B}$ shear are identified as major contributors to the generation of the $k_\parallel$-asymmetry needed for the residual stress generation.
The model predictions of core rotation based on global gyrokinetic simulations agree well with the experimental measurements of main ion toroidal
rotation for a set of DIII-D ECH discharges.
The validated model is further used to investigate the characteristic dependence of residual stress and intrinsic rotation profile structure on the multidimensional parametric space covering the turbulence type, q-profile structure, and up-down
asymmetry in magnetic geometry with the goal of developing the physics understanding needed for
rotation profile control and optimization. It is shown that in the flat-q profile regime, intrinsic rotations
driven by ITG and TEM turbulence are in the opposite direction (i.e., intrinsic rotation
reverses). The predictive model also produces reversed intrinsic rotation for plasmas with weak
and normal shear q-profiles.
Gyrokinetic particle simulations of the effects of compressional magnetic perturbations on drift-Alfvénic instabilities in tokamaks
The compressional component of magnetic perturbation $\delta B_\parallel$ can play an important role in drift- Alfvenic instabilities in tokamaks, especially as the plasma $\beta$ increases ($\beta$ is the ratio of kinetic pressure to magnetic pressure).
In this work, we have formulated a gyrokinetic particle simulation model incorporating $\delta B_\parallel$, and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry.
Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when $\delta B_\parallel$ is neglected for $\beta_e=0.02$, and that $\delta B_\parallel$ has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode.
The KBM growth rate decreases about 15% when equilibrium current is neglected.
Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER
The XGC1 edge gyrokinetic code is used for a high fidelity prediction for the width of the heat-flux to divertor plates in attached plasma condition.
The simulation results are validated against the empirical scaling $\lambda_q \propto B_P^{−\gamma}$ obtained from present tokamak devices, where $\lambda_q$ is the divertor heat-flux width mapped to the outboard midplane and $\lambda_q=1.19$ as defined by
T. Eich et al. [Nucl. Fusion 53 (2013) 093031],
and $B_P$ is the magnitude of the poloidal magnetic field at outboard midplane separatrix surface.
This empirical scaling predicts $\lambda_q ≤ 1mm$ when extrapolated to ITER, which would require operation with very high separatrix densities ($n_{sep}/n_{Greenwald}>0.6$) (Kukushkin et al. [2013 J. Nucl. Mater. 438 S203]) in the Q=10 scenario to achieve semi-detached plasma operation and high radiative fractions leading to acceptable divertor power fluxes.
XGC1 predicts, however, that $\lambda_q$ for ITER is over 5mm, suggesting that operation in the ITER Q=10 scenario with acceptable divertor power loads could be obtained over a wider range of plasma separatrix densities and radiative fractions.
The physics reason behind this difference is, according to the XGC1 results, that while the ion magnetic drift contribution to the divertor heat-flux width is wider in the present tokamaks, the turbulent electron contribution is wider in ITER.
A high current C-Mod discharge is found to be in a mixed regime: While the heat-flux width by the ion neoclassical magnetic drift is still wider than the turbulent electron heat-flux width, the heat-flux magnitude is dominated by the narrower electron heat-flux.
Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power
Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in
the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method
to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling
process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data
and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably well–understood in the linear regime, nonlinear physics arising from high input power has not been previously
quantified. To tackle this problem, we have performed one- and two-dimensional fully kinetic particle-in-cell
simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that
the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude shortscale
oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior
to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant
scattering into an EBW and a lower-hybrid wave. We calculate the instability rate analytically and find this
basic theory to be in reasonable agreement with our simulation results.
Simulations of anti-parallel reconnection using a nonlocal heat flux closure
The integration of kinetic effects in fluid models is important for global simulations of the Earth’s
magnetosphere. In particular, it has been shown that ion kinetics play a crucial role in the dynamics
of large reconnecting systems, and that higher-order fluid moment models can account for some of
these effects. Here, we use a ten-moment model for electrons and ions, which includes the off diagonal
elements of the pressure tensor that are important for magnetic reconnection. Kinetic effects
are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in
the fluid framework. The closure is tested using the island coalescence problem, which is sensitive
to ion dynamics. We demonstrate that the nonlocal closure is able to self-consistently reproduce
the structure of the ion diffusion region, pressure tensor, and ion velocity without the need for finetuning
of relaxation coefficients present in earlier models.
In situ diagnostics for nanomaterial synthesis in carbon arc plasma
Developments in the recent application of in situ diagnostics to improve understanding of nanomaterial synthesis processes in carbon arc plasma are summarized. These diagnostics measure the plasma conditions in the arc core and the precursor species to nanoparticle formation and the presence and sizes of nanoparticles in the synthesis region surrounding the hot arc core. They provide information that could not be obtained by the ex situ diagnostics used in previous studies of nanomaterial synthesis in arc plasma. The following diagnostics are covered: optical emission spectroscopy, planar laser induced fluorescence, laser induced incandescence, fast frame imaging, coherent Rayleigh Brillouin scattering, and the nanomaterial extractor probe. The diagnostic measurements are consistent with a recently developed two-dimensional fluid model of nanomaterial synthesis in the arc plasma.
Evolution of the magnetorotational instability on initially tangled magnetic fields
The initial magnetic field of previous magnetorotational instability (MRI) simulations has always included a significant system-scale component, even if stochastic. However, it is of conceptual and practical interest to assess whether the MRI can grow when the initial field is turbulent. The ubiquitous presence of turbulent or random flows in astrophysical plasmas generically leads to a small-scale dynamo (SSD), which would provide initial seed turbulent velocity and magnetic fields in the plasma that becomes an accretion disc. Can the MRI grow from these more realistic initial conditions? To address this, we supply a standard shearing box with isotropically forced SSD generated magnetic and velocity fields as initial conditions and remove the forcing. We find that if the initially supplied fields are too weak or too incoherent, they decay from the initial turbulent cascade faster than they can grow via the MRI. When the initially supplied fields are sufficient to allow MRI growth and sustenance, the saturated stresses, large-scale fields and power spectra match those of the standard zero net flux MRI simulation with an initial large-scale vertical field.
Modeling of 3D magnetic equilibrium effects
on edge turbulence stability during RMP
ELM suppression in tokamaks
Recent experimental observations have found turbulent fluctuation structures that are
non-axisymmetric in a tokamak with applied 3D fields. In this paper, two fluid resistive
effects are shown to produce changes relevant to turbulent transport in the modeled 3D
magnetohydrodynamic (MHD) equilibrium of tokamak pedestals with these 3D fields applied.
Ideal MHD models are insufficient to reproduce the relevant effects. By calculating the ideal
3D equilibrium using the VMEC code, the geometric shaping parameters that determine linear
turbulence stability, including the normal curvature and local magnetic shear, are shown to be
only weakly modified by applied 3D fields in the DIII-D tokamak. These ideal MHD effects
are therefore not sufficient to explain the observed changes to fluctuations and transport.
Using the M3D-C1 code to model the 3D equilibrium, density is shown to be redistributed on
flux surfaces in the pedestal when resistive two fluid effects are included, while islands are
screened by rotation in this region. The redistribution of density results in density and pressure
gradient scale lengths that vary within pedestal flux surfaces between different helically
localized flux tubes. This would produce different drive terms for trapped electron mode and
kinetic ballooning mode turbulence, the latter of which is expected to be the limiting factor for
pedestal pressure gradients in DIII-D.
Major results from the first plasma
campaign of the Wendelstein 7-X stellarator
After completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015.
Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign.
Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6s, reaching an injected energy of 4MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign.
At power levels of 4MW central electron densities reached $3 \times 10^{19} m^{−3}$, central electron temperatures reached values
of 7keV and ion temperatures reached just above 2 keV.
Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass
absorption, and current drive experiments using electron cyclotron current drive.
As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.
Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields
A brief critique is presented of some different classes of magnetohydrodynamic equilibrium
solutions based on their continuity properties and whether the magnetic field is
integrable or not. A generalized energy functional is introduced that is comprised of alternating
ideal regions, with nested flux surfaces with irrational rotational-transform, and
Taylor-relaxed regions, possibly with magnetic islands and chaos. The equilibrium states
have globally continuous magnetic fields, and may be constructed for arbitrary three dimensional
plasma boundaries and appropriately prescribed pressure and rotational-transform
profiles.
Diagnosing collisionless energy transfer using
field–particle correlations:
gyrokinetic turbulence
Determining the physical mechanisms that extract energy from turbulent fluctuations
in weakly collisional magnetized plasmas is necessary for a more complete
characterization of the behaviour of a variety of space and astrophysical plasmas.
Such a determination is complicated by the complex nature of the turbulence as
well as observational constraints, chiefly that in situ measurements of such plasmas
are typically only available at a single point in space. Recent work has shown that
correlations between electric fields and particle velocity distributions constructed from
single-point measurements produce a velocity-dependent signature of the collisionless
damping mechanism. We extend this work by constructing field–particle correlations
using data sets drawn from single points in strongly driven, turbulent, electromagnetic
gyrokinetic simulations to demonstrate that this technique can identify the collisionless
mechanisms operating in such systems. The velocity-space structure of the correlation
between proton distributions and parallel electric fields agrees with expectations of
resonant mechanisms transferring energy collisionlessly in turbulent systems. This
work motivates the eventual application of field–particle correlations to spacecraft
measurements in the solar wind, with the ultimate goal to determine the physical
mechanisms that dissipate magnetized plasma turbulence.
Centrifugal instability in the regime of fast rotation
Centrifugal instability, which stems from a difference between the azimuthal angular drift velocity
of ions and electrons, is studied in the limit of fast rotation for which ions can rotate up to twice as
fast as electrons. As the angular velocity approaches the so-called Brillouin limit, the growth rate for
the centrifugal instability in a collisionless solid-body rotating plasma increases markedly and is proportional
to the azimuthal mode number. For large wavenumbers, electron inertia effects set in and
lead to a cut-off. Interestingly, conditions for the onset of this instability appear to overlap with the
operating conditions envisioned for plasma mass separation devices.
We identify a single-particle drift resulting from collisional interactions with a background species, in the presence of a collisionality gradient and background net flow.
We analyze this drift in different limits, showing how it reduces to the well known impurity pinch for high-$Z_i$ impurities.
We find that in the low-temperature, singly ionized limit, the magnitude of the drift becomes mass-dependent and energy-dependent.
By solving for the resulting diffusion-advection motion, we propose a mass-separation scheme that takes advantage of this drift, and analyze the separative capability as a function of collisionally dissipated energy.
Generation and Evolution of High-Mach-Number Laser-Driven Magnetized Collisionless Shocks in the Laboratory
We present the first laboratory generation of high-Mach-number magnetized collisionless shocks created through the interaction of an expanding laser-driven plasma with a magnetized ambient plasma.
Time-resolved, two-dimensional imaging of plasma density and magnetic fields shows the formation and evolution of a supercritical shock propagating at magnetosonic Mach number $M_{ms}≈12$.
Particle-in-cell simulations constrained by experimental data further detail the shock formation and separate dynamics of the multi-ion-species ambient plasma.
The results show that the shocks form on time scales as fast as one gyroperiod, aided by the efficient coupling of energy, and the generation of a magnetic barrier between the piston and ambient ions.
The development of this experimental platform complements present remote sensing and spacecraft observations, and opens the way for controlled laboratory investigations of high-Mach number collisionless shocks, including the mechanisms and efficiency of particle acceleration.
An often-neglected portion of the radial $\boldsymbol{E}\times \boldsymbol{B}$ drift is shown to drive an outward flux of co-current momentum when free energy is transferred from the electrostatic potential to ion parallel flows. This symmetry breaking is fully nonlinear, not quasilinear, necessitated simply by free-energy balance in parameter regimes for which significant energy is dissipated via ion parallel flows. The resulting rotation peaking is counter-current and has a scaling and order of magnitude that are comparable with experimental observations. The residual stress becomes inactive when frequencies are much higher than the ion transit frequency, which may explain the observed relation of density peaking and counter-current rotation peaking in the core.
Laser Pulse Sharpening with Electromagnetically Induced Transparency in Plasma
We propose a laser-controlled plasma shutter technique to generate sharp laser pulses using a process analogous to electromagnetically induced transparency in atoms. The shutter is controlled by a laser with moderately strong intensity, which induces a transparency window below the cutoff frequency, and hence enables propagation of a low frequency laser pulse. Numerical simulations demonstrate that it is possible to generate a sharp pulse wavefront (sub-ps) using two broad pulses in high density plasma. The technique can work in a regime that is not accessible by plasma mirrors when the pulse pedestals are stronger than the ionization intensity.
The effects of recycled neutral atoms on tokamak ion temperature gradient (ITG) driven turbulence have been investigated in a steep edge pedestal, magnetic separatrix configuration, with the full-$f$ edge gryokinetic code XGC1. An adiabatic electron model has been used; hence, the impacts of neutral particles and turbulence on the density gradient are not considered, nor are electromagnetic turbulence effects. The neutral atoms enhance the ITG turbulence, first, by increasing the ion temperature gradient in the pedestal via the cooling effects of charge exchange and, second, by a relative reduction in the ${\bf E} \times {\bf B}$ shearing rate.
Suppression of Alfvén Modes on the National Spherical Torus Experiment Upgrade with Outboard Beam Injection
In this Letter we present data from experiments on the National Spherical Torus Experiment Upgrade, where it is shown for the first time that small amounts of high pitch-angle beam ions can strongly suppress the counterpropagating global Alfvén eigenmodes (GAE). GAE have been implicated in the redistribution of fast ions and modification of the electron power balance in previous experiments on NSTX. The ability to predict the stability of Alfvén modes, and developing methods to control them, is important for fusion reactors like the International Tokamak Experimental Reactor, which are heated by a large population of nonthermal, super-Alfvénic ions consisting of fusion generated α’s and beam ions injected for current profile control. We present a qualitative interpretation of these observations using an analytic model of the Doppler-shifted ion-cyclotron resonance drive responsible for GAE instability which has an important dependence on $k_\perp \rho_L$. A quantitative analysis of this data with the hym stability code predicts both the frequencies and instability of the GAE prior to, and suppression of the GAE after the injection of high pitch-angle beam ions.
Ionospheric control of the dawn-dusk asymmetry of the Mars magnetotail current sheet
This study investigates the role of solar EUV intensity at controlling the location of the Mars magnetotail current sheet and the structure of the lobes. Four simulation results are examined from a multifluid magnetohydrodynamic model. The solar wind and interplanetary magnetic field (IMF) conditions are held constant, and the Mars crustal field sources are omitted from the simulation configuration. This isolates the influence of solar EUV. It is found that solar maximum conditions, regardless of season, result in a Venus-like tail configuration with the current sheet shifted to the −Y (dawnside) direction. Solar minimum conditions result in a flipped tail configuration with the current sheet shifted to the +Y (duskside) direction. The lobes follow this pattern, with the current sheet shifting away from the larger lobe with the higher magnetic field magnitude. The physical process responsible for this solar EUV control of the magnetotail is the magnetization of the dayside ionosphere. During solar maximum, the ionosphere is relatively strong and the draped IMF field lines quickly slip past Mars. At solar minimum, the weaker ionosphere allows the draped IMF to move closer to the planet. These lower altitudes of the closest approach of the field line to Mars greatly hinder the day-to-night flow of magnetic flux. This results in a buildup of magnetic flux in the dawnside lobe as the S-shaped topology on that side of the magnetosheath extends farther downtail. The study demonstrates that the Mars dayside ionosphere exerts significant control over the nightside induced magnetosphere of that planet.
Spatiotemporal Evolution of Runaway Electron Momentum Distributions in Tokamaks
Novel spatial, temporal, and energetically resolved measurements of bremsstrahlung hard-x-ray (HXR) emission from runaway electron (RE) populations in tokamaks reveal nonmonotonic RE distribution functions whose properties depend on the interplay of electric field acceleration with collisional and synchrotron damping. Measurements are consistent with theoretical predictions of momentum-space attractors that accumulate runaway electrons. RE distribution functions are measured to shift to a higher energy when the synchrotron force is reduced by decreasing the toroidal magnetic field strength. Increasing the collisional damping by increasing the electron density (at a fixed magnetic and electric field) reduces the energy of the nonmonotonic feature and reduces the HXR growth rate at all energies. Higher-energy HXR growth rates extrapolate to zero at the expected threshold electric field for RE sustainment, while low-energy REs are anomalously lost. The compilation of HXR emission from different sight lines into the plasma yields energy and pitch-angle-resolved RE distributions and demonstrates increasing pitch-angle and radial gradients with energy.
Local energy conservation law for a spatially-discretized Hamiltonian Vlasov-Maxwell system
Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local energy conservation law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local conservation laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
Parametric Thermal and Flow Analysis of ITER Diagnostic Shield Module
As part of the diagnostic port plug assembly, the ITER Diagnostic Shield Module (DSM) is
designed to provide mechanical support and the plasma shielding while allowing access to plasma diagnostics.
Thermal and hydraulic analysis of the DSM was performed using a conjugate heat transfer approach, in which
heat transfer was resolved in both solid and liquid parts, and simultaneously, fluid dynamics analysis was
performed only in the liquid part. ITER Diagnostic First Wall (DFW) and cooling tubing were also included in
the analysis. This allowed direct modeling of the interface between DSM and DFW, and also direct assessment
of the coolant flow distribution between the parts of DSM and DFW to ensure DSM design meets the DFW
cooling requirements. Design of the DSM included voids filled with Boron Carbide pellets, allowing weight
reduction while keeping shielding capability of the DSM. These voids were modeled as a continuous solid with
smeared material properties using analytical relation for thermal conductivity. Results of the analysis lead to
design modifications improving heat transfer efficiency of the DSM. Effect of design modifications on thermal
performance as well as effect of Boron Carbide will be presented.
The response of Mars to the major space weather events called interplanetary coronal mass ejections (ICMEs) is of interest for both general planetary solar wind interaction studies and related speculations on their evolutionary consequences—especially with respect to atmosphere escape. Various particle and field signatures of ICMEs have been observed on Phobos-2, Mars Global Surveyor (MGS), Mars Express (MEX), and now Mars Atmosphere and Volatile EvolutioN (MAVEN). Of these, MAVEN's combined instrumentation and orbit geometry is particularly well suited to characterize both the event drivers and their consequences. However, MAVEN has detected only moderate disturbances at Mars due in large part to the general weakness of the present solar cycle. Nevertheless, the strongest event observed by MAVEN in March 2015 provides an example illustrating how further insights can be gained from available models. Here we first look more closely at what previously run BATS-R-US MHD simulations of the combined MAVEN observations tell us about the March 2015 event consequences. We then use analogous models to infer those same responses, including magnetic field topology changes and ionospheric consequences, to a hypothetical extreme ICME at Mars based on STEREO A measurements in July 2012. The results suggest how greatly enhanced, yet realistic, solar wind pressure, magnetic field, and convection electric field combine to produce strong magnetospheric coupling with important consequences for upper atmosphere and ionosphere energization.
Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic
oscillations
New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-$n$ kink-peeling mode as the additional drive mechanism for the EHO.
The observed minimum edge ${\bf E}\times{\bf B}$ shear required for the EHO decreases linearly with pedestal collisionality $\nu _{\text{e}}^{\ast}$, which is favorable for operating QH-mode in machines with low collisionality and low rotation such as ITER.
In addition, the QH-mode regime in DIII-D has recently been found to bifurcate into a new 'wide-pedestal' state at low torque in double-null shaped plasmas, characterized by increased pedestal height, width and thermal energy confinement (Burrell et al., 2016 Phys. Plasmas 23 056103; Chen et al., 2017 Nucl. Fusion 57 022007). This potentially provides an alternate path for achieving high performance ELM-stable operation at low torque, in addition to the low-torque QH-mode sustained with applied 3D fields.
Multi-branch low-$k$ and intermediate-$k$ turbulences are observed in the 'wide-pedestal'.
New experiments support the hypothesis that the decreased edge ${\bf E}\times{\bf B}$ shear enables destabilization of broadband turbulence, which relaxes edge pressure gradients, improves peeling-ballooning stability and allows a wider and thus higher pedestal. The ability to accurately predict the critical ${\bf E}\times{\bf B}$ shear for EHO and maintain high performance QH-mode at low torque is an essential requirement for projecting QH-mode operation to ITER and future machines.
Modelling of advanced three-ion ICRF heating and fast ion generation scheme for tokamaks and stellarators
Absorption of ion-cyclotron range of frequencies waves at the fundamental resonance is an efficient source of plasma heating and fast ion generation in tokamaks and stellarators. This heating method is planned to be exploited as a fast ion source in the Wendelstein 7-X stellarator. The work presented here assesses the possibility of using the newly developed three-ion species scheme (Kazakov et al., (2015) Nucl. Fusion 55 032001) in tokamak and stellarator plasmas, which could offer the capability of generating more energetic ions than the traditional minority heating scheme with moderate input power. Using the SCENIC code, it is found that fast ions in the MeV range of energy can be produced in JET-like plasmas. The RF-induced particle pinch is seen to strongly impact the fast ion pressure profile in particular. Our results show that in typical high-density W7-X plasmas, the three-ion species scheme generates more energetic ions than the more traditional minority heating scheme, which makes three-ion scenario promising for fast-ion confinement studies in W7-X.
Phase-space dependent critical gradient behavior of fast-ion transport due to Alfvén eigenmodes
Experiments in the DIII-D tokamak show that many overlapping small-amplitude Alfvén
eigenmodes (AEs) cause fast-ion transport to sharply increase above a critical threshold in
beam power, leading to fast-ion density profile resilience and reduced fusion performance. The
threshold is above the AE linear stability limit and varies between diagnostics that are sensitive
to different parts of fast-ion phase-space. Comparison with theoretical analysis using the nova
and orbit codes shows that, for the neutral particle diagnostic, the threshold corresponds
to the onset of stochastic particle orbits due to wave-particle resonances with AEs in the
measured region of phase space. The bulk fast-ion distribution and instability behavior was
manipulated through variations in beam deposition geometry, and no significant differences
in the onset threshold outside of measurement uncertainties were found, in agreement with
the theoretical stochastic threshold analysis. Simulations using the ‘kick model’ produce
beam ion density gradients consistent with the empirically measured radial critical gradient
and highlight the importance of including the energy and pitch dependence of the fast-ion
distribution function in critical gradient models. The addition of electron cyclotron heating
changes the types of AEs present in the experiment, comparatively increasing the measured
fast-ion density and radial gradient. These studies provide the basis for understanding how
to avoid AE transport that can undesirably redistribute current and cause fast-ion losses, and
the measurements are being used to validate AE-induced transport models that use the critical
gradient paradigm, giving greater confidence when applied to ITER.
Investigation of Neutral Particle Dynamics in Aditya Tokamak Plasma with
DEGAS2 Code
Neutral particle behavior in Aditya tokamak, which has a circular poloidal ring limiter at one particular toroidal location, has been investigated using DEGAS2 code. The code is based on the calculation using Monte Carlo algorithms and is mainly used in tokamaks with divertor configuration.
This code has been successfully implemented in Aditya tokamak with limiter configuration.
The penetration of neutral hydrogen atom is studied with various atomic and molecular contributions and it is found that the maximum contribution comes from the dissociation processes.
For the same, $H_\alpha$ spectrum is also simulated and matched with the experimental one.
The dominant contribution around 64% comes from molecular dissociation processes and neutral particle is generated by those processes have energy of ~2.0 eV. Furthermore, the variation of neutral hydrogen density and $H_\alpha$ emissivity profile are analysed for various edge temperature profiles and found that there is not much changes in $H_\alpha$ emission at the plasma edge with the variation of edge temperature (7–40 eV).
Full-f XGC1 gyrokinetic study of improved ion energy confinement
from impurity stabilization of ITG turbulence
Flux-driven full-$f$ gyrokinetic simulations are performed to study carbon impurity effects on the
ion temperature gradient (ITG) turbulence and ion thermal transport in a toroidal geometry.
Employing the full-$f$ gyrokinetic code XGC1, both main ions and impurities are evolved
self-consistently including turbulence and neoclassical physics. It is found that the carbon impurity
profile self-organizes to form an inwardly peaked density profile, which weakens the ITG instabilities
and reduces the overall fluctuations and ion thermal transport. A stronger reduction appears in
the low frequency components of the fluctuations. The global structure of ${\bf E}\times{\bf B}$ flow also changes,
resulting in the reduction of global avalanche like transport events in the impure plasma. Detailed
properties of impurity transport are also studied, and it is revealed that both the inward neoclassical
pinch and the outward turbulent transport are equally important in the formation of the steady state
impurity profile.
A model of energetic ion effects on pressure driven tearing modes in tokamaks
The effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping in the particle distribution, in an otherwise cylindrical model. The focus is on a configuration that is driven unstable to the $m/n = 2/1$ mode by increasing pressure, where $m$ is the poloidal mode number and $n$ is the toroidal. The particles and pressure can affect the mode both in the core region where there can be low and reversed shear and outside the resonant surface in significant positive shear. The results show that the energetic ions damp and stabilize the mode when orbiting in significant positive shear, increasing the marginal stability boundary. However, the inner core region contribution with low and reversed shear can drive the mode unstable. This effect of shear on the energetic ion pressure contribution is found to be consistent with the literature. These results explain the observation that the $2/1$ mode was found to be damped and stabilized by energetic ions in $\delta f$-MHD simulations of tokamak experiments with positive shear throughout, while the $2/1$ mode was found to be driven unstable in simulations of experiments with weakly reversed shear in the core. This is also found to be consistent with related experimental observations of the stability of the $2/1$ mode changing significantly with core shear.
Investigation of the plasma shaping effects on the H-mode pedestal structure using coupled kinetic neoclassical/MHD stability simulations
The effects of plasma shaping on the H-mode pedestal structure are investigated. High fidelity kinetic simulations of the neoclassical pedestal dynamics are combined with the magnetohydrodynamic (MHD) stability conditions for triggering edge localized mode (ELM) instabilities that limit the pedestal width and height in H-mode plasmas.
The neoclassical kinetic XGC0 code [Chang et al., Phys. Plasmas 11, 2649 (2004)] is used in carrying out a scan over plasma elongation and triangularity.
As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD ELITE code [Snyder et al., Phys. Plasmas 9, 2037 (2002)].
Simulations with the XGC0 code, which includes coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles.
The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities are discussed.
For the discharges with higher elongation, it is found that the gradients of the plasma profiles in the H-mode pedestal reach semi-steady states.
In these simulations, the pedestal slowly continues to evolve to higher pedestal pressures and bootstrap currents until the peeling-ballooning stability conditions are satisfied.
The discharges with lower elongation do not reach the semi-steady state, and ELM crashes are triggered at earlier times. The plasma elongation is found to have a stronger stabilizing effect than the plasma triangularity. For the discharges with lower elongation and lower triangularity, the ELM frequency is large, and the H-mode pedestal evolves rapidly. It is found that the temperature of neutrals in the scrape-off-layer (SOL) region can affect the dynamics of the H-mode pedestal buildup.
However, the final pedestal profiles are nearly independent of the neutral temperature. The elongation and triangularity affect the pedestal widths of plasma density and electron temperature profiles differently. This provides a new mechanism of controlling the pedestal bootstrap current and the pedestal stability.
Overview of NSTX Upgrade Initial Results and Modeling Highlights
Five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.
As the exascale computing age emerges, data related issues are becoming critical factors that determine how and where we do computing.
Popular approaches used by traditional I/O solution and storage libraries become increasingly bottlenecked due to their assumptions about data movement, re-organization, and storage.
While, new technologies, such as “burst buffers”, can help address some of the short-term performance issues, it is essential that we reexamine the underlying storage and I/O infrastructure to effectively support requirements and challenges at exascale and beyond.
In this paper we present a new approach to the exascale Storage System and I/O (SSIO), which is based on allowing users to inject application knowledge into the system and leverage this knowledge to better manage, store, and access large data volumes so as to minimize the time to scientific insights.
Central to our approach is the distinction between the data, metadata, and the knowledge contained therein, transferred from the user to the system by describing “utility” of data as it ages.
Visualization and Analysis for Near-Real-Time Decision Making in Distributed Workflows
Data driven science is becoming increasingly more common, complex, and is placing tremendous stresses on visualization and analysis frameworks. Data sources producing 10GB per second (and more) are becoming increasingly commonplace in both simulation, sensor and experimental sciences. These data sources, which are often distributed around the world, must be analyzed by teams of scientists that are also distributed. Enabling scientists to view, query and interact with such large volumes of data in near-real-time requires a rich fusion of visualization and analysis techniques, middleware and workflow systems. This paper discusses initial research into visualization and analysis of distributed data workflows that enables scientists to make near-real-time decisions of large volumes of time varying data.
Preparing for in situ processing on upcoming leading-edge supercomputers
High performance computing applications are producing increasingly large amounts of data and placing enormous stress on current capabilities for traditional post-hoc visualization techniques.
Because of the growing compute and I/O imbalance, data reductions, including in situ visualization, are required.
These reduced data are used for analysis and visualization in a variety of different ways.
Many of the visualization and analysis requirements are known a priori, but when they are not, scientists are dependent on the reduced data to accurately represent the simulation in post hoc analysis.
The contributions of this paper is a description of the directions we are pursuing to assist a large scale fusion simulation code succeed on the next generation of supercomputers.
These directions include the role of in situ processing for performing data reductions, as well as the tradeoffs between data size and data integrity within the context of complex operations in a typical scientific workflow.
Kinetic simulations of ladder climbing by electron plasma waves
The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma
parameters, which can be driven by external fields. Depending on whether the wave spectrum is discrete (bounded
plasma) or continuous (boundless plasma), this phenomenon is called ladder climbing (LC) or autoresonant
acceleration of plasmons. It was first proposed by Barth et al. [Phys. Rev. Lett. 115, 075001 (2015)] based on a
linear fluid model. In this paper, LC of electron plasma waves is investigated using fully nonlinear Vlasov-Poisson
simulations of collisionless bounded plasma. It is shown that, in agreement with the basic theory, plasmons survive
substantial transformations of the spectrum and are destroyed only when their wave numbers become large enough
to trigger Landau damping. Since nonlinear effects decrease the damping rate, LC is even more efficient when
practiced on structures like quasiperiodic Bernstein-Greene-Kruskal (BGK) waves rather than on Langmuir
waves per se.
Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code
As an alternative option to kinetic electrons, the gyrokinetic total-$f$ particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons analogous to Chen and Parker [Phys. Plasmas 8, 441 (2001)].
Two representative long wavelength modes, shear Alfvén waves and resistive tearing modes, are verified in cylindrical and toroidal magnetic field geometries.
Nonlinear reconnecting edge localized modes in current-carrying plasmas
Nonlinear edge localized modes in a tokamak are examined using global three-dimensional resistive magnetohydrodynamics simulations. Coherent current-carrying filament (ribbon-like) structures wrapped around the torus are nonlinearly formed due to nonaxisymmetric reconnecting current sheet instabilities, the so-called peeling-like edge localized modes. These fast growing modes saturate by breaking axisymmetric current layers isolated near the plasma edge and go through repetitive relaxation cycles by expelling current radially outward and relaxing it back. The local bi-directional fluctuation-induced electromotive force (emf) from the edge localized modes, the dynamo action, relaxes the axisymmetric current density and forms current holes near the edge. The three-dimensional coherent current-carrying filament structures (sometimes referred to as 3-D plasmoids) observed here should also have strong implications for solar and astrophysical reconnection.
A Monte Carlo model of crustal field influences on solar energetic particle precipitation into the Martian atmosphere
Solar energetic particles (SEPs) can precipitate directly into the atmospheres of weakly magnetized planets, causing increased ionization, heating, and altered neutral chemistry. However, strong localized crustal magnetism at Mars can deflect energetic charged particles and reduce precipitation. In order to quantify these effects, we have developed a model of proton transport and energy deposition in spatially varying magnetic fields, called Atmospheric Scattering of Protons and Energetic Neutrals. We benchmark the model's particle tracing algorithm, collisional physics, and heating rates, comparing against previously published work in the latter two cases. We find that energetic nonrelativistic protons precipitating in proximity to a crustal field anomaly will primarily deposit energy at either their stopping altitude or magnetic reflection altitude. We compared atmospheric ionization in the presence and absence of crustal magnetic fields at 50°S and 182°E during the peak flux of the 29 October 2003 “Halloween storm” SEP event. The presence of crustal magnetic fields reduced total ionization by ~30% but caused ionization to occur over a wider geographic area.
Conductivity tensor for anisotropic plasma in gyrokinetic theory
It has been argued that oblique firehose and mirror instabilities are important candidates for the regulation of temperature anisotropy in solar wind. To quantify the role of anisotropy driven instabilities, global kinetic simulations of the solar wind would be extremely useful. However, due to long time scales involved, such simulations are prohibitively expensive. Gyrokinetic theory and simulations have proven to be valuable tools for the study of low frequency phenomena in nonuniform plasmas; however, there are discrepancies between the anisotropy driven instabilities appearing in the gyrokinetic theory and those of a fully kinetic one. We present a derivation of the conductivity tensor based on the arbitrary frequency gyrokinetics and show that relaxing the condition ω/Ω ≪ 1, where ω is the wave frequency, and the Ω is the cyclotron frequency, eliminates these discrepancies, while preserving the advantages of the gyorkinetic theory for global kinetic simulations.
M3D-C1 simulations of the plasma response to RMPs in NSTX-U single-null and snowflake divertor configurations
n this work, single- and two-fluid resistive magnetohydrodynamic calculations of the plasma response to $n=3$ magnetic perturbations in single-null (SN) and snowflake (SF) divertor configurations are compared with those based on the vacuum approach. The calculations are performed using the code M3D-C1 and are based on simulated NSTX-U plasmas. Significantly different plasma responses were found from these calculations, with the difference between the single- and two-fluid plasma responses being caused mainly by the different screening mechanism intrinsic to each of these models. Although different plasma responses were obtained from these different plasma models, no significant difference between the SN and SF plasma responses were found. However, due to their different equilibrium properties, magnetic perturbations cause the SF configuration to develop additional and longer magnetic lobes in the null-point region than the SN, regardless of the plasma model used. The intersection of these longer and additional lobes with the divertor plates are expected to cause more striations in the particle and heat flux target profiles. In addition, the results indicate that the size of the magnetic lobes, in both single-null and snowflake configurations, are more sensitive to resonant magnetic perturbations than to non-resonant magnetic perturbations.
Energy exchange dynamics across L–H transitions in NSTX
We studied the energy exchange dynamics across the low-to-high-confinement (L–H) transition in NSTX discharges using the gas-puff imaging (GPI) diagnostic. The investigation
focused on the energy exchange between flows and turbulence to help clarify the mechanism of the L–H transition. We applied this study to three types of heating schemes, including a
total of 17 shots from the NSTX 2010 campaign run. Results show that the edge fluctuation characteristics (fluctuation levels, radial and poloidal correlation lengths) measured using
GPI do not vary just prior to the H-mode transition, but change after the transition. Using a velocimetry approach (orthogonal-dynamics programming), velocity fields of a $24 \times 30$ cm
GPI view during the L–H transition were obtained with good spatial (∼1 cm) and temporal
(∼2.5 μs) resolutions. Analysis using these velocity fields shows that the production term is
systematically negative just prior to the L–H transition, indicating a transfer from mean flows
to turbulence, which is inconsistent with the predator–prey paradigm. Moreover, the inferred
absolute value of the production term is two orders of magnitude too small to explain the
observed rapid L–H transition. These discrepancies are further reinforced by consideration
of the ratio between the kinetic energy in the mean flow to the thermal free energy, which is
estimated to be much less than 1, suggesting again that the turbulence depletion mechanism
may not play an important role in the transition to the H-mode. Although the Reynolds work
therefore appears to be too small to directly deplete the turbulent free energy reservoir,
order-of-magnitude analysis shows that the Reynolds stress may still make a non-negligible
contribution to the observed poloidal flows.
Explicit symplectic methods for solving charged particle trajectories
In this paper, we consider the Lorentz force system based on its Hamiltonian formulation. We decompose the Lorentz force system into four subsystems which can be solved with the help of coordinate transformations. Via the coordinate transformations, three kinds of explicit symplectic numerical methods have been established for simulating the motion of charged particles under the time-independent electromagnetic field. We generalize our methods to solve the system with time-dependent external electromagnetic fields, and also the system with a relativistic effect. In numerical experiments, the computing efficiency and accuracy over a long time for the newly derived methods are demonstrated. Also, the long-term simulation for the dynamics of runaway electrons is performed.
Statistical validation of predictive TRANSP simulations of baseline discharges in preparation for extrapolation to JET D–T
This paper presents for the first time a statistical validation of predictive TRANSP simulations
of plasma temperature using two transport models, GLF23 and TGLF, over a database of
80 baseline H-mode discharges in JET-ILW. While the accuracy of the predicted Te with
TRANSP-GLF23 is affected by plasma collisionality, the dependency of predictions on
collisionality is less significant when using TRANSP-TGLF, indicating that the latter model
has a broader applicability across plasma regimes. TRANSP-TGLF also shows a good
matching of predicted Ti with experimental measurements allowing for a more accurate
prediction of the neutron yields. The impact of input data and assumptions prescribed in the
simulations are also investigated in this paper. The statistical validation and the assessment of
uncertainty level in predictive TRANSP simulations for JET-ILW-DD will constitute the basis
for the extrapolation to JET-ILW-DT experiments.
Gas Puff Imaging Diagnostics of Edge Plasma Turbulence in Magnetic
Fusion Devices
Gas puff imaging (GPI) is a diagnostic of plasma turbulence which uses a puff of neutral gas at the plasma edge to increase the local visible light emission for improved space-time resolution of plasma fluctuations. This paper reviews gas puff imaging diagnostics of edge plasma turbulence in magnetic fusion research, with a focus on the instrumentation, diagnostic cross-checks, and interpretation issues. The gas puff imaging hardware, optics, and detectors are described for about 10 GPI systems implemented over the past ∼15 years. Comparison of GPI results with other edge turbulence diagnostic results is described, and many common features are observed. Several issues in the interpretation of GPI measurements are discussed, and potential improvements in hardware and modeling are suggested.
Fast Low-to-High Confinement Mode Bifurcation Dynamics in a Tokamak Edge Plasma Gyrokinetic Simulation
Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a realistic diverted tokamak edge geometry under strong forcing by a high rate of heat deposition. The results show that turbulent Reynolds-stress-driven sheared
${\bf E}\times {\bf B}$ flows act in concert with neoclassical orbit loss to quench turbulent transport and form a transport barrier just inside the last closed magnetic flux surface.
Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas
In this paper, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell's equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change $(\dot W)$ is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmor radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.
Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear
Linear and nonlinear simulations of high-order harmonics $q=1$ energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics $(m=n>1$) driven by energetic trapped particles can be higher than the $m/n=1/1$ component. The high $m=n>1$ modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonics modes, whereas there is only one precessional resonance for the $m/n=1/1$ harmonics. The fluid nonlinearity reduces the saturation level of the $n=1$ component, while it hardly affects those of the high $n$ components, especially the modes with $m=n=3,4$. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. In addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to $m/n=1/1$ component, although the $m/n=1/1$ component has a higher saturation amplitude.
Modeling of lithium granule injection in NSTX with M3D-C1
In this paper we present initial simulations of pedestal control by Lithium Granule Injection (LGI) in NSTX.
A model for small granule ablation has been implemented in the M3D-C1 code [Comp. Sci. & Discovery 5, 014002 (2012)], allowing the simulation of realistic Lithium granule injections. 2D simulations in NSTX L-mode and H-mode plasmas are done and the effect of granule size, injection angle and velocity on the pedestal gradient increase are studied.
For H-mode cases, the amplitude of the local pressure perturbation caused by the granules is highly dependent on the solid granule size.
In our simulations, reducing the granule injection velocity allows one to inject more particles at the pedestal top.
Exact collisional moments for plasma fluid theories
The velocity-space moments of the often troublesome nonlinear Landau collision operator are
expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions.
The collisional moments are shown to be generated by derivatives of two well-known functions,
namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The
resulting formula has a nonlinear dependency on the relative mean flow of the colliding species
normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency
on densities and higher-order velocity moments of the distribution functions, with no restriction
on temperature, flow, or mass ratio of the species. The result can be applied to both the classic
transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional
fluid equations that follow Grad’s moment approach. As an illustrative example, we provide
the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer
rates.
Nonlinear Resistivity for Magnetohydrodynamical Models
A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate
between electrons and ions is presented. The resistivity computed herein is shown to depend not
only on the temperature and density but also on all other polynomial velocity-space moments of
the distribution function, such as the pressure tensor and heat flux vector. The full expression for
the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic
resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal
force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if
the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity.
The relative importance of the nonlinear term(s) with respect to the well-established electron inertia
and Hall terms is also examined. The subtle implications of the nonlinear resistivity, and its dependence
on the fluid variables, are discussed in the context of magnetized plasma environments and
phenomena such as magnetic reconnection.
It is proposed to replace the traditional counterpropagating laser seed in backward Raman amplifiers with a plasma wave seed. In the linear regime, namely, for a constant pump amplitude, a plasma wave seed may be found by construction that strictly produces the same output pulse as does a counterpropagating laser seed. In the nonlinear regime, or pump-depletion regime, the plasma-wave-initiated output pulse can be shown numerically to approach the same self-similar attractor solution for the corresponding laser seed. In addition, chirping the plasma wave wavelength can produce the same beneficial effects as chirping the seed wave frequency. This methodology is attractive because it avoids issues in preparing and synchronizing a frequency-shifted laser seed.
Ultrafast proton radiography of the magnetic fields generated by a laser-driven coil current
Magnetic fields generated by a current flowing through a U-shaped coil connecting two copper foils were measured using ultrafast proton radiography.
Two 1.25 kJ, 1-ns laser pulses propagated
through laser entrance holes in the front foil and were focused to the back foil with an intensity of $3 \times 10^{16}W/cm^2$. The intense laser-solid interaction induced a high voltage between the copperfoils and generated a large current in the connecting coil. The proton data show 40–50 T magnetic fields at the center of the coil 3–4 ns after laser irradiation. The experiments provide significant insight for future target designs that aim to develop a powerful source of external magnetic fields for various applications in high-energy-density science.
The Mars crustal magnetic field control of plasma boundary locations and atmospheric loss: MHD prediction and comparison with MAVEN
We present results from a global Mars time-dependent MHD simulation under constant solar wind and solar radiation impact considering inherent magnetic field variations due to continuous planetary rotation. We calculate the 3-D shapes and locations of the bow shock (BS) and the induced magnetospheric boundary (IMB) and then examine their dynamic changes with time. We develop a physics-based, empirical algorithm to effectively summarize the multidimensional crustal field distribution. It is found that by organizing the model results using this new approach, the Mars crustal field shows a clear, significant influence on both the IMB and the BS. Specifically, quantitative relationships have been established between the field distribution and the mean boundary distances and the cross-section areas in the terminator plane for both of the boundaries. The model-predicted relationships are further verified by the observations from the NASA Mars Atmosphere and Volatile EvolutioN (MAVEN) mission. Our analysis shows that the boundaries are collectively affected by the global crustal field distribution, which, however, cannot be simply parameterized by a local parameter like the widely used subsolar longitude. Our calculations show that the variability of the intrinsic crustal field distribution in Mars-centered Solar Orbital itself may account for ∼60% of the variation in total atmospheric loss, when external drivers are static. It is found that the crustal field has not only a shielding effect for atmospheric loss but also an escape-fostering effect by positively affecting the transterminator ion flow cross-section area.
Recent advances towards a lithium vapor box divertor
Fusion power plants are likely to require near complete detachment of the divertor plasma from the divertor target plates, in order to have both acceptable heat flux at the target to avoid prompt damage and also acceptable plasma temperature at the target surface, to minimize long-term erosion.
However hydrogenic and impurity puffing experiments show that detached operation leads easily to x-point MARFEs, impure plasmas, degradation in confinement, and lower helium pressure at the exhaust. The concept of the Lithium Vapor Box Divertor is to use local evaporation and strong differential pumping through condensation to localize low-Z gas-phase material that absorbs the plasma heat flux and so achieve detachment while avoiding these difficulties.
The vapor localization has been confirmed using preliminary Navier–Stokes calculations. We use ADAS calculations of $\epsilon_{cool}$, the plasma energy lost per injected lithium atom, to estimate the lithium vapor pressure, and so temperature, required for detachment, taking into account power balance.
We also develop a simple model of detachment to evaluate the required upstream density, based on further taking into account dynamic pressure balance.
A remarkable general result is found, not just for lithium-vapor-induced detachment, that the upstream density divided by the Greenwald-limit density scales as $n_{up}/n_{GW} \propto (P^{5/8}/B^{3/8}) T_{det}^{1/2}/(\epsilon_{cool} + \gamma T_{det})$, with no explicit size scaling. $T_{det}$ is the temperature just before strong pressure loss, assumed to be $\sim 1/2$ of the ionization potential of the dominant recycling species, and $\gamma$ is the sheath heat transmission factor.
Modeling of lithium granule injection in NSTX with M3D-C1
In this paper, we present simulations of pedestal control by lithium granule injection (LGI) in
NSTX. A model for small granule ablation has been implemented in the M3D-C1 code [Jardin
et al., Comput. Sci. Discovery 5, 014002 (2012)], allowing the simulation of realistic lithium
granule injections. 2D and 3D simulations of Li injections in NSTX H-mode plasmas are
performed and the effect of granule size, injection angle and velocity on the pedestal gradient
increase is studied. The amplitude of the local pressure perturbation caused by the granules
is found to be highly dependent on the solid granule size. Adjusting the granule injection
velocity allows one to inject more particles at the pedestal top.
3D simulations show the destabilization of high order MHD modes whose amplitude is
directly linked to the localized pressure perturbation, which is found to depend on the toroidal
localization of the granule density source.
Full-wave simulations of ICRF heating regimes in toroidal plasma with non-Maxwellian distribution functions
At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely [Stix, Nucl. Fusion 15, 737 (1975)], with consequent changes in wave propagation and in
the location and amount of absorption.
In order to study these effects computationally, both the finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the full-wave, hot-plasma toroidal simulation code TORIC
[Brambilla, Plasma Phys. Control. Fusion 41, 1 (1999) and
Brambilla, Plasma Phys. Control. Fusion 44, 2423 (2002)], have been extended to allow the prescription of arbitrary velocity distributions of the form $f(v_\parallel,v_\perp,\psi,\theta)$, . For hydrogen
(H) minority heating of a deuterium (D) plasma with anisotropic Maxwellian H distributions,
the fractional H absorption varies significantly with changes in parallel temperature but is
essentially independent of perpendicular temperature. On the other hand, for HHFW regime
with anisotropic Maxwellian fast ion distribution, the fractional beam ion absorption varies
mainly with changes in the perpendicular temperature. The evaluation of the wave-field and
power absorption, through the full wave solver, with the ion distribution function provided by
either a Monte-Carlo particle and Fokker–Planck codes is also examined for Alcator C-Mod
and NSTX plasmas. Non-Maxwellian effects generally tend to increase the absorption with
respect to the equivalent Maxwellian distribution.
Zonostrophic instability driven by discrete particle noise
The consequences of discrete particle noise for a system possessing a possibly unstable collective
mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the
formation of zonal flows) occurs just below the threshold for linear instability. The scenario
provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic
models such as the second-order cumulant expansion or stochastic structural instability theory; neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To the extent that the damping of zonal flows is controlled by theion–ion collision rate, the point of zonostrophic instability is independent of that rate.
Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries --- resonant response of a plasma slab
The adiabatic limit of a recently proposed dynamical extension of Taylor relaxation, multi-region relaxed magnetohydrodynamics (MRxMHD), is summarized, with special attention to the appropriate definition of a relative magnetic helicity. The formalism is illustrated using a simple two-region, sheared-magnetic-field model similar to the Hahm–Kulsrud–Taylor (HKT) rippled-boundary slab model. In MRxMHD, a linear Grad–Shafranov equation applies, even at finite ripple amplitude. The adiabatic switching on of boundary ripple excites a shielding current sheet opposing reconnection at a resonant surface. The perturbed magnetic field as a function of ripple amplitude is calculated by invoking the conservation of magnetic helicity in the two regions separated by the current sheet. At low ripple amplitude, “half islands” appear on each side of the current sheet, locking the rotational transform at the resonant value. Beyond a critical amplitude, these islands disappear and the rotational transform develops a discontinuity across the current sheet.
Performance portability of HPC Discovery Science software: Fusion energy turbulence simulations at extreme scale
As HPC R&D moves forward on a variety of “path to exascale” architectures today, an associated objective is to demonstrate performance portability of discovery-science-capable software. Important application domains, such as Magnetic Fusion Energy (MFE), have improved modelling of increasingly complex physical systems -- especially with respect to reducing “time-to-solution” as well as “energy to solution.” The emergence of new insights on confinement scaling in MFE systems has been aided significantly by efficient software capable of harnessing powerful supercomputers to carry out simulations with unprecedented resolution and temporal duration to address increasing problem sizes. Specifically, highly scalable particle-in-cell (PIC) programing methodology is used in this paper to demonstrate how modern scientific applications can achieve efficient architecture-dependent optimizations of performance scaling and code portability for path-to-exascale platforms.
A Lower Bound on Adiabatic Heating of Compressed Turbulence for Simulation and Model Validation
The energy in turbulent flow can be amplified by compression, when the compression occurs on a timescale shorter
than the turbulent dissipation time. This mechanism may play a part in sustaining turbulence in various
astrophysical systems, including molecular clouds. The amount of turbulent amplification depends on the net effect
of the compressive forcing and turbulent dissipation. By giving an argument for a bound on this dissipation, we
give a lower bound for the scaling of the turbulent velocity with the compression ratio in compressed turbulence.
That is, turbulence undergoing compression will be enhanced at least as much as the bound given here, subject to a
set of caveats that will be outlined. Used as a validation check, this lower bound suggests that some models of
compressing astrophysical turbulence are too dissipative. The technique used highlights the relationship between
compressed turbulence and decaying turbulence.
Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, $n=4$−$9$, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.
Pedestal-to-wall 3D fluid transport simulations on DIII-D
The 3D fluid-plasma edge transport code EMC3-EIRENE is used to test several magnetic field models with and without plasma response against DIII-D experimental data for even and odd-parity $n = 3$ magnetic field perturbations. The field models include ideal and extended MHD equilibria, and the vacuum approximation. Plasma response is required to reduce the stochasticity in the pedestal region for even-parity fields, however too much screening suppresses the measured splitting of the downstream $T_e$ profile. Odd-parity perturbations result in weak tearing and only small additional peaks in the downstream measurements. In this case plasma response is required to increase the size of the lobe structure. No single model is able to simultaneously reproduce the upstream and downstream characteristics for both odd and even-parity perturbations.
Collisional considerations in axial-collection plasma mass filters
The chemical inhomogeneity of nuclear waste makes chemical separations difficult,
while the correlation between radioactivity and nuclear mass makes mass-based
separation, and in particular plasma-based separation, an attractive alternative.
Here, we examine a particular class of plasma mass filters, namely filters in which
(a) species of different mass are collected along magnetic field lines at opposite
ends of an open-field-line plasma device, and (b) gyro-drift effects are important
to the separation process. Using an idealized cylindrical model, we derive a set of
dimensionless parameters which provide minimum necessary conditions for effective
mass filter function in the presence of ion-ion and ion-neutral collisions. Through
simulations of constant-density profile, turbulence-free devices, we find that these
parameters accurately describe mass filter performance in more general magnetic
geometries. We then use these parameters to inform on the design and upgrade
of current experiments, as well as deriving general scalings for the throughput of
production mass filters. Importantly, we find that ion temperatures above 3 eV and
magnetic fields above $10^4$ Gauss are critical to ensure feasible mass filter function
when operating at ion densities of $10^{13} cm^{−3}$.
Parametric decay of plasma waves near the upper-hybrid resonance
An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate $\gamma$ ceases to be a linear function of the incident-wave amplitude. An explicit formula for $\gamma$ is derived and expressed in terms of cold-plasma parameters. Theory predictions are in reasonable agreement
with the results of the particle-in-cell simulations presented in a separate publication.
Conservative discretization of the Landau collision integral
We describe a density-, momentum-, and energy-conserving discretization of the nonlinear Landau
collision integral. The method is suitable for both the finite-element and discontinuous Galerkin
methods and does not require structured meshes. The conservation laws for the discretization are
proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation
problem using a finite-element implementation.
Improving fast-ion confinement in high-performance discharges by suppressing Alfvén eigenmodes
We show that the degradation of fast-ion confinement in steady-state DIII-D discharges is
quantitatively consistent with predictions based on the effects of multiple unstable Alfvén
eigenmodes on beam-ion transport. Simulation and experiment show that increasing the
radius where the magnetic safety factor has its minimum is effective in minimizing beam-ion
transport. This is favorable for achieving high performance steady-state operation in DIII-D
and future reactors. A comparison between the experiments and a critical gradient model, in
which only equilibrium profiles were used to predict the most unstable modes, show that in a
number of cases this model reproduces the measured neutron rate well.
Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks
The confinement of energetic particles (EPs) is crucial in the efficient heating of tokamak plasmas.
Plasma instabilities such as Alfvén eigenmodes (AEs) can redistribute the EP population, making the
plasma heating less effective and leading to additional loads on the walls. The nonlinear dynamics of
toroidicity induced AEs (TAEs) is investigated by means of the global gyrokinetic particle-in-cell
code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EPs
due to the wave–particle nonlinearity is studied. In particular, we focus on the linear modification of
the frequency, growth rate and radial structure of the TAE, caused by the nonlinear evolution of the
EP distribution function. For the ITPA benchmark case, we find that the frequency increases when
the growth rate decreases, and the mode shrinks radially. The theoretical interpretation is given in
terms of a nonperturbative nonlinear evolution of the AE in relation to the Alfvén continuum.
Role of magnetosonic solitons in perpendicular collisionless shock reformation,
The nature of the magnetic structure arising from ion specular reflection in shock compression studies is
examined by means of 1D particle-in-cell simulations. Propagation speed, field profiles, and supporting
currents for this magnetic structure are shown to be consistent with a magnetosonic soliton. Coincidentally,
this structure and its evolution are typical of foot structures observed in perpendicular shock reformation.
To reconcile these two observations, we propose, for the first time, that shock reformation can be explained
as the result of the formation, growth, and subsequent transition to a supercritical shock of a magnetosonic
soliton. This argument is further supported by the remarkable agreement found between the period of the
soliton evolution cycle and classical reformation results. This new result suggests that the unique properties
of solitons can be used to shed new light on the long-standing issue of shock nonstationarity and its role
on particle acceleration.
High frequency fishbone driven by passing energetic ions in tokamak plasmas
High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al., Phys. Rev. Lett. 57, 835 (2986)).
It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles.
In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability.
For purely passing energetic ions with zero drift orbit width, the kinetic energy $\delta {{W}_{k}}$ is derived analytically.
The derived analytic expression is more accurate as compared to the result of previous work (Wang, Phys. Rev. Lett. 86, 5286 (2001)).
For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically.
Numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold ${{\beta}_{c}}$ for instability and decrease mode frequency.
Experimental Verification of the Role of Electron Pressure in Fast Magnetic Reconnection with a Guide Field
We report detailed laboratory observations of the structure of a reconnection current sheet in a two-fluid
plasma regime with a guide magnetic field. We observe and quantitatively analyze the quadrupolar electron
pressure variation in the ion-diffusion region, as originally predicted by extended magnetohydrodynamics
simulations. The projection of the electron pressure gradient parallel to the magnetic field contributes
significantly to balancing the parallel electric field, and the resulting cross-field electron jets in the
reconnection layer are diamagnetic in origin. These results demonstrate how parallel and perpendicular
force balance are coupled in guide field reconnection and confirm basic theoretical models of the
importance of electron pressure gradients for obtaining fast magnetic reconnection.
On the evaluation of Pierce parameters C and Q in a traveling wave tube
A study of an exactly solvable model of a traveling wave tube (TWT) shows that Pierce gain parameter $C$ and space charge parameter $Q$ generally depend on wavenumber $k$ in addition to frequency $\omega$.
The choice of $k$ at which $C$ and $Q$ are evaluated may strongly affect their values and, consequently, the values of the small signal gain obtained from 3- and 4-wave Pierce theory.
In order to illustrate this effect, we calculate the spatial amplification rate, $k_i$, from the exact dispersion relation for a dielectric TWT model which is exactly solvable. We compare this exact value of $k_i$ with approximate values obtained from Pierce's classical 3-wave and 4-wave dispersion relations, obtained by making various assumptions on $k$ in the evaluation of $C$ and $Q$.
We find that the various ways to approximate $C$ and $Q$ will have a significant influence on the numerical values of $k_i$. For our dielectric TWT example, Pierce's 4-wave TWT dispersion relation generally yields the most accurate values of $k_i$ if $Q$ is evaluated for $k = \omega/v_0$, where $v_0$ is the beam velocity, and if the complete frequency and wavelength dependence of $C$ is retained. Pierce's 3-wave theory also yields accurate values of $k_i$ using a different form of $Q$ from the 4-wave theory. The implications of this result for TWT design are explored.
Prediction of nonlinear evolution character of energetic-particle-driven instabilities
A general criterion is proposed and found to successfully predict the emergence of chirping
oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model
includes realistic eigenfunction structure, detailed phase-space dependences of the instability
drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the
effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter
mechanism is essential to accurately identify the transition between the fixed-frequency mode
behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping
observation in spherical and conventional tokamaks.
Extending geometrical optics: A Lagrangian theory for vector waves
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are
not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely
described by their coordinates and momenta, but vector-wave rays have another degree of freedom,
namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical)
“wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A
well-known manifestation of polarization dynamics is mode conversion, which is the linear
exchange of quanta between different wave modes and can be interpreted as a rotation of the wave
spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories.
This work presents an extension and reformulation of GO as a first-principle Lagrangian theory,
whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously.
As an example, the theory is applied to describe the polarization-driven divergence of right-hand
and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.
On Coupling Fluid Plasma and Kinetic Neutral Physics Models
The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases.
It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability.
Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium.
For explicit coupling, the present implementation of Monte Carlo correlated sampling techniques does not allow for complete convergence in slab geometry.
For the benchmark case, residuals decay with particle number and increase with grid size, indicating that they scale in a manner that is similar to the theoretical prediction for nonlinear bias error.
Progress is reported on implementation of a fully implicit Jacobian-free Newton–Krylov coupling scheme.
The present block Jacobi preconditioning method is still sensitive to time step and methods that better precondition the coupled system are under investigation.
Higher order Larmor radius corrections to guiding-centre equations and application to fast ion equilibrium distributions
An improved set of guiding-centre equations, expanded to one order higher in Larmor radius than usually written for guiding-centre codes, are derived for curvilinear flux coordinates and implemented into the orbit following code VENUS-LEVIS. Aside from greatly improving the correspondence between guiding-centre and full particle trajectories, the most important effect of the additional Larmor radius corrections is to modify the definition of the guiding-centre's parallel velocity via the so-called Baños drift. The correct treatment of the guiding-centre push-forward with the Baños term leads to an anisotropic shift in the phase-space distribution of guiding-centres, consistent with the well-known magnetization term. The consequence of these higher order terms are quantified in three cases where energetic ions are usually followed with standard guiding-centre equations: (1) neutral beam injection in a MAST-like low aspect-ratio spherical equilibrium where the fast ion driven current is significantly larger with respect to previous calculations, (2) fast ion losses due to resonant magnetic perturbations where a lower lost fraction and a better confinement is confirmed, (3) alpha particles in the ripple field of the European DEMO where the effect is found to be marginal.
Ponderomotive dynamics of waves in quasiperiodically modulated media
Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields,
linear waves also experience time-averaged refraction in modulated media. Here we propose a covariant
variational theory of this ponderomotive effect on waves for a general nondissipative linear medium. Using
the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of
the modulation (provided that parametric resonances are avoided). Our theory also shows that any wave is, in
fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. The dynamics
of quantum particles is subsumed as a special case. As an illustration, ponderomotive Hamiltonians of quantum
particles and photons are calculated within a number of models. We also explain a fundamental connection
between these results and the well-known electrostatic dielectric tensor of quantum plasmas.
Distribution of Rydberg atoms acceleration by a laser pulse
Simulations of the movement of the excited neutral atoms were performed with random sampling
and the ponderomotive model. The modeling parameters were setup according to the experiment of
laser acceleration of neutral helium [Nature 431(7268), 1261 (2009)]. A comparison between the
simulation results and the experiment measurements is made in detail, and the characteristics of the
final distribution of the Rydberg neutral atoms are analyzed. Two important factors that determine
the final distribution of Rydberg neutral atoms, namely, the ponderomotive force and the original
distribution of the Rydberg atoms corresponding to the distribution of the laser intensity, are
discussed.
Total fluid pressure imbalance in the scrape-off layer of tokamak plasmas
Simulations using the fully kinetic neoclassical code XGCa ( X-point included guiding- center
axisymmetric) were undertaken to explore the impact of kinetic effects on scrape-off layer
(SOL) physics in DIII-D H-mode plasmas. XGCa is a total-f, gyrokinetic code which selfconsistently
calculates the axisymmetric electrostatic potential and plasma dynamics, and
includes modules for Monte Carlo neutral transport.
Previously presented XGCa results showed several noteworthy features, including large
variations of ion density and pressure along field lines in the SOL, experimentally relevant
levels of SOL parallel ion flow (Mach number ∼ 0.5), skewed ion distributions near the sheath
entrance leading to subsonic flow there, and elevated sheath potentials (Churchill 2016 Nucl.
Mater. Energy 1–6).
In this paper, we explore in detail the question of pressure balance in the SOL, as it was
observed in the simulation that there was a large deviation from a simple total pressure balance
(the sum of ion and electron static pressure plus ion inertia). It will be shown that both the
contributions from the ion viscosity (driven by ion temperature anisotropy) and neutral source
terms can be substantial, and should be retained in the parallel momentum equation in the
SOL, but still falls short of accounting for the observed fluid pressure imbalance in the XGCa
simulation results.
Recent progress in understanding electron thermal transport in NSTX
The anomalous level of electron thermal transport inferred in magnetically confined configurations is one of the most challenging problems for the ultimate realization of fusion power using toroidal devices: tokamaks, spherical tori and stellarators. It is generally believed that plasma instabilities driven by the abundant free energy in fusion plasmas are responsible for the electron thermal transport. The National Spherical Torus eXperiment (NSTX) [Ono et al., Nucl. Fusion 40, 557 (2000)] provides a unique laboratory for studying plasma instabilities and their relation to electron thermal transport due to its low toroidal field, high plasma beta, low aspect ratio and large ${\bf E} \times {\bf B}$ flow shear. Recent findings on NSTX have shown that multiple instabilities are required to explain observed electron thermal transport, given the wide range of equilibrium parameters due to different operational scenarios and radial regions in fusion plasmas. Here we review the recent progresses in understanding anomalous electron thermal transport in NSTX and focus on mechanisms that could drive electron thermal transport in the core region. The synergy between experiment and theoretical/numerical modeling is essential to achieving these progresses. The plans for newly commissioned NSTX-Upgrade will also be discussed.
Is Proxima Centauri B Habitable? - A study of atmospheric loss
We address the important question of whether the newly discovered exoplanet, Proxima Centauri b (PCb), is capable
of retaining an atmosphere over long periods of time. This is done by adapting a sophisticated multi-species MHD
model originally developed for Venus and Mars, and computing the ion escape losses from PCb. The results suggest
that the ion escape rates are about two orders of magnitude higher than the terrestrial planets of our Solar system if
PCb is unmagnetized. In contrast, if the planet does have an intrinsic dipole magnetic field, the rates are lowered for
certain values of the stellar wind dynamic pressure, but they are still higher than the observed values for our Solar
system’s terrestrial planets. These results must be interpreted with due caution, since most of the relevant parameters
for PCb remain partly or wholly unknown.
Saturation of Alfvén modes in tokamak plasmas investigated by Hamiltonian mapping techniques
Nonlinear dynamics of single toroidal number Alfvén eigenmodes destabilised by the
the resonant interaction with fast ions is investigated, in tokamak equilibria, by means of
Hamiltonian mapping techniques. The results obtained by two different simulation codes,
XHMGC and HAGIS, are presented for $n = 2$ Beta induced Alfvén eigenmodes and,
respectively $n = 6$ toroidal Alfvén eigenmodes. Simulations of the bump-on-tail instability
performed by a 1-dimensional code, PIC1DP, are also analysed for comparison. As a general
feature, modes saturate as the resonant-particle distribution function is flattened over the whole
region where mode-particle power transfer can take place in the linear phase. Such region
is limited by the narrowest of resonance width and mode width. In the former case, mode
amplitude at saturation exhibits a quadratic scaling with the linear growth rate; in the latter
case, the scaling is linear. These results are explained in terms of the approximate analytic
solution of a nonlinear pendulum model. They are also used to prove that the radial width of
the single poloidal harmonic sets an upper limit to the radial displacement of circulating fast
ions produced by a single-toroidal-number gap mode in the large $n$ limit, irrespectively of the
possible existence of a large global mode structure formed by many harmonics.
Efficiency of Wave-Driven Rigid Body Rotation Toroidal Confinement, .
The compensation of vertical drifts in toroidal magnetic fields through a wave-driven poloidal rotation
is compared with compensation through the wave driven toroidal current generation to support
the classical magnetic rotational transform. The advantages and drawbacks associated with the sustainment
of a radial electric field are compared with those associated with the sustainment of a
poloidal magnetic field both in terms of energy content and power dissipation. The energy content
of a radial electric field is found to be smaller than the energy content of a poloidal magnetic field
for a similar set of orbits. The wave driven radial electric field generation efficiency is similarly
shown, at least in the limit of large aspect ratio, to be larger than the efficiency of wave-driven
toroidal current generation.
A geometrical correction to the ${\bf E}\times{\bf B}$ drift causes an outward flux of co-current momentum whenever
electrostatic potential energy is transferred to ion parallel flows. The robust, fully nonlinear
symmetry breaking follows from the free-energy flow in phase space and does not depend on any
assumed linear eigenmode structure. The resulting rotation peaking is counter-current and scales as
temperature over plasma current. This peaking mechanism can only act when fluctuations are low-frequency
enough to excite ion parallel flows, which may explain some recent experimental observations
related to rotation reversals.
Photon polarizability and its effect on the dispersion of plasma waves
High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.
Proposals to reach the next generation of laser intensities through Raman or Brillouin backscattering have centered on optical frequencies. Higher frequencies are beyond the range of such methods mainly due to the wave damping that accompanies the higher-density plasmas necessary for compressing higher frequency lasers. However, we find that an external magnetic field transverse to the direction of laser propagation can reduce the required plasma density. Using parametric interactions in magnetized plasmas to mediate pulse compression, both reduces the wave damping and alleviates instabilities, thereby enabling higher frequency or lower intensity pumps to produce pulses at higher intensities and longer durations. In addition to these theoretical advantages, our method in which strong uniform magnetic fields lessen the need for high-density uniform plasmas also lessens key engineering challenges or at least exchanges them for different challenges.
The role of guide field in magnetic reconnection driven by island
coalescence
A number of studies have considered how the rate of magnetic reconnection scales in large and
weakly collisional systems by the modelling of long reconnecting current sheets. However, this setup
neglects both the formation of the current sheet and the coupling between the diffusion region
and a larger system that supplies the magnetic flux. Recent studies of magnetic island merging,
which naturally include these features, have found that ion kinetic physics is crucial to describe the
reconnection rate and global evolution of such systems. In this paper, the effect of a guide field on
reconnection during island merging is considered. In contrast to the earlier current sheet studies,
we identify a limited range of guide fields for which the reconnection rate, outflow velocity, and
pile-up magnetic field increase in magnitude as the guide field increases. The Hall-MHD fluid
model is found to reproduce kinetic reconnection rates only for a sufficiently strong guide field, for
which ion inertia breaks the frozen-in condition and the outflow becomes Alfvenic in the kinetic
system. The merging of large islands occurs on a longer timescale in the zero guide field limit,
which may in part be due to a mirror-like instability that occurs upstream of the reconnection
region.
Three-dimensional geometry of magnetic reconnection induced by ballooning instability in a generalized Harris sheet
We report for the first time the intrinsically three-dimensional (3D) geometry of the magnetic
reconnection process induced by ballooning instability in a generalized Harris sheet. The spatial
distribution and the structure of the quasi-separatrix layers, as well as their temporal emergence
and evolution, indicate that the associated magnetic reconnection can only occur in a 3D geometry,
which is irreducible to that of any two-dimensional reconnection process. Such a finding provides a
new perspective to the long-standing controversy over the substorm onset problem and elucidates
the combined roles of reconnection and ballooning instabilities. It also connects to the universal
presence of 3D reconnection processes previously discovered in various natural and laboratory
plasmas.
Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. Here, a different approach is proposed. We show that, for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. In particular, we present a variational formulation for linear geometrical optics in a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.
Toroidal Alfvén eigenmodes with nonlinear gyrokinetic and fluid hybrid models
Alfven eigenmodes may be important in driving fast particle transport in magnetic confinement fusion devices, with potentially deleterious results.
To explain and predict this behaviour, numerical simulations are necessary.
In order to predict transport, modes must be simulated through to their nonlinear saturated state.
In this work, the first simulations of non-linear wave-particle interaction between an energetic particle population and a Toroidal Alfvén Eigenmode are
performed in which fluctuations responding self-consistently to modification of the fast particle profile are calculated with gyrokinetic treatment of all plasma species. Results from two such gyrokinetic codes are compared with new results from non-perturbative and perturbative fluidgyrokinetic hybrid codes.
There is a power-law relationship between the saturated magnetic perturbation amplitude, $\delta B / B_0$, and the linear mode growth rate, $\gamma_L$.
All models show a transition from a
higher to a lower exponent regime with increasing $\gamma_L$.
Measured values of the higher exponent
from different codes fall in a range between 1.45 and 1.79, while the lower exponent falls in a range
between 0.47 and 0.79. There is a consistent difference of 1.0 between the higher and lower exponents
independent of the model. The absolute level of saturated $\delta B / B_0$ is determined by the damping
rate. In the fluid-gyrokinetic hybrid codes, an ad-hoc damping is applied, while in the
gyrokinetic case the measured damping is consistent with the estimated rate of physical electron
Landau damping.
On the correspondence between classical geometric phase of gyro-motion and quantum Berry phase
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the Schrödinger equation or the Dirac equation. This correspondence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that the orbital Berry phases of the eigenstates interfere coherently to produce an observable effect (which we termed “coherent Berry phase”), which is exactly the geometric phase of the classical gyro-motion. This technique works for the particles with and without spin. For particles with spin, on each of the eigenstates that make up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the orbital Berry phases that interfere coherently to produce a coherent Berry phase corresponding to the classical geometric phase of the gyro-motion. The spin Berry phases of the eigenstates, on the other hand, remain to be quantum phase factors for the coherent states and have no classical counterpart.
Continuum kinetic and multi-fluid simulations of classical sheaths
The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of
heat on walls, the effect of sputtering, and contamination of the plasma with detrimental impurities.
The plasma sheath also provides a boundary condition and can often have a significant global
impact on the bulk plasma. In this paper, kinetic studies of classical sheaths are performed with the
continuum kinetic code, Gkeyll, which directly solves the Vlasov-Maxwell equations. The code
uses a novel version of the finite-element discontinuous Galerkin scheme that conserves energy in
the continuous-time limit. The fields are computed using Maxwell equations. Ionization and scattering
collisions are included; however, surface effects are neglected. The aim of this work is to
introduce the continuum kinetic method and compare its results with those obtained from an
already established finite-volume multi-fluid model also implemented in Gkeyll. Novel boundary
conditions on the fluids allow the sheath to form without specifying wall fluxes, so the fluids and
fields adjust self-consistently at the wall. The work presented here demonstrates that the kinetic
and fluid results are in agreement for the momentum flux, showing that in certain regimes, a multi-
fluid model can be a useful approximation for simulating the plasma boundary. There are differences
in the electrostatic potential between the fluid and kinetic results. Further, the direct solutions
of the distribution function presented here highlight the non-Maxwellian distribution of electrons in
the sheath, emphasizing the need for a kinetic model. The densities, velocities, and the potential
show a good agreement between the kinetic and fluid results. However, kinetic physics is
highlighted through higher moments such as parallel and perpendicular temperatures which provide
significant differences from the fluid results in which the temperature is assumed to be isotropic.
Besides decompression cooling, the heat flux is shown to play a role in the temperature differences
that are observed, especially inside the collisionless sheath.
Detection of nanoparticles in carbon arc discharge with laser-induced incandescence
Laser-induced incandescence measurements were conducted in the carbon arc discharge, used for
synthesis of carbon nanostructures. The results reveal two spatial regions occupied by dominant populations
of carbon particles with different sizes. Close to the axis of the arc, large micron size particles
dominate the incandescence signal. In the arc periphery, the dominant population of nanoparticles has
diameter of 20 nm. Using a heat transfer model between the gas, arc plasma and the particles, it is shown
that such a drastic difference in the particle sizes can be explained by evaporation of the micron-scale
particles which move across the arc plasma towards the arc periphery. It is also hypothesized that
mass evaporated from the micro particles contributes to the carbon feedstock for the formation of
nanostructures.
Effect of rotation zero-crossing on single-fluid plasma response to three-dimensional magnetic perturbations
In order to understand the effect of rotation on the response of a plasma to three-dimensional
magnetic perturbations, we perform a systematic scan of the zero-crossing of the rotation profile
in a DIII-D ITER-similar shape equilibrium using linear, time-independent modeling with the
M3D-C1 extended magnetohydrodynamics code. We confirm that the local resonant magnetic
field generally increases as the rotation decreases at a rational surface. Multiple peaks in the
resonant field are observed near rational surfaces, however, and the maximum resonant field does
not always correspond to zero rotation at the surface. Furthermore, we show that non-resonant
current can be driven at zero-crossings not aligned with rational surfaces if there is sufficient
shear in the rotation profile there, leading to amplification of near-resonant Fourier harmonics of
the perturbed magnetic field and a decrease in the far-off-resonant harmonics. The quasilinear
electromagnetic torque induced by this non-resonant plasma response provides drive to flatten
the rotation, possibly allowing for increased transport in the pedestal by the destabilization of
turbulent modes. In addition, this torque acts to drive the rotation zero-crossing to dynamically
stable points near rational surfaces, which would allow for increased resonant penetration. By
one or both of these mechanisms, this torque may play an important role in bifurcations into
suppression of edge-localized modes. Finally, we discuss how these changes to the plasma
response could be detected by tokamak diagnostics. In particular, we show that the changes to
the resonant field discussed here have a significant impact on the external perturbed magnetic
field, which should be observable by magnetic sensors on the high-field side of tokamaks but not
on the low-field side. In addition, TRIP3D-MAFOT simulations show that none of the changes
to the plasma response described here substantially affects the divertor footprint structure.
Variations of the Martian plasma environment during the ICME passage on 8 March 2015: A time-dependent MHD study
The Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft observed a strong interplanetary coronal mass ejection (ICME) impacting Mars on 8 March 2015. We use a time-dependent global MHD model to investigate the response of the Martian ionosphere and induced magnetosphere to the large solar wind disturbance associated with the ICME. Taking observed upstream solar wind conditions from MAVEN as inputs to the MHD model, the variations of the Martian plasma environments are simulated realistically in a time period from 2.5 h prior to the arrival of the ICME shock to about 12 h after the impact. Detailed comparisons between the model results and the relevant MAVEN plasma measurements are presented, which clearly show that the time-dependent multispecies single-fluid MHD model is able to reproduce the main features observed by the spacecraft during the ICME passage. Model results suggest that the induced magnetosphere responds to solar wind variation on a very short time scale (approximately minutes). The variations of the plasma boundaries' distances from the planet along the subsolar line are examined in detail, which show a clear anticorrelation with the magnetosonic Mach number. Plasma properties in the ionosphere (especially the induced magnetic field) varied rapidly with solar wind changes. Model results also show that ion escape rates could be enhanced by an order of magnitude in response to the high solar wind dynamic pressure during the ICME event.
Explicit K-symplectic algorithms for charged particle dynamics
We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.
Compressibility and heat capacity of rotating plasma
A rotating plasma column is shown to exhibit unusual heat capacity effects under compression. For
near equilibrium thermodynamics and smooth wall conditions, the heat capacity depends on the
plasma density, on the speed of the rotation, and on the mass ratio. For a certain range of parameters,
the storage of energy in the electric field produces a significant increase in the heat capacity.
Photons, phonons, and plasmons with orbital angular momentum in plasmas
Exact eigen modes with orbital angular momentum (OAM) in the complex media of unmagnetized homogeneous plasmas are studied. Three exact eigen modes with OAM are derived, i.e., photons, phonons, and plasmons. The OAM of different plasma components are closely related to the charge polarities. For photons, the OAM of electrons and ions are of the same magnitude but opposite direction, and the total OAM is carried by the field. For the phonons and plasmons, their OAM are carried by the electrons and ions. The OAM modes in plasmas and their characteristics can be explored for potential applications in plasma physics and accelerator physics.
Relativistic Magnetic Reconnection in Kerr Spacetime
The magnetic reconnection process is analyzed for relativistic magnetohydrodynamical plasmas around
rotating black holes. A simple generalization of the Sweet-Parker model is used as a first approximation to
the problem. The reconnection rate, as well as other important properties of the reconnection layer, has been
calculated taking into account the effect of spacetime curvature. Azimuthal and radial current sheet
configurations in the equatorial plane of the black hole have been studied, and the case of small black hole
rotation rate has been analyzed. For the azimuthal configuration, it is found that the black hole rotation
decreases the reconnection rate. On the other hand, in the radial configuration, it is the gravitational force
created by the black hole mass that decreases the reconnection rate. These results establish a fundamental
interaction between gravity and magnetic reconnection in astrophysical contexts.
Migration of a carbon adatom on a charged single-walled carbon nanotube
We find that negative charges on an armchair single-walled carbon nanotube (SWCNT) can significantly enhance the migration of a carbon adatom on the external surfaces of SWCNTs, along the direction of the tube axis.
Nanotube charging results in stronger binding of adatoms to SWCNTs and consequent longer lifetimes of adatoms before desorption, which in turn increases their migration distance several orders of magnitude.
These results support the hypothesis of diffusion enhanced SWCNT growth in the volume of arc plasma.
This process could enhance effective carbon flux to the metal catalyst.
Investigation of instabilities and rotation alteration in high beta KSTAR plasmas
H-mode plasma operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) device has been expanded to significantly surpass the ideal MHD no-wall beta limit. Plasmas with high normalized beta, $\beta_N$, up to 4.3 have been achieved with reduced plasma internal inductance, $l_i$, to near 0.7, exceeding the computed $n=1$ ideal no-wall limit by a factor of 1.6. Pulse lengths at maximum $\beta_N$ were extended to longer pulses by new, more rapid control.
The stability of the observed $m/n$$=$$2/1$ tearing mode that limited the achieved high $\beta_N$ is computed by the M3D-$C^1$ code, and the effect of sheared toroidal rotation to tearing stability is examined.
As a method to affect the mode stability in high $\beta_N$ plasmas, the non-resonant alteration of the rotation profile by non-axisymmetric magnetic fields has been used, enabling a study of the underlying neoclassical toroidal viscosity (NTV) physics and stability dependence on rotation. Non-axisymmetric field spectra were applied using in-vessel control coils (IVCCs) with varied $n=2$ field configurations to alter the plasma toroidal rotation profile in high beta H-mode plasmas and to analyze their effects on the rotation. The rotation profile was significantly altered with rotation reduced by more than 60% without tearing activity or mode locking. To investigate the physical characteristics and scaling of the measured rotation braking by NTV, changes in the rotation profile are analytically examined in steady state. The expected NTV scaling with the square of the normalized applied field perturbation agrees with the measured profile change $\delta B^{2.1-2.3}$. The NTV is also found to scale as $T_i^{2.1-2.4}$, in general agreement with the low collisionality “1/$\nu$” regime scaling of the NTV theory $(T_{NTV . (1/\nu)} \propto T_i^{2.5})$.
What happens to full-f gyrokinetic transport and turbulence in a toroidal wedge simulation?
In order to save the computing time or to fit the simulation size into a limited computing hardware in a gyrokinetic turbulence simulation of a tokamak plasma, a toroidal wedge simulation may be utilized in which only a partial toroidal section is modeled with a periodic boundary condition in the toroidal direction.
The most severe restriction in the wedge simulation is expected to be in the longest wavelength turbulence, i.e., ion temperature gradient (ITG) driven turbulence.
The global full-$f$ gyrokinetic code XGC1 is used to compare the transport and turbulence properties from a toroidal wedge simulation against the full torus simulation in an ITG unstable plasma in a model toroidal geometry.
It is found that
(1) the convergence study in the wedge number needs to be conducted all the way down to the full torus in order to avoid a false convergence,
(2) a reasonably accurate simulation can be performed if the correct wedge number $N$ can be identified,
(3) the validity of a wedge simulation may be checked by performing a wave-number spectral analysis of the turbulence amplitude $|\delta \Phi|$ and assuring that the variation of $\delta \Phi$ between the discrete $k_\theta$ values is less than 25% compared to the peak $\delta \Phi$, and
(4) a frequency spectrum may not be used for the validity check of a wedge simulation.
Magnetic fields in rotating and radiating astrophysical plasma can be produced due to a radiative interaction
between plasma layers moving relative to each other. The efficiency of current drive, and with it the associated
dynamo effect, is considered in a number of limits. It is shown here, however, that predictions for these generated
magnetic fields can be significantly higher when kinetic effects, previously neglected, are taken into account.
Radial localization of edge modes in Alcator C-Mod pedestals using optical diagnostics
Dedicated experiments in ion cyclotron range heated enhanced D-alpha (EDA) H-mode and I-mode plasmas have been performed on Alcator C-Mod to identify the location of edge fluctuations inside the pedestal and to determine their plasma frame phase velocity.
For this purpose, measurements from gas puff imaging (GPI) and gas puff charge exchange recombination spectroscopy (GP-CXRS) have been collected using the same optical views.
The data suggest that the EDA H-mode-specific quasi-coherent mode (QCM) is centered near the radial electric field ($E_r$) well minimum and propagates along the ion diamagnetic drift direction in the plasma frame.
The weakly coherent mode (WCM) and the geodesic acoustic mode observed in I-mode, on the other hand, are found to be located around the outer shear layer of the $E_r$ well.
This results in a weak plasma frame phase velocity mostly along the electron diamagnetic drift direction for the WCM.
The findings in these EDA H-mode plasmas differ from probe measurements in ohmic EDA H-mode [LaBombard et al., Phys. Plasmas 21, 056108 (2014)], where the QCM was identified as an electron drift-wave located several mm outside the $E_r$ well minimum in a region of positive $E_r$.
To explore if instrumental effects of the optical diagnostics could be the cause of the difference, a synthetic diagnostic for GPI is introduced.
This diagnostic reproduces amplitude ratios and relative radial shifts of the mode profiles determined from poloidally and toroidally oriented optics and, if instrumental effects related to GP-CXRS are also included, indicates that the measured location of the QCM and WCM relative to the $E_r$ well reported here is only weakly affected by instrumental effects.
Synthetic diagnostic for the beam emission spectroscopy diagnostic using a full optical integration
The beam emission spectroscopy (BES) diagnostic is used to measure fluctuations of electron
density in the edge and core of fusion plasmas, and is a key in understanding turbulence in a
plasma reactor. A synthetic BES diagnostic for the turbulence simulation code XGC1 has been
developed using a realistic neutral beam model and an optical system easily adaptable to
different kinds of tokamaks. The beam is modeled using multiple beam energy components, each
one with a fraction of the total energy and their own mass and energy (mono-energetic
components). The optical system consists of a lens focusing a bundle of optical fibers and
resulting in a 2D measurement. The synthetic diagnostic gives similar correlation functions and
behaviour of the turbulences than the usual methods that do not take into account the full 3D
optical effects. The results, based on a simulation of XGC1, contain an analysis of the correlation
(in space and time), a comparison of different approximations possible and their importance in
accurately modeling the BES diagnostic.
Simulations of ion velocity distribution functions taking into account both elastic and charge exchange collisions
Based on accurate representation of the $He^+–He$ angular differential scattering cross sections consisting of both elastic and charge exchange collisions, we performed detailed numerical simulations of the ion velocity distribution functions (IVDF) by Monte Carlo collision method (MCC).
The results of simulations are validated by comparison with the experimental data of the ion mobility and the transverse diffusion.
The IVDF simulation study shows that due to significant effect of scattering in elastic collisions IVDF cannot be separated into product of two independent IVDFs in the transverse and parallel to the electric field directions.
Ion velocity distribution functions in argon and helium discharges: detailed comparison of numerical simulation results and experimental data
Using the Monte Carlo collision method, we have performed simulations of ion velocity distribution functions (IVDF) taking into account both elastic collisions and charge exchange collisions of ions with atoms in uniform electric fields for argon and helium background gases. The simulation results are verified by comparison with the experiment data of the ion mobilities and the ion transverse diffusion coefficients in argon and helium. The recently published experimental data for the first seven coefficients of the Legendre polynomial expansion of the ion energy and angular distribution functions are used to validate simulation results for IVDF. Good agreement between measured and simulated IVDFs shows that the developed simulation model can be used for accurate calculations of IVDFs.
Main-Ion Intrinsic Toroidal Rotation Profile Driven by Residual Stress Torque from Ion Temperature Gradient Turbulence in the DIII-D Tokamak
Intrinsic toroidal rotation of the deuterium main ions in the core of the DIII-D tokamak is observed to transition from flat to hollow, forming an off-axis peak, above a threshold level of direct electron heating. Nonlinear gyrokinetic simulations show that the residual stress associated with electrostatic ion temperature gradient turbulence possesses the correct radial location and stress structure to cause the observed hollow rotation profile. Residual stress momentum flux in the gyrokinetic simulations is balanced by turbulent momentum diffusion, with negligible contributions from turbulent pinch. The prediction of the velocity profile by integrating the momentum balance equation produces a rotation profile that qualitatively and quantitatively agrees with the measured main-ion profile, demonstrating that fluctuation-induced residual stress can drive the observed intrinsic velocity profile.
Differential formulation of the gyrokinetic Landau operator
Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.
We consider a class of diffusion problems defined on simple graphs in which the populations at any two vertices may be averaged if they are connected by an edge.
The diffusion polytope is the convex hull of the set of population vectors attainable using finite sequences of these operations.
A number of physical problems have linear programming solutions taking the diffusion polytope as the feasible region, e.g. the free energy that can be removed from plasma using waves, so there is a need to describe and enumerate its extreme points.
We review known results for the case of the complete graph $K_n$, and study a variety of problems for the path graph $P_n$ and the cyclic graph $C_n$.
We describe the different kinds of extreme points that arise, and identify the diffusion polytope in a number of simple cases.
In the case of increasing initial populations on $P_n$ the diffusion polytope is topologically an n-dimensional hypercube.
Kinetic Neoclassical Calculations of Impurity Radiation Profiles
Modifications of the drift-kinetic transport code XGC0 to include the transport, ionization, and recombination of individual charge states, as well as the associated radiation, are described. The code is first applied to a simulation of an NSTX H-mode discharge with carbon impurity to demonstrate the approach to coronal equilibrium. The effects of neoclassical phenomena on the radiated power profile are examined sequentially through the activation of individual physics modules in the code. Orbit squeezing and the neoclassical inward pinch result in increased radiation for temperatures above a few hundred eV and changes to the ratios of charge state emissions at a given electron temperature. Analogous simulations with a neon impurity yield qualitatively similar results.
Lorentz covariant canonical symplectic algorithms for dynamics of charged particles
In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSAs) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of a discrete symplectic structure and the Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which are difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when the Lorentz factor varies.
A family of new explicit, revertible, volume-preserving numerical schemes for the system of Lorentz force
The Lorentz system underlies the fundamental rules for the motion of charged particle in electromagnetic field, which is proved volume-preserving. In this paper, we construct a family of new revertible numerical schemes for general autonomous systems, which in particular, are explicit and volume-preserving for Lorentz systems. These new schemes can prevent the extra numerical errors caused by mismatched initial half-step values in the Boris-like algorithm. Numerical experiments demonstrate the superiorities of our second-order methods in long-term simulations and energy preservation over the Boris algorithm and a higher order Runge-Kutta method (RK3). We also apply these new methods to the guiding center system and find that they behave much better than RK3.
Kinetic simulations of scrape-off layer physics in the DIII-D tokamak
Simulations using the fully kinetic code XGCa were undertaken to explore the impact of kinetic effects on scrape-off layer (SOL) physics in DIII-D H-mode plasmas.
XGCa is a total-$f$, gyrokinetic code which self-consistently calculates the axisymmetric electrostatic potential and plasma dynamics, and includes modules for Monte Carlo neutral transport.
Fluid simulations are normally used to simulate the SOL, due to its high collisionality.
However, depending on plasma conditions, a number of discrepancies have been observed between experiment and leading SOL fluid codes (e.g. SOLPS), including underestimating outer target temperatures, radial electric field in the SOL, parallel ion SOL flows at the low field side, and impurity radiation.
Many of these discrepancies may be linked to the fluid treatment, and might be resolved by including kinetic effects in SOL simulations.
The XGCa simulation of the DIII-D tokamak in a nominally sheath-limited regime show many noteworthy features in the SOL.
The density and ion temperature are higher at the low-field side, indicative of ion orbit loss.
The SOL ion Mach flows are at experimentally relevant levels ($M_i ∼ 0.5$), with similar shapes and poloidal variation as observed in various tokamaks.
Surprisingly, the ion Mach flows close to the sheath edge remain subsonic, in contrast to the typical fluid Bohm criterion requiring ion flows to be above sonic at the sheath edge.
Related to this are the presence of elevated sheath potentials, $e\Delta\Phi/T_e\sim 3-4$, over most of the SOL, with regions in the near-SOL close to the separatrix having $e\Delta\Phi/T_e > 4$.
These two results at the sheath edge are a consequence of non-Maxwellian features in the ions and electrons there.
Effect of collisions on the two-stream instability in a finite length plasma
The instability of a monoenergetic electron beam in a collisional one-dimensional plasma bounded between grounded walls is considered both analytically and numerically. Collisions between electrons and neutrals are accounted for the plasma electrons only. Solution of a dispersion equation shows that the temporal growth rate of the instability is a decreasing linear function of the collision frequency which becomes zero when the collision frequency is two times the collisionless growth rate. This result is confirmed by fluid simulations. Practical formulas are given for the estimate of the threshold beam current which is required for the two-stream instability to develop for a given system length, neutral gas pressure, plasma density, and beam energy. Particle-in-cell simulations carried out with different neutral densities and beam currents demonstrate a good agreement with the fluid theory predictions for both the growth rate and the threshold beam current.
Scalable Visualization of Time-varying Multi-parameter Distributions Using Spatially Organized Histograms
Visualizing distributions from data samples as well as spatial and temporal trends of multiple variables is fundamental to analyzing the output of today's scientific simulations. However, traditional visualization techniques are often subject to a trade-off between visual clutter and loss of detail, especially in a large-scale setting. In this work, we extend the use of spatially organized histograms into a sophisticated visualization system that can more effectively study trends between multiple variables throughout a spatial domain. Furthermore, we exploit the use of isosurfaces to visualize time-varying trends found within histogram distributions. This technique is adapted into both an on-the-fly scheme as well as an in situ scheme to maintain real-time interactivity at a variety of data scales.
Numerical simulations of the Princeton magnetorotational instability experiment with conducting axial boundaries
We investigate numerically the Princeton magnetorotational instability (MRI) experiment and the effect of conducting axial boundaries or endcaps.
MRI is identified and found to reach a much higher saturation than for insulating endcaps.
This is probably due to stronger driving of the base flow by the magnetically rather than viscously coupled boundaries.
Although the computations are necessarily limited to lower Reynolds numbers (Re) than their experimental counterparts, it appears that the saturation level becomes independent of Re when Re is sufficiently large, whereas it has been found previously to decrease roughly as Re$^{−1/4}$ with insulating endcaps.
The much higher saturation levels will allow for the positive detection of MRI beyond its theoretical and numerical predictions.
The adjoint method for the study of runaway electron dynamics in momentum space Liu et al., [Phys. Plasmas 23, 010702 (2016)] is rederived using the Green's function method, for both the runaway probability function (RPF) and the expected loss time (ELT).
The RPF and ELT obtained using the adjoint method are presented, both with and without the synchrotron radiation reaction force.
The adjoint method is then applied to study the runaway electron avalanche. Both the critical electric field and the growth rate for the avalanche are calculated using this fast and novel approach.
Zonal-flow dynamics from a phase-space perspective
The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the
studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the
exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometricaloptics
limit. We derive a modified theory that takes both of these effects into account, while still
treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by
an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation
of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms
missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system,
in addition to the total energy, which is the only conserved invariant in previous theories based on
the WKE. Numerical simulations are presented to illustrate the importance of these additional
terms. The proposed formulation can be considered as a phase-space representation of the second order
cumulant expansion, or CE2.
Numerical simulations of the Princeton magnetorotational instability experiment with conducting axial boundaries
We investigate numerically the Princeton magnetorotational instability (MRI) experiment and the effect of conducting axial boundaries or endcaps. MRI is identified and found to reach a much higher saturation than for insulating endcaps. This is probably due to stronger driving of the base flow by the magnetically rather than viscously coupled boundaries. Although the computations are necessarily limited to lower Reynolds numbers ($Re$) than their experimental counterparts, it appears that the saturation level becomes independent of $Re$ when $Re$ is sufficiently large, whereas it has been found previously to decrease roughly as $Re^{-1/4}$ with insulating endcaps. The much higher saturation levels will allow for the positive detection of MRI beyond its theoretical and numerical predictions.
Local properties of magnetic reconnection in nonlinear resistive- and extended-magnetohydrodynamic toroidal simulations of the sawtooth crash
We diagnose local properties of magnetic reconnection during a sawtooth crash employing the three-dimensional toroidal, extended-magnetohydrodynamic (MHD) code M3D-C1. To do so, we sample simulation data in the plane in which reconnection occurs, the plane perpendicular to the helical $(m,n)=(1,1)$ mode at the $q = 1$ surface, where $m$ and $n$ are the poloidal and toroidal mode numbers and $q$ is the safety factor. We study the nonlinear evolution of a particular test equilibrium in a non-reduced field representation using both resistive-MHD and extended-MHD models. We find growth rates for the extended-MHD reconnection process exhibit a nonlinear acceleration and greatly exceed that of the resistive-MHD model, as is expected from previous experimental, theoretical, and computational work. We compare the properties of reconnection in the two simulations, revealing the reconnecting current sheets are locally different in the two models and we present the first observation of the quadrupole out-of-plane Hall magnetic field that appears during extended-MHD reconnection in a 3D toroidal simulation (but not in resistive-MHD). We also explore the dependence on toroidal angle of the properties of reconnection as viewed in the plane perpendicular to the helical magnetic field, finding qualitative and quantitative effects due to changes in the symmetry of the reconnection process. This study is potentially important for a wide range of magnetically confined fusion applications, from confirming simulations with extended-MHD effects are sufficiently resolved to describe reconnection, to quantifying local reconnection rates for purposes of understanding and predicting transport, not only at the $q = 1$ rational surface for sawteeth, but also at higher order rational surfaces that play a role in disruptions and edge-confinement degradation.
Dynamo-driven plasmoid formation from a current-sheet instability
Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations
during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry.
We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal
guide field. As helicity is injected, two types of current sheets are formed from (1) the oppositely
directed field lines in the injector region (primary reconnecting current sheet), and (2) the
poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetric
fluctuations arising from the current-sheet instability isolated near the plasma edge have
tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate
by breaking up the current sheet. Second, for the first time, a dynamo poloidal flux amplification
is observed at the reconnection site (in the region of the oppositely directed magnetic field).
This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers
a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids
formation driven by large-scale flux amplification, i.e., a large-scale dynamo, observed here
has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory
plasmas.
Structure of nonlocal gradient-drift instabilities in Hall E x B discharges
Gradient-drift (collisionless Simon-Hoh) instability is a robust instability often considered to be important for Hall plasma discharges supported by the electron current due to the ${\bf E} \times {\bf B}$ drift. Most of the previous studies of this mode were based on the local approximation. Here, we consider the nonlocal model which takes into account the electron inertia as well as the effects of the entire profiles of plasma parameters such as the electric, magnetic fields, and plasma density. Contrary to local models, nonlocal analysis predicts multiple unstable modes, which exist in the regions, where local instability criteria are not satisfied. This is especially pronounced for the long wavelength modes which provide larger contribution to the anomalous transport.
Local properties of magnetic reconnection in nonlinear resistive- and extended-magnetohydrodynamic toroidal simulations of the sawtooth crash
We diagnose local properties of magnetic reconnection during a sawtooth crash employing the three-dimensional toroidal, extended-magnetohydrodynamic (MHD) code M3D-$C^1$.
To do so, we sample simulation data in the plane in which reconnection occurs, the plane perpendicular to the helical $(m,n)$$=$$(1,1)$ mode at the $q=1$ surface, where $m$ and $n$ are the poloidal and toroidal mode numbers and $q$ is the safety factor.
We study the nonlinear evolution of a particular test equilibrium in a non-reduced field representation using both resistive-MHD and extended-MHD models.
We find growth rates for the extended-MHD reconnection process exhibit a nonlinear acceleration and greatly exceed that of the resistive-MHD model, as is expected from previous experimental, theoretical, and computational work.
We compare the properties of reconnection in the two simulations, revealing the reconnecting current sheets are locally different in the two models and we present the first observation of the quadrupole out-of-plane Hall magnetic field that appears during extended-MHD reconnection in a 3D toroidal simulation (but not in resistive-MHD).
We also explore the dependence on toroidal angle of the properties of reconnection as viewed in the plane perpendicular to the helical magnetic field, finding qualitative and quantitative effects due to changes in the symmetry of the reconnection process.
This study is potentially important for a wide range of magnetically confined fusion applications, from confirming simulations with extended-MHD effects are sufficiently resolved to describe reconnection, to quantifying local reconnection rates for purposes of understanding and predicting transport, not only at the $q=1$ rational surface for sawteeth, but also at higher order rational surfaces that play a role in disruptions and edge-confinement degradation.
We describe a quantitative model for heat separation in a fluid due to motion along a pressure gradient.
The physical model involved is relevant to one explanation for the temperature separation in a vortex
tube. This effect has a point of saturation in which the fluid’s temperature and pressure are related at
its boundaries by an adiabatic law. Vortex tube models sometimes assume that this saturation is achieved
in physical devices. We conclude that this is likely to be a safe assumption much of the time, but we
describe circumstances in which saturation might not be achieved. We propose a test of our model of
temperature separation.
Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures
The Landau collision integral is an accurate model for the small-angle dominated Coulomb collisions in fusion plasmas.
We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear multi-species Landau integral with adaptive mesh refinement using the PETSc library (www.mcs.anl.gov/petsc).
We develop algorithms and techniques to efficiently utilize emerging architectures with an approach that minimizes memory usage and movement and is suitable for vector processing.
The Landau collision integral is vectorized with Intel AVX-512 intrinsics and the solver sustains as much as 22% of the theoretical peak flop rate of the Second Generation Intel Xeon Phi, Knights Landing, processor.
Modeling of reduced effective secondary electron emission yield from a velvet surface
Complex structures on a material surface can significantly reduce total secondary electron emission from that surface. A velvet is a surface that consists of an array of vertically standing whiskers. The reduction occurs due to the capture of low-energy, true secondary electrons emitted at the bottom of the structure and on the sides of the velvet whiskers. We performed numerical simulations and developed an approximate analytical model that calculates the net secondary electron emission yield from a velvet surface as a function of the velvet whisker length and packing density, and the angle of incidence of primary electrons. We found that to suppress secondary electrons, the following condition on dimensionless parameters must be met: (π/2)DA tan θ≫1(π/2)DA tan θ≫1, where θ is the angle of incidence of the primary electron from the normal, D is the fraction of surface area taken up by the velvet whisker bases, and A is the aspect ratio, A ≡ h/r, the ratio of height to radius of the velvet whiskers. We find that velvets available today can reduce the secondary electron yield by 90% from the value of a flat surface. The values of optimal velvet whisker packing density that maximally suppresses the secondary electron emission yield are determined as a function of velvet aspect ratio and the electron angle of incidence.
Magnetorotational Turbulence and Dynamo in a Collisionless Plasma
We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and
dynamo, using the local shearing-box model of a collisionless accretion disk. The kinetic magnetorotational
instability grows from a subthermal magnetic field having zero net flux over the computational
domain to generate self-sustained turbulence and outward angular-momentum transport. Significant
Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned
ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through
particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is
biased with respect to the magnetic-field direction and spatiotemporally variable. Energy spectra suggest an
Alfvén-wave cascade at large scales and a kinetic-Alfvén-wave cascade at small scales, with strong smallscale
density fluctuations and weak nonaxisymmetric density waves. Ions undergo nonthermal particle
acceleration, their distribution accurately described by a κ distribution. These results have implications for
the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.
Validation and benchmarking of two particle-in-cell codes for a glow discharge
The two particle-in-cell codes EDIPIC and LSP are benchmarked and validated for a
parallel-plate glow discharge in helium, in which the axial electric field had been carefully
measured, primarily to investigate and improve the fidelity of their collision models. The
scattering anisotropy of electron-impact ionization, as well as the value of the secondaryelectron
emission yield, are not well known in this case. The experimental uncertainty for the
emission yield corresponds to a factor of two variation in the cathode current. If the emission
yield is tuned to make the cathode current computed by each code match the experiment,
the computed electric fields are in excellent agreement with each other, and within about
10% of the experimental value. The non-monotonic variation of the width of the cathode fall
with the applied voltage seen in the experiment is reproduced by both codes. The electron
temperature in the negative glow is within experimental error bars for both codes, but the
density of slow trapped electrons is underestimated. A more detailed code comparison done
for several synthetic cases of electron-beam injection into helium gas shows that the codes are
in excellent agreement for ionization rate, as well as for elastic and excitation collisions with
isotropic scattering pattern. The remaining significant discrepancies between the two codes are
due to differences in their electron binary-collision models, and for anisotropic scattering due
to elastic and excitation collisions.
Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams
In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the
basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the
analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several
decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations
by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV
model by including all of the linear (both external and space-charge) coupling forces, beam energy
variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations.
The new generalized KV model yields spatially uniform density profiles and corresponding linear
self-field forces as desired. The corresponding matrix envelope equations and beam matrix for the
generalized KV model provide important new theoretical tools for the detailed design and analysis of
high-intensity beam manipulations, for which previous theoretical models are not easily applicable.
Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. The results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturates due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. A substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.
Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma
This paper presents a study of the two-stream instability of an electron beam propagating in a finite-size plasma placed between two electrodes. It is shown that the growth rate in such a system is much smaller than that of an infinite plasma or a finite size plasma with periodic boundary conditions.
Even if the width of the plasma matches the resonance condition for a standing wave, a spatially growing wave is excited instead with the growth rate small compared to that of the standing wave in a periodic system.
The approximate expression for this growth rate is
$γ$ $\approx$ $(1/13)$ $\omega_{pe}(n_b/n_p)$ $(L\omega_{pe}/v_b)$ $\ln(L \omega_{pe}/v_b)$ $[1−0.18 \cos (L \omega_{pe}/v_b+\pi/2)]$ $γ$ $≈$ $(1/13)$ $\omega_{pe}(n_b/n_p)$ $(L \omega_{pe}/v_b)$ $ln(L \omega_{pe}/v_b)$ $[1−0.18 cos (L \omega_{pe}/v_b+π/2)]$, where $\omega_{pe}$ is the electron plasma frequency, $n_b$ and $n_p$ are the beam and the plasma densities, respectively, $v_b$ is the beam velocity, and $L$ is the plasma width. The frequency, wave number, and the spatial and temporal growth rates, as functions of the plasma size, exhibit band structure. The amplitude of saturation of the instability depends on the system length, not on the beam current. For short systems, the amplitude may exceed values predicted for infinite plasmas by more than an order of magnitude.
Open problems of magnetic island control by electron cyclotron current drive
This paper reviews key aspects of the problem of magnetic islands control by
electron cyclotron current drive in fusion devices. On the basis of the ordering of
the basic spatial and time scales of the magnetic reconnection physics, we present
the established results, highlighting some of the open issues posed by the small-scale
structures that typically accompany the nonlinear evolution of the magnetic islands
and constrain the effect of the control action.
Verification of the SPEC code in stellarator geometries
We present the first calculations performed with the Stepped-Pressure Equilibrium Code (SPEC) in stellarator geometry. Provided a boundary magnetic surface, stellarator vacuum fields with islands are computed and verified to machine precision, for both a classical $l = 2$ stellarator field and a Wendelstein 7-X limiter configuration of the first experimental campaign. Beyond verification, a detailed comparison of SPEC solutions to Biot-Savart solutions for the corresponding coil currents is shown. The level of agreement is quantified, and the error is shown to be dominated by the accuracy with which the boundary representation is given. Finally, partially relaxed stellarator equilibria are computed with SPEC, and verification is presented with force-balance down to machine precision.
An advection–diffusion model for cross-field runaway electron transport in perturbed magnetic fields
Disruption-generated runaway electrons (RE) present an outstanding issue for ITER. The predictive computational studies of RE generation rely on orbit-averaged computations and, as such, they lack the effects from the magnetic field stochasticity. Since stochasticity is naturally present in post-disruption plasma, and externally induced stochastization offers a prominent mechanism to mitigate RE avalanche, we present an advection–diffusion model that can be used to couple an orbit-following code to an orbit-averaged tool in order to capture the cross-field transport and to overcome the latter's limitation. The transport coefficients are evaluated via a Monte Carlo method. We show that the diffusion coefficient differs significantly from the well-known Rechester–Rosenbluth result. We also demonstrate the importance of including the advection: it has a two-fold role both in modelling transport barriers created by magnetic islands and in amplifying losses in regions where the islands are not present.
Open problems of magnetic island control by electron cyclotron current drive
This paper reviews key aspects of the problem of magnetic islands control by electron cyclotron current drive in fusion devices. On the basis of the ordering of the basic spatial and time scales of the magnetic reconnection physics, we present the established results, highlighting some of the open issues posed by the small-scale structures that typically accompany the nonlinear evolution of the magnetic islands and constrain the effect of the control action.
Fluid theory and simulations of instabilities, turbulent transport and coherent structures in partially-magnetized plasmas of E x B discharges
Partially-magnetized plasmas with magnetized electrons and non-magnetized ions are common in Hall thrusters for electric propulsion and magnetron material processing devices. These plasmas are usually in strongly non-equilibrium state due to presence of crossed electric and magnetic fields, inhomogeneities of plasma density, temperature, magnetic field and beams of accelerated ions. Free energy from these sources make such plasmas prone to various instabilities resulting in turbulence, anomalous transport, and appearance of coherent structures as found in experiments. This paper provides an overview of instabilities that exist in such plasmas. A nonlinear fluid model has been developed for description of the Simon-Hoh, lower-hybrid and ion-sound instabilities. The model also incorporates electron gyroviscosity describing the effects of finite electron temperature. The nonlinear fluid model has been implemented in the BOUT++ framework. The results of nonlinear simulations are presented demonstrating turbulence, anomalous current and tendency toward the formation of coherent structures.
Compressing turbulence and sudden viscous dissipation with compression-dependent ionization state
Turbulent plasma flow, amplified by rapid three-dimensional compression, can be suddenly dissipated under
continuing compression. This effect relies on the sensitivity of the plasma viscosity to the temperature,
$\mu ∼ T^{5/2}$. The plasma viscosity is also sensitive to the plasma ionization state. We show that the sudden
dissipation phenomenon may be prevented when the plasma ionization state increases during compression, and
we demonstrate the regime of net viscosity dependence on compression where sudden dissipation is guaranteed.
Additionally, it is shown that, compared to cases with no ionization, ionization during compression is associated
with larger increases in turbulent energy and can make the difference between growing and decreasing turbulent
energy.
Experiences of Applying One-Sided Communication to Nearest-Neighbor Communication
Nearest-neighbor communication is one of the most
important communication patterns appearing in many scientific
applications. In this paper, we discuss the results of applying
UPC++, a library-based partitioned global address space (PGAS)
programming extension to C++, to an adaptive mesh framework
(BoxLib), and a full scientific application GTC-P, whose communications
are dominated by the nearest-neighbor communication.
The results on a Cray XC40 system show that compared with the
highly-tuned MPI two-sided implementations, UPC++ improves
the communication performance up to 60% and 90% for BoxLib
and GTC-P, respectively. We also implement the nearest-neighbor
communication using MPI one-sided messages. The performance
comparison demonstrates that the MPI one-sided implementation
can also improve the communication performance over the twosided
version but not so significantly as UPC++ does.
Ion gyroradius effects on particle trapping in kinetic Alfvén waves along auroral ﬁeld lines
In this study, a 2-D self-consistent hybrid gyroﬂuid-kinetic electron model is used to investigate Alfvén wave propagation along dipolar magnetic ﬁeld lines for a range of ion to electron temperature ratios.
The focus of the investigation is on understanding the role of these eﬀects on electron trapping in kinetic Alfvén waves sourced in the plasma sheet and the role of this trapping in contributing to the overall electron energization at the ionosphere.
This work also builds on our previous eﬀort by considering a similar system in the limit of ﬁxed initial parallel current, rather than ﬁxed initial perpendicular electric ﬁeld.
It is found that the eﬀects of particle trapping are strongest in the cold ion limit and the kinetic Alfvén wave is able to carry trapped electrons a large distance along the ﬁeld line yielding a relatively large net energization of the trapped electron population as the phase speed of the wave is increased.
However, as the ion temperature is increased, the ability of the kinetic Alfvén wave to carry and energize trapped electrons is reduced by more signiﬁcant wave energy dispersion perpendicular to the ambient magnetic ﬁeld which reduces the amplitude of the wave.
This reduction of wave amplitude in turn reduces both the parallel current and the extent of the high-energy tails evident in the energized electron populations at the ionospheric boundary (which may serve to explain the limited extent of the broadband electron energization seen in observations).
Even in the cold ion limit, trapping eﬀects in kinetic Alfvén waves lead to only modest electron energization for the parameters considered (on the order of tens of eV) and the primary energization of electrons to keV levels coincides with the arrival of the wave at the ionospheric boundary.
Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed.
The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh.
With the assistance of Whitney interpolating forms [H. Whitney, Geometric Integration Theory (Princeton University Press, 1957); M. Desbrun et al., Discrete Differential Geometry (Springer, 2008); J. Xiao et al., Phys. Plasmas 22, 112504 (2015)], this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy.
The whole system is solved using the Hamiltonian splitting method discovered by He et al., [Phys. Plasmas 22, 124503 (2015)], which was been successfully adopted in constructing symplectic particle-in-cell schemes
[J. Xiao et al., Phys. Plasmas 22, 112504 (2015)].
Because of its structure preserving and explicit nature, this algorithm is especially suitable for large-scale simulations for physics problems that are multi-scale and require long-term fidelity and accuracy.
The algorithm is verified via two tests: studies of the dispersion relation of waves in a two-fluid plasma system and the oscillating two-stream instability.
Numerical simulations have consistently shown that the reconnection rate in certain collisionless regimes can be fast, of the order of $0.1\nu_A B_u$, where $\nu_A$ and $B_u$ are the Alfvén speed and the reconnecting magnetic field upstream of the ion diffusion region.
This particular value has been reported in myriad numerical simulations under disparate conditions.
However, despite decades of research, the reasons underpinning this specific value remain mysterious.
Here, we present an overview of this problem and discuss the conditions under which the ‘0.1 value’ is attained.
Furthermore, we explain why this problem should be interpreted in terms of the ion diffusion region length.
Extreme Scale Plasma Turbulence Simulations on Top Supercomputers Worldwide
The goal of the extreme scale plasma turbulence studies described in this paper is to expedite the delivery of reliable predictions on confinement physics in large magnetic fusion systems by using world-class supercomputers to carry out simulations with unprecedented resolution and temporal duration. This has involved architecture-dependent optimizations of performance scaling and addressing code portability and energy issues, with the metrics for multi-platform comparisons being “time-to-solution” and “energy-to-solution”. Realistic results addressing how confinement losses caused by plasma turbulence scale from present-day devices to the much larger $25 billion international ITER fusion facility have been enabled by innovative advances in the GTC-P code including (i) implementation of one-sided communication from MPI 3.0 standard; (ii) creative optimization techniques on Xeon Phi processors; and (iii) development of a novel performance model for the key kernels of the PIC code. Results show that modeling data movement is sufficient to predict performance on modern supercomputer platforms.
Energetic particle-driven compressional Alfvén eigenmodes and prospects for ion cyclotron emission studies in fusion plasmas
As a fundamental plasma oscillation the compressional Alfvén waves(CAWs) are interesting for
plasma scientists both academically and in applications for fusion plasmas. They are believed to be
responsible for the ion cyclotron emission (ICE) observed in many tokamaks. The theory of CAW and
ICE was significantly advanced at the end of 20th century in particular motivated by first DT
experiments on TFTR and subsequent JET DT experimental studies. More recently, ICE theory was
advanced by ST (or spherical torus) experiments with the detailed theoretical and experimental studies
of the properties of each instability signal. There the instability responsible for ICE signals previously
indistinguishable in high aspect ratio tokamaks became the subjects of experimental studies. We
discuss further the prospects of ICE theory and its applications for future burning plasma experiments
such as the ITER tokamak-reactor prototype being build in France where neutrons and gamma rays
escaping the plasma create extremely challenging conditions for fusion alpha particle diagnostics.
Impact of ideal MHD stability limits on high-beta hybrid operation
The hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in
ITER and DEMO. To obtain such performance, the energy confinement and the normalized
pressure $\beta_N$ must be maximized, which requires operating near or above ideal MHD no-wall
limits. New experimental findings show how these limits can affect hybrid operation. Even
if hybrids are mainly limited by tearing modes, proximity to the no-wall limit leads to 3D
field amplification that affects plasma profiles, e.g. rotation braking is observed in ASDEX
Upgrade throughout the plasma and peaks in the core. As a result, even the small ASDEX
Upgrade error fields are amplified and their effects become visible. To quantify such effects,
ASDEX Upgrade measured the response to 3D fields applied by 8×2 non-axisymmetric coils
as $\beta_N$ approaches the no-wall limit. The full n = 1 response profile and poloidal structure were
measured by a suite of diagnostics and compared with linear MHD simulations, revealing
a characteristic feature of hybrids: the n = 1 response is due to a global, marginally-stable
n = 1 kink characterized by a large m = 1, n = 1 core harmonic due to qmin being just above
1. A helical core distortion of a few cm forms and affects various core quantities, including
plasma rotation, electron and ion temperature, and intrinsic W density. In similar experiments,
DIII-D also measured the effect of this helical core on the internal current profile, providing
information useful to understanding of the physics of magnetic flux pumping, i.e. anomalous
current redistribution by MHD modes that keeps qmin>1. Thanks to flux pumping, a broad
current profile is maintained in DIII-D even with large on-axis current drive, enabling fully
non-inductive operation at high $\beta_N$ up to 3.5–4.
Nonlinear asymmetric tearing mode evolution in cylindrical geometry
The growth of a tearing mode is described by reduced MHD equations.
For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the
nonlinear $\Delta^\prime(\omega)$.
For a low beta plasma without external heating, $\Delta^\prime(\omega)$ can be approximately
described by two terms, $\Delta^\prime_{ql}(\omega)$, $\Delta^\prime_A(\omega)$
[White et al., Phys. Fluids 20, 800 (1977);
Phys. Plasmas 22, 022514 (2015)].
In this work, we present a simple method to calculate the quasilinear stability
index $\Delta^\prime_{ql}$ rigorously, for poloidal mode number $m \ge 2$.
$\Delta^\prime_{ql}(\omega)$ is derived by solving the outer equation through the Frobenius method.
$\Delta^\prime_{ql}$ is composed of four terms proportional to: constant $\Delta^\prime_{0}$, $\omega$, $\omega \ln \omega$ and $\omega^2$.
$\Delta^\prime_{A}(\omega)$ is proportional to the asymmetry of island that is roughly proportional to $\omega$.
The sum of $\Delta^\prime_{ql}(\omega)$ and $\Delta^\prime_{A}(\omega)$ is consistent with the more accurate expression calculated perturbatively
[Arcis et al., Phys. Plasmas 13, 052305 (2006)].
The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)].
The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results.
It is also confirmed by the simulation that the $\Delta^\prime_{A}(\omega)$ has to be considered in calculating island saturation.
Collisional dependence of Alfvén mode saturation in tokamaks
Saturation of Alfvén modes driven unstable by a distribution of high energy particles as a function of collisionality is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and numerical high energy particle distributions. The most important resonance is found and it is shown that when the resonance domain is bounded, not allowing particles to collisionlessly escape, the saturation amplitude is given by the balance of the resonance mixing time with the time for nearby particles to collisionally diffuse across the resonance width. Saturation amplitudes are in agreement with theoretical predictions as long as the mode amplitude is not so large that it produces stochastic loss from the resonance domain.
Protecting ITER walls: fast ion power loads in 3D magnetic field
The fusion alpha and beam ion with steady-state power loads in all four main operating
scenarios of ITER have been evaluated by the ASCOT code. For this purpose, high-fidelity
magnetic backgrounds were reconstructed, taking into account even the internal structure
of the ferritic inserts and tritium breeding modules (TBM). The beam ions were found to be
almost perfectly confined in all scenarios, and only the so-called hybrid scenario featured
alpha loads reaching 0.5 MW due to its more triangular plasma. The TBMs were not found
to jeopardize the alpha confinement, nor cause any hot spots. Including plasma response did
not bring dramatic changes to the load. The ELM control coils (ECC) were simulated in the
baseline scenario and found to seriously deteriorate even the beam confinement. However, the
edge perturbation in this case is so large that the sources have to be re-evaluated with plasma
profiles that take into account the ECC perturbation.
Linear Vlasov theory of a magnetised, thermally stratified atmosphere
The stability of a collisionless, magnetised plasma to local convective disturbances is examined, with a focus on kinetic and finite-Larmor-radius effects. Specific application is made to the outskirts of galaxy clusters, which contain hot and tenuous plasma whose temperature increases in the direction of gravity. At long wavelengths (the ‘drift-kinetic’ limit), we obtain the kinetic version of the magnetothermal instability (MTI) and its Alfvénic counterpart (Alfvénic MTI), which were previously discovered and analysed using a magnetofluid (i.e. Braginskii) description. At sub-ion-Larmor scales, we discover an overstability driven by the electron-temperature gradient of kinetic-Alfvén drift waves – the electron MTI (eMTI) – whose growth rate is even larger than the standard MTI. At intermediate scales, we find that ion finite-Larmor-radius effects tend to stabilise the plasma. We discuss the physical interpretation of these instabilities in detail, and compare them both with previous work on magnetised convection in a collisional plasma and with temperature-gradient-driven drift-wave instabilities well known to the magnetic-confinement-fusion community. The implications of having both fluid and kinetic scales simultaneously driven unstable by the same temperature gradient are briefly discussed.
A spinning gas, heated adiabatically through axial compression, is known to exhibit a rotation-dependent heat
capacity. However, as equilibrium is approached, an effect is identified here wherein the temperature does not
grow homogeneously in the radial direction, but develops a temperature differential with the hottest region on
axis, at the maximum of the centrifugal potential energy. This phenomenon, which we call a piezothermal effect,
is shown to grow bilinearly with the compression rate and the amplitude of the potential. Numerical simulations
confirm a simple model of this effect, which can be generalized to other forms of potential energy and methods
of heating.
Runaway electron mitigation by applied magnetic perturbations in RFX-mod tokamak plasmas
Thanks to its advanced system for the control of magnetohydrodynamic modes, the RFX-mod device run as a tokamak is particularly suited to the study of the possible impact on runaway electron (RE) de-confinement in response to applied magnetic perturbations.
This paper shows that during the flat-top phase in RFX-mod discharges, with a plasma current of ${{I}_{\text{p}}}\sim 150$ kA and a low density (${{n}_{\text{e}}}<{{10}^{19}}$ m−3), the amount of REs scales with the $m=2$, $n=1$ perturbation both in $q(a)<2$ and $q(a)>2$ plasmas.
Similar results have also been obtained in post-disruption phases, but still with limited statistics.
The mechanisms generating REs and the effect of magnetic perturbation (MP) on their confinement are interpreted by numerical simulations with the relativistic guiding center code ORBIT.
The role played by different magnetic equilibria on the energy of REs and on their loss rates is investigated.
ORBIT simulations indicate that RE-enhanced losses are associated with a raised level of stochasticity, the effect being more pronounced when the MP amplitude is higher and internally resonant.
Reducing parametric backscattering by polarization rotation,
When a laser passes through underdense plasmas, Raman and Brillouin Backscattering can reflect a
substantial portion of the incident laser energy. This is a major loss mechanism, for example, in
employing lasers in inertial confinement fusion. However, by slow rotation of the incident linear
polarization, the overall reflectivity can be reduced significantly. Particle in cell simulations show
that, for parameters similar to those of indirect drive fusion experiments, polarization rotation
reduces the reflectivity by a factor of 5. A general, fluid-model based analytical estimation for the
reflectivity reduction agrees with simulations. However, in identifying the source of the backscatter
reduction, it is difficult to disentangle the rotating polarization from the frequency separation based
approach used to engineer the beam’s polarization. Although the backscatter reduction arises similarly
to other approaches that employ frequency separation, in the case here, the intensity remains
constant in time.
A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time.
The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids are derived and shown to depend on the initial
perturbation amplitude $(\hat w_0)$, the characteristic rate of current sheet evolution $(1/\tau)$, and the Lundquist number $(S)$.
They are not simple power laws, and are proportional to $S^\alpha \tau^\beta [\ln f(S,\tau,\hat w)]^\sigma$.
The detailed dynamics of the instability is also elucidated, and shown to comprise of a period of
quiescence followed by sudden growth over a short time scale.
Electron energy enhancement by frequency chirp of a radially polarized laser pulse during ionization of low density gases
A scheme is proposed to enhance the energy of the electrons generated during the ionization
of low-density krypton ions Kr$^{32+}$ and argon ions Ar$^{16+}$ by a radially polarized laser pulse
using a negative frequency chirp. If a suitable frequency chirp is introduced then the energy
of the electrons increases significantly and scattering decreases. The optimum value of the
frequency chirp decreases with laser intensity and as well as spot size. The laser spot size
also has an optimum value. The electron energy shows strong initial phase dependence. The
scheme can be used to obtain quasi-monoenergetic collimated MeV/GeV electrons using the
right choice of parameters. The chirped radially polarized laser pulse is more efficient than
a chirped circularly polarized laser pulse to enhance energy and obtain quasi-monoenergetic
electron beams.
Information theoretical approach to discovering solar wind drivers of the outer radiation belt
The solar wind-magnetosphere system is nonlinear.
The solar wind drivers of geosynchronouselectrons with energy range of 1.8–3.5 MeV are investigated using mutual information, conditional mutualinformation (CMI), and transfer entropy (TE). These information theoretical tools can establish linear andnonlinear relationships as well as information transfer.
The information transfer from solar wind velocity ($V_{sw}$)to geosynchronous MeV electron ﬂux ($J_e$) peaks with a lag time of 2 days. As previously reported, $J_e$ is anticorrelated with solar wind density ($n_{sw}$) with a lag of 1 day.
However, this lag time and anticorrelation can be attributed at least partly to the $J_e$(t + 2 days) correlation with $V_{sw}(t)$ and $n_{sw}$(t + 1 day) anticorrelation with $V_{sw}(t)$. Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days,in the ($V_{sw}$, $n_{sw}$) anticorrelation.
Using CMI to remove the effects of $V_{sw}$, the response of $J_e$ to $n_{sw}$ is 30% smaller and has a lag time < 24 h,
suggesting that the MeV electron loss mechanism due to $n_{sw}$ or solar wind dynamic pressure has to start operating in < 24 h.
$n_{sw}$ transfers about 36% as much information as $V_{sw}$ (the primary driver) to $J_e$.
Nonstationarity in the system dynamics is investigated using windowed TE. When thedata are ordered according to transfer entropy value, it is possible to understand details of the triangle distribution that has been identiﬁed between $J_e$(t + 2 days) versus $V_{sw}$(t).
Approach to Chandrasekhar-Kendall-Woltjer state in a chiral plasma
We study the time evolution of the magnetic field in a plasma with a chiral magnetic current. The vector spherical harmonic (VSH) functions are used to expand all fields. We define a measure for the Chandrasekhar-Kendall-Woltjer (CKW) state, which has a simple form in VSH expansion. We propose the conditions for a general class of initial momentum spectra that will evolve into the CKW state. For this class of initial conditions, to approach the CKW state, (i) a nonvanishing chiral magnetic conductivity is necessary, and (ii) the time integration of the product of the electric resistivity and chiral magnetic conductivity must grow faster than the time integration of the resistivity. We give a few examples to test these conditions numerically, which work very well.
A simple model for estimating a magnetic field in laser-driven coils
Magnetic field generation by laser-driven coils is a promising way of magnetizing plasma in
laboratory high-energy-density plasma experiments. A typical configuration consists of two electrodes—one
electrode is irradiated with a high-intensity laser beam and another electrode collects
charged particles from the expanding plasma. The two electrodes are separated by a narrow gap
forming a capacitor-like configuration and are connected with a conducting wire-coil. The chargeseparation
in the expanding plasma builds up a potential difference between the electrodes that
drives the electrical current in the coil. A magnetic field of tens to hundreds of Teslas generated
inside the coil has been reported. This paper presents a simple model that estimates the magnetic
field using simple assumptions. The results are compared with the published experimental data.
Ion gyroscale fluctuation measurement with microwave imaging reflectometer on KSTAR
Ion gyroscale turbulent fluctuations with the poloidal wavenumber $k_\theta \sim 3 cm^{−1}$ have been measured
in the core region of the neutral beam (NB) injected low confinement (L-mode) plasmas on Korea
superconducting tokamak advanced research. The turbulence poloidal wavenumbers are deduced
from the frequencies and poloidal rotation velocities in the laboratory frame, measured by the multichannel
microwave imaging reflectometer. Linear and nonlinear gyrokinetic simulations also predict
the unstable modes with the normalized wavenumber $k_\theta \rho_s \sim 0.4$, consistent with the measurement.
Comparison of the measured frequencies with the intrinsic mode frequencies from the linear simulations
indicates that the measured ones are primarily due to the E × B flow velocity in the NB-injected
fast rotating plasmas.
Evidence of Toroidally Localized Turbulence with Applied 3D Fields in the DIII-D Tokamak
New evidence indicates that there is significant 3D variation in density fluctuations near the boundary
of weakly 3D tokamak plasmas when resonant magnetic perturbations are applied to suppress transient
edge instabilities. The increase in fluctuations is concomitant with an increase in the measured density
gradient, suggesting that this toroidally localized gradient increase could be a mechanism for turbulence
destabilization in localized flux tubes. Two-fluid magnetohydrodynamic simulations find that, although
changes to the magnetic field topology are small, there is a significant 3D variation of the density gradient
within the flux surfaces that is extended along field lines. This modeling agrees qualitatively with the
measurements. The observed gradient and fluctuation asymmetries are proposed as a mechanism by which
global profile gradients in the pedestal could be relaxed due to a local change in the 3D equilibrium. These
processes may play an important role in pedestal and scrape-off layer transport in ITER and other future
tokamak devices with small applied 3D fields.
The role of the Hall term on large-scale dynamo action is investigated by means of the first-order smoothing approximation. It is shown that the standard α coefficient is altered, and is zero when a specific double Beltrami state is attained, in contrast to the Alfvénic state for magnetohydrodynamical dynamos. The β coefficient is no longer positive definite, and thereby enables dynamo action even if α-quenching were to operate. The similarities and differences with the (magnetic) shear-current effect are pointed out, and a mechanism that may be potentially responsible for $\beta \lt 0$ is advanced. The results are compared against previous studies, and their astrophysical relevance is also highlighted.
Experimental evidence of edge intrinsic momentum source driven by kinetic ion loss and edge radial electric fields in tokamaks
Bulk ion toroidal velocity profiles, $\nu_\parallel^{D+}$, peaking at 40–60 km/s are observed with Mach probes in a
narrow edge region of DIII-D discharges without external momentum input. This intrinsic rotation can
be well reproduced by a first principle, collisionless kinetic loss model of thermal ion loss that predicts
the existence of a loss-cone distribution in velocity space resulting in a co-Ip directed velocity. We consider
two kinetic models, one of which includes turbulence-enhanced momentum transport, as well as
the Pfirsch-Schluter (P-S) fluid mechanism. We measure a fine structure of the boundary radial electric
field, Er, insofar ignored, featuring large (10–20 kV/m) positive peaks in the scrape off layer (SOL) at,
or slightly inside, the last closed flux surface of these low power L- and H-mode discharges in DIII-D.
The Er structure significantly affects the ion-loss model, extended to account for a non-uniform electric
field. We also find that VDþ
jj is reduced when the magnetic topology is changed from lower single null
to upper single null. The kinetic ion loss model containing turbulence-enhanced momentum transport
can explain the reduction, as we find that the potential fluctuations decay with radius, while we need to
invoke a topology-enhanced collisionality on the simpler kinetic model. The P-S mechanism fails to
reproduce the damping. We show a clear correlation between the near core VC6þ
jj velocity and the peak
edge VDþ
jj in discharges with no external torque, further supporting the hypothesis that ion loss is the
source for intrinsic torque in the present tokamaks. However, we also show that when external torque
is injected in the core, it can complete with, and eventually overwhelm, the edge source, thus determining
the near SOL flows. Finally, we show some additional evidence that the ion/electron distribution in
the SOL is non-Maxwellian
High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracy-enhancing processing technique, the explicit methods obtain high-order accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations.
Growth of Alfvén modes driven unstable by a distribution of high energy particles up to saturation is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and a numerical high energy particle distribution, in order to make detailed comparison with experiment and with models for saturation amplitudes and the modification of beam profiles. Two innovations are introduced. First, a very noise free means of obtaining the mode-particle energy and momentum transfer is introduced, and secondly, a spline representation of the actual beam particle distribution is used.
Extended propagation of powerful laser pulses in focusing Kerr media
Powerful incoherent laser pulses can propagate in focusing Kerr media much longer distances than can
coherent pulses, due to the fast phase mixing that prevents transverse filamentation. This distance is limited
by 4-wave scattering, which accumulates waves at small transverse wave numbers, where phase mixing is
too slow to retain the incoherence and thus prevent the filamentation. However, we identify how this
theoretical limit can be overcome by countering this accumulation through transverse heating of the pulse
by random fluctuations of the refractive index. Thus, the laser pulse propagation distances are significantly
extended, making feasible, in particular, the generation of unprecedentedly intense and powerful short laser
pulses in a plasma by means of backward Raman amplification in new random laser regimes.
Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
In this paper, we study the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semi-discrete system that possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nédélec's mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semi-discrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. The structure-preserving nature of the algorithm ensures accuracy and fidelity of the numerical simulations over long time.
Action principle for Coulomb collisions in plasmas
An action principle for Coulomb collisions in plasmas is proposed. Although no natural
Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is
found considering the system of partial differential equations that couple the distribution function
and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing
the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle
population in a given plasma background, the action principle is shown to correspond to the
Langevin equation for individual particles.
Deep nightside photoelectron observations by MAVEN SWEA: Implications for Martian northern hemispheric magnetic topology and nightside ionosphere source
The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission samples the Mars ionosphere down to altitudes of ∼150 km over a wide range of local times and solar zenith angles.
On 5 January 2015 (Orbit 520) when the spacecraft was in darkness at high northern latitudes (solar zenith angle, SZA >120°; latitude >60°), the Solar Wind Electron Analyzer (SWEA) instrument observed photoelectrons at altitudes below 200 km.
Such observations imply the presence of closed crustal magnetic field loops that cross the terminator and extend thousands of kilometers to the deep nightside.
This occurs over the weak northern crustal magnetic source regions, where the magnetic field has been thought to be dominated by draped interplanetary magnetic fields (IMF).
Such a day-night magnetic connectivity also provides a source of plasma and energy to the deep nightside.
Simulations with the SuperThermal Electron Transport (STET) model show that photoelectron fluxes measured by SWEA precipitating onto the nightside atmosphere provide a source of ionization that can account for the $O_2^+$ density measured by the Suprathermal and Thermal Ion Composition (STATIC) instrument below 200 km.
This finding indicates another channel for Martian energy redistribution to the deep nightside and consequently localized ionosphere patches and potentially aurora.
Harmonic generation under small signal conditions in a traveling wave tube
In a klystron, charge overtaking of electrons leads to an infinity of AC current.
The harmonic content therein can be calculated exactly, with or without space charge effects.
This paper extends the klystron theory to a traveling wave tube (TWT).
We assume that the electron motion is described by linear theory. The crowding of these
linear orbits may lead to harmonic generation, as in a
klystron. We calculate the buildup of harmonic content as a
function of distance from the input, and compare these
analytic results with the CHRISTINE code. Reasonable
agreement was found. A dimensionless “bunching parameter” for TWT, $x = \sqrt{2 P_{in}/(P_bC)}$, is identified, which
characterizes the harmonic content in the AC current, where
$P_{in}$ is the power of the input signal, $P_b$ is the DC beam power,
and $C$ is Pierce’s gain parameter.
A Synthetic Diagnostics Platform (SDP) for fusion plasmas has been developed which provides state of the art synthetic reflectometry, beam emission spectroscopy, and Electron Cyclotron Emission (ECE) diagnostics. Interfaces to the plasma simulation codes GTC, XGC-1, GTS, and M3D-C1 are provided, enabling detailed validation of these codes. In this paper, we give an overview of SDP’s capabilities, and introduce the synthetic diagnostic modules. A recently developed synthetic ECE Imaging module which self-consistently includes refraction, diffraction, emission, and absorption effects is discussed in detail. Its capabilities are demonstrated on two model plasmas. The importance of synthetic diagnostics in validation is shown by applying the SDP to M3D-C1 output and comparing it with measurements from an edge harmonic oscillation mode on DIII-D.
Laboratory Observation of Resistive Electron Tearing in a Two-Fluid Reconnecting Current Sheet
The spontaneous formation of plasmoids via the resistive electron tearing of a reconnecting current sheet is observed in the laboratory. These experiments are performed during driven, antiparallel reconnection in the two-fluid regime within the Magnetic Reconnection Experiment. It is found that plasmoids are present even at a very low Lundquist number, and the number of plasmoids scales with both the current sheet aspect ratio and the Lundquist number. The reconnection electric field increases when plasmoids are formed, leading to an enhanced reconnection rate.
High-Flux Femtosecond X-Ray Emission from Controlled Generation of Annular Electron Beams in a Laser Wakefield Accelerator
Annular quasimonoenergetic electron beams with a mean energy in the range 200–400 MeV and charge on the order of several picocoulombs were generated in a laser wakefield accelerator and subsequently accelerated using a plasma afterburner in a two-stage gas cell. Generation of these beams is associated with injection occurring on the density down ramp between the stages. This well-localized injection produces a bunch of electrons performing coherent betatron oscillations in the wakefield, resulting in a significant increase in the x-ray yield. Annular electron distributions are detected in 40% of shots under optimal conditions. Simultaneous control of the pulse duration and frequency chirp enables optimization of both the energy and the energy spread of the annular beam and boosts the radiant energy per unit charge by almost an order of magnitude. These well-defined annular distributions of electrons are a promising source of high-brightness laser plasma-based x rays.
Short-Pulse Amplification by Strongly-Coupled Brillouin Scattering,
We examine the feasibility of strongly coupled stimulated Brillouin scattering as a mechanism for
the plasma-based amplification of sub-picosecond pulses. In particular, we use fluid theory and particle-in-cell
simulations to compare the relative advantages of Raman and Brillouin amplification
over a broad range of achievable parameters.
Towards Real-Time Detection and Tracking of Blob-Filaments in Fusion Plasma Big Data
A novel algorithm and implementation of real-time identification and tracking of blob-filaments in fusion reactor data is presented. Similar spatio-temporal features are important in many other applications, for example, ignition kernels in combustion and tumor cells in a medical image. This work presents an approach for extracting these features by dividing the overall task into three steps: local identification of feature cells, grouping feature cells into extended feature, and tracking movement of feature through overlapping in space. Through our extensive work in parallelization, we demonstrate that this approach can effectively make use of a large number of compute nodes to detect and track blob-filaments in real time in fusion plasma. On a set of 30 GB fusion simulation data, we observed linear speedup on 1,024 processes and completed blob detection in less than three milliseconds using Edison, a Cray XC30 system at NERSC.
A reduced fluid model of Raman backscattering is proposed that describes backward Raman amplification (BRA) of pulses with duration s0 comparable to or even smaller than the plasma period $2\pi/\omega_p$.
At such a small $\tau_0$, a seed pulse can be amplified even if it has the same frequency
as the pump (which is technologically advantageous), as opposed to that satisfying the Raman
resonance condition. Using our theoretical model, we numerically calculate the BRA efficiency for
such pulses as a function of s0 and show that it remains reasonably high up to $\tau_0 \approx 2\pi/\omega_p$. We also
show that using short seed pulses in BRA makes the amplification less sensitive to quasistatic
inhomogeneities of the plasma density. Amplification can persist even when the density
perturbations are large enough to violate the commonly known condition of resonant amplification.
Analyzing Large Data Sets from XGC1 Magnetic Fusion Simulations Using Apache Spark
Apache Spark is explored as a tool for analyzing large data sets from the magnetic fusion simulation code XGC1. Implementation details of Apache Spark on the NERSC Edison supercomputer are discussed, including binary file reading, and parameter setup. An unsupervised machine learning algorithm, k-means clustering, is applied to XGC1 particle distribution function data, showing that highly turbulent spatial regions do not have common coherent structures, but rather broad, ring- like structures in velocity space.
Fluid moments of the nonlinear Landau collision operator
An important problem in plasma physics is the lack of an accurate and complete description of
Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces
an integral identity involving the multivariate Hermite tensor polynomials and presents a method
for computing exact expressions for the fluid moments of the nonlinear Landau collision operator.
The proposed methodology provides a systematic and rigorous means of extending the validity of
fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality
and flow.
Multi-region relaxed Hall magnetohydrodynamics with flow
The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of “ideal barriers” that prevent global relaxation and flow. In this paper, we generalize MRxMHD with flow to include Hall effects, and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.
Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method
A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and this trend continues through all scale-lengths. The physics of this interesting nonlinear dynamics is numerically analyzed.
Effective-action approach to wave propagation in scalar QED plasmas
A relativistic quantum field theory with nontrivial background fields is developed and applied to study waves in plasmas. The effective action of the electromagnetic 4-potential is calculated ab initio from the standard action of scalar QED using path integrals. The resultant effective action is gauge invariant and contains nonlocal interactions, from which gauge bosons acquire masses without breaking the local gauge symmetry. To demonstrate how the general theory can be applied, we give two examples: a cold unmagnetized plasma and a cold uniformly magnetized plasma. Using these two examples, we show that all linear waves well known in classical plasma physics can be recovered from relativistic quantum results when taking the classical limit. In the opposite limit, classical wave dispersion relations are modified substantially. In unmagnetized plasmas, longitudinal waves propagate with nonzero group velocities even when plasmas are cold. In magnetized plasmas, anharmonically spaced Bernstein waves persist even when plasmas are cold. These waves account for cyclotron absorption features observed in spectra of x-ray pulsars. Moreover, cutoff frequencies of the two nondegenerate electromagnetic waves are red-shifted by different amounts. These corrections need to be taken into account in order to correctly interpret diagnostic results in laser plasma experiments.
Impact of magnetic topology on radial electric field profile and comparisons with models of edge transport in the Large Helical Device
The radial electric field in the plasma edge is studied in the Large Helical Device (LHD) experiments. When magnetic field lines become stochastic or open at the plasma edge and connected to the vessel, electrons are lost faster than ions along these field lines. Then, a positive electric field appears in the plasma edge. The radial electric field profile can be used to detect the effective plasma boundary. Magnetic topology is an important issue in stellarator and tokamak research because the 3D boundary has the important role of controlling MHD edge stability with respect to ELMs, and plasma detachment. Since the stochastic magnetic field layer can be controlled in the LHD by changing the preset vacuum magnetic axis, this device is a good platform to study the properties of the radial electric field that appear with the different stochastic layer width. Two magnetic configurations with different widths of the stochastic layer as simulated in vacuum are studied for low-β discharges. It has been found that a positive electric field appeared outside of the last closed flux surface. In fact the positions of the positive electric field are found in the boundary between of the stochastic layer and the scrape-off layer. To understand where is the boundary of the stochastic layer and the scrape-off layer, the magnetic field lines are analyzed statistically. The variance of the magnetic field lines in the stochastic layer is increased outwards for both configurations. However, the skewness, which means the asymmetry of the distribution of the magnetic field line, increases for only one configuration. If the skewness is large, the connection length becomes effectively short. Since that is consistent with the experimental observation, the radial electric field can be considered as an index of the magnetic topology..
The Greenwald density limit, found in all tokamak experiments, is reproduced for the first time using a phenomenologically correct model with parameters in the range of experiments. A simple model of equilibrium evolution and local power balance inside the island has been implemented to calculate the radiation-driven thermo-resistive tearing mode growth and explain the density limit. Strong destabilization of the tearing mode due to an imbalance of local Ohmic heating and radiative cooling in the island predicts the density limit within a few percent. The density limit is found to be a local edge limit and weakly dependent on impurity densities. Results are robust to a substantial variation in model parameters within the range of experiments.
Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective
The effort to obtain a set of MagnetoHydroDynamic (MHD) equations for a magnetized collisionless plasma was started nearly 60 years ago by Chew et al. [Proc. R. Soc. London, Ser. A 236(1204), 112–118 (1956)].
Many attempts have been made ever since.
Here, we will show the derivation of a set of these equations from the gyrokinetic perspective, which we call it gyrokinetic MHD, and it is different from the conventional ideal MHD.
However, this new set of equations still has conservation properties and, in the absence of fluctuations, recovers the usual MHD equilibrium.
Furthermore, the resulting equations allow for the plasma pressure balance to be further modified by finite-Larmor-radius effects in regions with steep pressure gradients.
The present work is an outgrowth of the paper on “Alfvén Waves in Gyrokinetic Plasmas” by Lee and Qin [Phys. Plasmas 10, 3196 (2003)].
Validating predictive models for fast ion profile relaxation in burning plasmas
The redistribution and potential loss of energetic particles due to MHD modes can limit
the performance of fusion plasmas by reducing the plasma heating rate. In this work, we
present validation studies of the 1.5D critical gradient model (CGM) for Alfvén eigenmode
(AE) induced EP transport in NSTX and DIII-D neutral beam heated plasmas. In previous
comparisons with a single DIII-D L-mode case, the CGM model was found to be responsible
for 75% of measured AE induced neutron deficit [1]. A fully kinetic HINST is used to
compute mode stability for the non-perturbative version of CGM (or nCGM). We have
found that AEs show strong local instability drive up to γ ω/ ∼ 20% violating assumptions
of perturbative approaches used in NOVA-K code. We demonstrate that both models agree
with each other and both underestimate the neutron deficit measured in DIII-D shot by
approximately a factor of 2.
On the other hand in NSTX the application of CGM shows good agreement for the
measured flux deficit predictions. We attempt to understand these results with the help of
the so-called kick model which is based on the guiding center code ORBIT. The kick model
comparison gives important insight into the underlying velocity space dependence of the AE
induced EP transport as well as it allows the estimate of the neutron deficit in the presence of
the low frequency Alfvénic modes. Within the limitations of used models we infer that there
are missing modes in the analysis which could improve the agreement with the experiments.
Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity.
For long-term simulations with high efficiency, explicit symplectic algorithms are desirable.
However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics.
To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle.
The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of
$H({\bf x},{\bf p})=p_i f({\bf x})$ or $H(x,p)=x_i g({\bf p})$.
Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.
Advanced Algorithms for Local Routing Strategy on Complex Networks
Despite the significant improvement on network performance provided by global routing strategies, their applications are still limited to small-scale networks, due to the need for acquiring global information of the network which grows and changes rapidly with time.
Local routing strategies, however, need much less local information, though their transmission efficiency and network capacity are much lower than that of global routing strategies.
In view of this, three algorithms are proposed and a thorough investigation is conducted in this paper.
These algorithms include a node duplication avoidance algorithm, a next-nearest-neighbor algorithm and a restrictive queue length algorithm.
After applying them to typical local routing strategies, the critical generation rate of information packets $R_c$ increases by over ten-fold and the average transmission time 〈T〉 decreases by 70–90 percent, both of which are key physical quantities to assess the efficiency of routing strategies on complex networks.
More importantly, in comparison with global routing strategies, the improved local routing strategies can yield better network performance under certain circumstances.
This is a revolutionary leap for communication networks, because local routing strategy enjoys great superiority over global routing strategy not only in terms of the reduction of computational expense, but also in terms of the flexibility of implementation, especially for large-scale networks.
Kinetic Alfvén waves in three-dimensionalmagnetic reconnection
Alfvénic waves are believed to be fundamentally important in magnetic reconnection.
Kineticdynamics of particles can break the Alfvén speed limit in the evolution and propagation of perturbations during reconnection.
In this paper, the generation and signatures of kinetic Alfvén waves (KAWs) associated with magnetic reconnection in a current sheet is investigated using a three-dimensional (3-D) hybrid code under a zero or ﬁnite guide ﬁeld.
In order to understand the wave structures in the general cases of multiple X line reconnection, cases with a single X line of various lengths are examined.
The KAWs are identiﬁed using the wave dispersion relation, electromagnetic polarization relations, as well as spectral analysis.
In the cases in which the X line is so long to extend through the entire simulation domain in the current direction, quasi 2-D conﬁgurations of reconnection are developed behind a leading ﬂux/plasma bulge.
KAWs with perpendicular wave number $\kappa_\perp \rho_i \sim 1$ (with $\rho_i$ being the ion Larmor radius) are found throughout the transient plasma bulge region and propagate outward along magnetic ﬁeld lines with a slightly super-Alfvénic velocity.
These KAWs are generated from the X line and coexist with the whistler structure of the ion diﬀusion region under a small guide ﬁeld.
In the cases in which the X line has a ﬁnite length, $2\xi \sim 10 d_i$, with $\xi$ being the half length of the X line and $d_i$ the ion inertial length, the KAWs originated fromthe X line are of 3-D nature.
Under a ﬁnite guide ﬁeld, KAWs propagate along the oblique magnetic ﬁeld lines into the unperturbed regions in the current direction, carrying parallel electric ﬁeld and Poynting ﬂuxes.
The critical X line length for the generation of 3-D-like structures is found to be $2\xi_c \le 30 d_i$. The structure,propagation, energy, spectrum, and damping of the KAWs are examined. Dependence of the structure ofKAWs on the guide ﬁeld is also investigated.
This study analyzes results from a multifluid MHD simulation to investigate the shape and structure of the pressure and composition boundaries at Mars, which can provide physical insight for the observational analysis. These boundaries are examined via the unity contours and gradients of the plasma β, as well as β∗, which includes the dynamic pressure in the numerator, and the ion mass and number density ratios. It is found that unity contours are well aligned with the gradient extrema, indicating that the unity contour is a topological boundary. In addition, these two transitions of pressure and composition are of a thickness of 0.05–0.1 RM near the subsolar region to 1–1.5 RM in the tail. The comparison of the pressure and composition boundaries indicates that the two are very similar and that not only the plasma sheet but also the full volume of the lobes are dominated by planetary ions. It suggests that the tail escape for ions not only concentrates in the central plasma sheet but also the magnetic lobes. It is also worthy pointing out that the ion number density ratio unity contour is found to be systematically smaller than other unity boundaries, which calls for attention when the ion number density is used to identify such boundaries. Finally, the comparison between the boundaries of this study and two analytical fittings is carried out. We found a good agreement with the Vignes fitting, with little flaring in the tail, in contrast to a larger flaring angle from the Trotignon fitting.
Improved kinetic neoclassical transport calculation for a low-collisionality QH-mode pedestal
The role of neoclassical, anomalous and neutral transport to the overall H-mode pedestal and scrape-off layer (SOL) structure in an ELM-free QH-mode discharge on DIII-D is explored using XGC0, a 5D full-f multi-species particle-in-cell drift-kinetic solver with self-consistent neutral recycling and sheath potentials. The work in this paper builds on previous work aimed at achieving quantitative agreement between the flux-driven simulation and the experimental electron density, impurity density and orthogonal measurements of impurity temperature and flow profiles. Improved quantitative agreement is achieved by performing the calculations with a more realistic electron mass, larger neutral density and including finite-Larmor-radius corrections self-consistently in the drift-kinetic motion of the particles. Consequently, the simulations provide stronger evidence that the radial electric field (${{E}_{\text{r}}}$ ) in the pedestal is primarily established by the required balance between the loss of high-energy tail main ions against a pinch of colder main ions and impurities. The kinetic loss of a small population of ions carrying a large proportion of energy and momentum leads to a separation of the particle and energy transport rates and introduces a source of intrinsic edge torque. Ion orbit loss and finite orbit width effects drive the energy distributions away from Maxwellian, and describe the anisotropy, poloidal asymmetry and local minimum near the separatrix observed in the ${{T}_{i}}$ profile.
Density Waves in a System of Non-Interacting Particles
An ensemble of non-interacting bouncing balls being acted on by a constant gravitational force, starting
at rest from a uniform density distribution, will develop a structure of sharply peaked density waves. We
describe these waves by computing the density profile of such a system analytically, and we find that the
analytical results are in good agreement with numerical findings. We suggest that in a real system, these
density waves could be used to produce measurements of the strength of a gravitational field.
On the structure of the two-stream instability -- complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes
The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species, the instability diagram of the two-stream instability based on a 1D warm-fluid model exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between the stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.
Design of geometric phase measurement in EAST Tokamak
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
Multi-Species Measurements of the Firehose and Mirror Instability Thresholds
The firehose and mirror instabilities are thought to arise in a variety of space and astrophysical plasmas, constraining the pressure anisotropies and drifts between particle species. The plasma stability depends on all species simultaneously, meaning that a combined analysis is required. Here, we present the first such analysis in the solar wind, using the long-wavelength stability parameters to combine the anisotropies and drifts of all major species (core and beam protons, alphas, and electrons). At the threshold, the firehose parameter was found to be dominated by protons (67%), but also to have significant contributions from electrons (18%) and alphas (15%). Drifts were also found to be important, contributing 57% in the presence of a proton beam. A similar situation was found for the mirror, with contributions of 61%, 28%, and 11% for protons, electrons, and alphas, respectively. The parallel electric field contribution, however, was found to be small at 9%. Overall, the long-wavelength thresholds constrain the data well (${\text{}}\lt 1 \% $ unstable), and the implications of this are discussed.
Large-scale dynamo action precedes turbulence in shearing box simulations of the magnetorotational instability
We study the dynamo generation (exponential growth) of large-scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal (x–y) averaging, we also demonstrate the presence of large-scale fields when vertical (y–z) averaging is employed instead. By computing space–time planar averaged fields and power spectra, we find large-scale dynamo action in the early MRI growth phase – a previously unidentified feature. Non-axisymmetric linear MRI modes with low horizontal wavenumbers and vertical wavenumbers near that of expected maximal growth, amplify the large-scale fields exponentially before turbulence and high wavenumber fluctuations arise. Thus the large-scale dynamo requires only linear fluctuations but not non-linear turbulence (as defined by mode–mode coupling). Vertical averaging also allows for monitoring the evolution of the large-scale vertical field and we find that a feedback from horizontal low wavenumber MRI modes provides a clue as to why the large-scale vertical field sustains against turbulent diffusion in the non-linear saturation regime. We compute the terms in the mean field equations to identify the individual contributions to large-scale field growth for both types of averaging. The large-scale fields obtained from vertical averaging are found to compare well with global simulations and quasi-linear analytical analysis from a previous study by Ebrahimi & Blackman. We discuss the potential implications of these new results for understanding the large-scale MRI dynamo saturation and turbulence.
Stabilization of the vertical instability by non-axisymmetric coils
In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it
was shown that axisymmetric (or vertical) stability can be improved by placing a set of
parallelogram coils above and below the plasma oriented at an angle to the constant toroidal
planes. The physics of this stabilization can be understood as providing an effective additional
positive stability index. The original work was based on a simplified model of a straight
tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma
such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration
to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as
predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry
and 3D equilibria were computed using trapezium coil currents of 10 kA, 100 kA, and 500 kA.
The ideal magnetohydrodynamics growth rates were computed as a function of the conformal
wall position for the n = 0 symmetry-preserving family. The results show an insignificant
relative improvement in the stabilizing wall location for the two lower coil current cases, of
the order of 10−3
and less. In contrast, the marginal wall position is increased by 7% as the
coil current is increased to 500 kA, confirming the main prediction from the original study in
a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond
to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect
on the axisymmetric stability is real, it appears to require higher coil currents than could be
provided in an upgrade to existing facilities. Additional optimization over the pitch of the
coils, the number of field periods and the coil positions, as well as plasma parameters, such
as the internal inductivity $l_i$, $\beta$, and $q_{95}$ would mitigate this but seem unlikely to change the
conclusion
Pressure driven currents near magnetic islands in 3D MHD equilibria: Effects
of pressure variation within flux surfaces and of symmetry
In toroidal, magnetically confined plasmas, the heat and particle transport is strongly anisotropic, with transport along the field lines sufficiently strong relative to cross-field transport that the equilibrium pressure can generally be regarded as constant on the flux surfaces in much of the plasma.
The regions near small magnetic islands, and those near the X-lines of larger islands, are exceptions, having a significant variation of the pressure within the flux surfaces. It is shown here that the variation of the equilibrium pressure within the flux surfaces in those regions has significant consequences for the pressure driven currents.
It is further shown that the consequences are strongly affected by the symmetry of the magnetic field if the field is invariant under combined reflection in the poloidal and toroidal angles. (This symmetry property is called “stellarator symmetry.”) In non-stellarator-symmetric equilibria, the pressure-driven currents have logarithmic singularities at the X-lines. In stellarator-symmetric MHD equilibria, the singular components of the pressure-driven currents vanish. These equilibria are to be contrasted with equilibria having ${\bf B}\cdot \nabla p = 0$; where the singular components of the pressure-driven currents vanish regardless of the symmetry.
They are also to be contrasted with 3D MHD equilibrium solutions that are constrained to have simply nested flux surfaces, where the pressure-driven current goes like $1/x$ near rational surfaces, where x is the distance from the rational surface, except in the case of quasi-symmetric flux surfaces. For the purpose of calculating the pressure-driven currents near magnetic islands, we work with a closed subset of the MHD equilibrium equations that involves only perpendicular force balance, and is decoupled from parallel force balance.
It is not correct to use the parallel component of the conventional MHD force balance equation, ${\bf B}\cdot \nabla p=0$, near magnetic islands.
Small but nonzero values of ${\bf B}\cdot \nabla p$ are important in this region, and small non-MHD contributions to the parallel force balance equation cannot be neglected there.
Two approaches are pursued to solve our equations for the pressure driven currents.
First, the equilibrium equations are applied to an analytically tractable magnetic field with an island, obtaining explicit expressions for the rotational transform and magnetic coordinates, and for the pressure-driven current and its limiting behavior near the X-line.
The second approach utilizes an expansion about the X-line to provide a more general calculation of the pressure-driven current near an X-line and of the rotational transform near a separatrix.
The study presented in this paper is motivated, in part, by tokamak experiments with nonaxisymmetric magnetic perturbations, where significant differences are observed between the behavior of stellarator-symmetric and non-stellarator-symmetric configurations with regard to stabilization of edge localized modes by resonant magnetic perturbations. Implications for the coupling between neoclassical tearing modes, and for magnetic island stability calculations, are also discussed.
Mitigation of Alfvénic activity by 3D magnetic perturbations on NSTX
Observations on the National Spherical Torus Experiment (NSTX) indicate that externally
applied non-axisymmetric magnetic perturbations (MP) can reduce the amplitude of toroidal
Alfvén eigenmodes (TAE) and global Alfvén eigenmodes (GAE) in response to pulsed n = 3
non-resonant fields. From full-orbit following Monte Carlo simulations with the one- and
two-fluid resistive MHD plasma response to the magnetic perturbation included, it was found
that in response to MP pulses the fast-ion losses increased and the fast-ion drive for the GAEs
was reduced. The MP did not affect the fast-ion drive for the TAEs significantly but the Alfvén
continuum at the plasma edge was found to be altered due to the toroidal symmetry breaking
which leads to coupling of different toroidal harmonics. The TAE gap was reduced at the
edge creating enhanced continuum damping of the global TAEs, which is consistent with the
observations. The results suggest that optimized non-axisymmetric MP might be exploited to
control and mitigate Alfvén instabilities by tailoring the fast-ion distribution function and/or
continuum structure.
Third-order spectral analysis, in particular, the auto bicoherence, was applied to probe signals from
high-harmonic fast-wave heating experiments in the National Spherical Torus Experiment. Strong
evidence was found for parametric decay of the 30 MHz radio-frequency (RF) pump wave, with a
low-frequency daughter wave at 2.7 MHz, the local majority-ion cyclotron frequency. The primary
decay modes have auto bicoherence values around 0.85, very close to the theoretical value of one,
which corresponds to total phase coherence with the pump wave. The threshold RF pump power
for onset of parametric decay was found to be between 200 kW and 400 kW.
An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor $q$ at the 95% poloidal flux surface, $q_{95}$, is driven below $2.0$.
The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections [Shafranov, Sov. Phys. Tech. Phys. 15, 175 (1970)] when $q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value $m/n$.
Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and $q_{edge}$ decreases through successive rational surfaces.
For $q_{edge}<2$, the instability is always encountered and is highly disruptive.
However, diverted plasmas, in which $q_{edge}$ is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when $q_{95}$ reaches 2.
It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when $q_{95}<2$, but $q_{edge}>>2$.
The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component.
However, the growth rates scale with a fractional power of the resistivity near the $q=2$ surface.
The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.
Multi-scale full-orbit analysis on phase-space behavior of runaway electrons in tokamak fields with synchrotron radiation
In this paper, the secular full-orbit simulations of runaway electrons with synchrotron radiation in tokamak fields are carried out using a relativistic volume-preserving algorithm.
Detailed phase-space behaviors of runaway electrons are investigated in different dynamical timescales spanning 11 orders.
In the small timescale, i.e., the characteristic timescale imposed by Lorentz force, the severely deformed helical trajectory of energetic runaway electron is witnessed.
A qualitative analysis of the neoclassical scattering, a kind of collisionless pitch-angle scattering phenomena, is provided when considering the coupling between the rotation of momentum vector and the background magnetic field.
In large timescale up to 1s, it is found that the initial condition of runaway electrons in phase space globally influences the pitch-angle scattering, the momentum evolution, and the loss-gain ratio of runaway energy evidently.
However, the initial value has little impact on the synchrotron energy limit.
It is also discovered that the parameters of tokamak device, such as the toroidal magnetic field, the loop voltage, the safety factor profile, and the major radius, can modify the synchrotron energy limit and the strength of neoclassical scattering.
The maximum runaway energy is also proved to be lower than the synchrotron limit when the magnetic field ripple is considered.
Impact of resistive MHD plasma response on perturbation field sidebands
Single fluid linear simulations of a KSTAR RMP ELM suppressed discharge with the M3D-C1 resistive magnetohydrodynamic code have been performed for the first time.
The simulations show that the application of the $n=1$ perturbation using the KSTAR in-vessel control coils (IVCC), which apply modest levels of $n=3$ sidebands (~20% of the $n=1$), leads to levels of $n=3$ sideband that are comparable to the $n=1$ when plasma response is included.
This is due to the reduced level of screening of the rational-surface-resonant $n=3$ component relative to the rational-surface-resonant $n=1$ component.
The $n=3$ sidebands could play a similar role in ELM suppression on KSTAR as the toroidal sidebands ($n=1,2,4$) in DIII-D $n=3$ ELM suppression with missing I-coil segments
[Paz Soldan et al., Nucl. Fusion 54, 073013 (2014)].
This result may help to explain the uniqueness of ELM suppression with $n=1$ perturbations in KSTAR since the effective perturbation is a mixed $n=1/n=3$ perturbation similar to $n=3$ ELM suppression in DIII-D.
Multi-region approach to free-boundary three-dimensional tokamak equilibria and resistive wall instabilities
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new
resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding
vacuum region are included within the computational domain. This implementation contrasts
with the method typically used in fluid codes in which the resistive wall is treated as a boundary
condition on the computational domain boundary and has the advantage of maintaining purely local
coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary nonaxisymmetric
equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear
evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a
resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory.
Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic
values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption
extend into the current-quench phase, in which the plasma becomes limited by the first wall, and
strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics
Volume-preserving algorithms (VPAs) for the charged particles dynamics is preferred because of their long-term accuracy and conservativeness for phase space volume. Lie algebra and the Baker-Campbell-Hausdorff (BCH) formula can be used as a fundamental theoretical tool to construct VPAs. Using the Lie algebra structure of vector fields, we split the volume-preserving vector field for charged particle dynamics into three volume-preserving parts (sub-algebras), and find the corresponding Lie subgroups. Proper combinations of these subgroups generate volume preserving, second order approximations of the original solution group, and thus second order VPAs. The developed VPAs also show their significant effectiveness in conserving phase-space volume exactly and bounding energy error over long-term simulations.
ExB flow velocity deduced from the poloidal motion of fluctuation patterns in neutral beam injected L-mode plasmas on KSTAR
A method for direct assessment of the equilibrium ${\bf E}\times{\bf B}$ flow velocity (${\bf E}\times{\bf B}$ flow shear is responsible for the turbulence suppression and transport reduction in tokamak plasmas) is investigated based on two facts.
The first one is that the apparent poloidal rotation speed of density fluctuation patterns is close to the turbulence rotation speed in the direction perpendicular to the local magnetic field line within the flux surface.
And the second “well-known” fact is that the turbulence rotation velocity consists of the equilibrium ${\bf E}\times{\bf B}$ flow velocity and intrinsic phase velocity of turbulence in the ${\bf E}\times{\bf B}$ flow frame.
In the core region of the low confinement (L-mode) discharges where a strong toroidal rotation is induced by neutral beam injection, the apparent poloidal velocities (and turbulence rotation velocities) are good approximations of the ${\bf E}\times{\bf B}$ flow velocities since linear gyrokinetic simulations suggest that the intrinsic phase velocity of the dominant turbulence is significantly lower than the apparent poloidal velocity.
In the neutral beam injected L-mode plasmas, temporal and spatial scales of the measured turbulence are studied by comparing with the local equilibrium parameters relevant to the ion-scale turbulence.
Collisionless Pitch-Angle Scattering of Runaway Electrons
It is discovered that the tokamak field geometry generates a toroidicity induced broadening of
the pitch-angle distribution of runaway electrons. This collisionless pitch-angle scattering is
much stronger than the collisional scattering and invalidates the gyro-center model for runaway
electrons. As a result, the energy limit of runaway electrons is found to be larger than the
prediction of the gyro-center model and to depend heavily on the background magnetic field.
The Plasma Simulation Code: A modern particle-in-cell code with patch-based load-balancing
This work describes the Plasma Simulation Code (PSC), an explicit, electromagnetic particle-in-cell code with support for different order particle shape functions.
We review the basic components of the particle-in-cell method as well as the computational architecture of the PSC code that allows support for modular algorithms and data structure in the code.
We then describe and analyze in detail a distinguishing feature of psc: patch-based load balancing using space-filling curves which is shown to lead to major efficiency gains over
unbalanced methods and a previously used simpler balancing method.
Evaluation of Thermal Helium Beam and Line-Ratio
Fast Diagnostic on the National Spherical Torus Experiment-Upgrade
A 1-D kinetic collisional radiative model with state-of-the-art atomic data is developed and employed to simulate line emission to evaluate the Thermal Helium Beam (THB) diagnostic on NSTX-U. This diagnostic is currently in operation on RFX-mod, and it is proposed to be installed on NSTX-U. The THB system uses the intensity ratios of neutral helium lines 667.8, 706.5, and 728.1 nm to derive electron temperature (eV) and density ($cm^{−3}$) profiles. The purpose of the present analysis is to evaluate the applications of this diagnostic for determining fast (∽4 μs) electron temperature and density radial profiles on the scrape-off layer and edge regions of NSTX-U that are needed in turbulence studies. The diagnostic is limited by the level of detection of the 728.1 nm line, which is the weakest of the three. This study will also aid in future design of a similar 2-D diagnostic system on the divertor.
Ion Cyclotron Emission Studies: Retrospects and Prospects
Ion Cyclotron Emission (or ICE) studies emerged in part from the papers by A.B. Mikhailovskii published in s. Among the discussed subjects were electromagnetic compressional Alfvénic cyclotron instabilities with the linear growth rate driven by fusion products, -particles which draw a lot of attention to energetic particle physics. The theory of ICE excited by energetic particles was significantly advanced at the end of century motivated by first DT experiments on TFTR and subsequent JET experimental studies which we highlight. More recently ICE theory was advanced by detailed theoretical and experimental studies on ST (or spherical torus) fusion devices where the instability signals previously indistinguishable in high aspect ratio tokamaks due to high toroidal magnetic field became the subjects of experiments. We discuss further prospects of ICE theory applications for future burning plasma (BP) experiments such as those to be conducted in ITER device in France where neutron and gamma rays escaping the plasma create extremely challenging conditions fuison alpha particle diagnostics.
The unified ballooning theory with weak up-down asymmetric mode structure and the numerical studies
A unified ballooning theory, constructed on the basis of two special theories
[Zhang et al., Phys. Fluids B 4, 2729 (1992);
Y.Z. Zhang & T. Xie, Nucl. Fusion Plasma Phys. 33, 193 (2013)], shows that a weak up-down asymmetric mode structure is normally formed in an up-down symmetric equilibrium; the weak up-down asymmetry in mode structure is the manifestation of non-trivial higher order effects beyond the standard ballooning equation. It is shown that the asymmetric mode may have even higher growth rate than symmetric modes. The salient features of the theory are illustrated by investigating a fluid model for the ion temperature gradient (ITG) mode. The two dimensional (2D) analytical form of the ITG mode, solved in ballooning representation, is then converted into the radial-poloidal space to provide the natural boundary condition for solving the 2D mathematical local eigenmode problem. We find that the analytical expression of the mode structure is in a good agreement with finite difference solution. This sets a reliable framework for quasi-linear computation.
A heuristic model for MRI turbulent stresses in Hall MHD
Although the Shakura–Sunyaev α viscosity prescription has been highly successful in characterizing
myriad astrophysical environments, it has proven to be partly inadequate in modelling
turbulent stresses driven by the magnetorotational instability (MRI). Hence, we adopt the
approach employed by Ogilvie, but in the context of Hall magnetohydrodynamics (MHD),
to study MRI turbulence. We utilize the exact evolution equations for the stresses, and the
non-linear terms are closed through the invocation of dimensional analysis and physical considerations.
We demonstrate that the inclusion of the Hall term leads to non-trivial results,
including the modification of the Reynolds and Maxwell stresses, as well as the (asymptotic)
non-equipartition between the kinetic and magnetic energies; the latter issue is also addressed
via the analysis of non-linear waves. The asymptotic ratio of the kinetic to magnetic energies
is shown to be independent of the choice of initial conditions, but it is governed by the
Hall parameter. We contrast our model with an altered version of the Kazantsev prescription
from small-scale dynamo theory, and the Hall term does not generally contribute in the latter
approach, illustrating the limitations of this formalism. We indicate potential astrophysical
applications of our model, including the solar wind where a lack of equipartition has been
observed.
Dynamics of ion beam charge neutralization by ferroelectric plasma sources
Ferroelectric Plasma Sources (FEPSs) can generate plasma that provides effective space-charge neutralization of intense high-perveance ion beams, as has been demonstrated on the Neutralized Drift Compression Experiment NDCX-I and NDCX-II.
This article presents experimental results on charge neutralization of a high-perveance 38 keV $Ar^+$ beam by a plasma produced in a FEPS discharge.
By comparing the measured beam radius with the envelope model for space-charge expansion, it is shown that a charge neutralization fraction of 98% is attainable with sufficiently dense FEPS plasma.
The transverse electrostatic potential of the ion beam is reduced from 15 V before neutralization to 0.3 V, implying that the energy of the neutralizing electrons is below 0.3 eV.
Measurements of the time-evolution of beam radius show that near-complete charge neutralization is established ∼5 μs after the driving pulse is applied to the FEPS and can last for 35 μs.
It is argued that the duration of neutralization is much longer than a reasonable lifetime of the plasma produced in the sub-μs surface discharge.
Measurements of current flow in the driving circuit of the FEPS show the existence of electron emission into vacuum, which lasts for tens of μs after the high voltage pulse is applied.
It is argued that the beam is neutralized by the plasma produced by this process and not by a surface discharge plasma that is produced at the instant the high-voltage pulse is applied.
Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence
A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly
collisional plasma (e.g. drift-wave turbulence driven by ion temperature gradients)
is proposed, with account taken both of the nonlinear advection of the perturbed
particle distribution by fluctuating ${\bf E} \times {\bf B}$ flows and of its phase mixing, which is
caused by the streaming of the particles along the mean magnetic field and, in
a linear problem, would lead to Landau damping. It is found that it is possible
to construct a consistent theory in which very little free energy leaks into high
velocity moments of the distribution function, rendering the turbulent cascade in
the energetically relevant part of the wavenumber space essentially fluid-like. The
velocity-space spectra of free energy expressed in terms of Hermite-moment orders
are steep power laws and so the free-energy content of the phase space does not
diverge at infinitesimal collisionality (while it does for a linear problem); collisional
heating due to long-wavelength perturbations vanishes in this limit (also in contrast
with the linear problem, in which it occurs at the finite rate equal to the Landau
damping rate). The ability of the free energy to stay in the low velocity moments
of the distribution function is facilitated by the ‘anti-phase-mixing’ effect, whose
presence in the nonlinear system is due to the stochastic version of the plasma echo
(the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations).
The partitioning of the wavenumber space between the (energetically dominant) region
where this is the case and the region where linear phase mixing wins its competition
with nonlinear advection is governed by the ‘critical balance’ between linear and
nonlinear time scales (which for high Hermite moments splits into two thresholds,
one demarcating the wavenumber region where phase mixing predominates, the other
where plasma echo does).
Suppression of thermal conduction in a mirror-unstable plasma
The plasma of galaxy clusters is subject to firehose and mirror instabilities at scales of order the ion Larmor radius. The mirror instability generates fluctuations of magnetic-field strength δB/B ∼ 1. These fluctuations act as magnetic traps for the heat-conducting electrons, suppressing their transport. We calculate the effective parallel thermal conductivity in the ICM in the presence of the mirror fluctuations for different stages of the evolution of the instability. The mirror fluctuations are limited in amplitude by the maximum and minimum values of the field strength, with no large deviations from the mean value. This key property leads to a finite suppression of thermal conduction at large scales. We find suppression down to ≈0.2 of the Spitzer value for the secular phase of the perturbations’ growth, and ≈0.3 for their saturated phase. The effect operates in addition to other suppression mechanisms and independently of them. Globally, fluctuations δB/B ∼ 1 can be present on much larger scales, of the order of the scale of turbulent motions. However, we do not expect large suppression of thermal conduction by these, because their scale is considerably larger than the collisional mean free path of the ICM electrons. The obtained suppression of thermal conduction by a factor of ∼5 appears to be characteristic and potentially universal for a weakly collisional mirror-unstable plasma.
Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully nonlinear Coulomb collisions
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons.
Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal.
An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation.
The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Quantitative comparison of electron temperature fluctuations to nonlinear gyrokinetic simulations in C-Mod Ohmic L-mode discharges
Long wavelength turbulent electron temperature fluctuations $(k_y\rho_s < 0.3)$ are measured in the outer core region $(r/a > 0.8)$ of Ohmic L-mode plasmas at Alcator C-Mod [E.S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic.
The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy & R.E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime.
When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations $(k_y\rho_s ≲ 1.7)$ performed at $r/a ∼ 0.85$ reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars.
In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations.
If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges.
In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
A fully non-linear multi-species Fokker-Planck-Landau collision operator for simulation of fusion plasma
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations.
In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang [Phys. Plasmas 21, 032503 (2014)] is generalized to include multiple particle species.
The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy.
The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed.
Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
Equilibrium drives of the low and high field side $n=2$ plasma response and impact on global confinement
The nature of the multi-modal $n = 2$ plasma response and its impact on global confinement
is studied as a function of the axisymmetric equilibrium pressure, edge safety factor,
collisionality, and L-versus H-mode conditions.
Varying the relative phase ($\Delta\phi_{UL}$)
between upper and lower in-vessel coils demonstrates that different $n = 2$ poloidal spectra
preferentially excite different plasma responses. These different plasma response modes
are preferentially detected on the tokamak high-field side (HFS) or low-field side (LFS)
midplanes, have different radial extents, couple differently to the resonant surfaces, and have
variable impacts on edge stability and global confinement. In all equilibrium conditions
studied, the observed confinement degradation shares the same $\Delta\phi_{UL}$ dependence as the
coupling to the resonant surfaces given by both ideal (IPEC) and resistive (MARS-F) MHD
computation. Varying the edge safety factor shifts the equilibrium field-line pitch and thus
the $\Delta\phi_{UL}$ dependence of both the global confinement and the $n = 2$ magnetic response.
As edge safety factor is varied, modeling finds that the HFS response (but not the LFS
response), the resonant surface coupling, and the edge displacements near the X-point all
share the same $\Delta\phi_{UL}$ dependence. The LFS response magnitude is strongly sensitive to the
core pressure and is insensitive to the collisionality and edge safety factor. This indicates that
the LFS measurements are primarily sensitive to a pressure-driven kink-ballooning mode that
couples to the core plasma. MHD modeling accurately reproduces these (and indeed all) LFS
experimental trends and supports this interpretation. In contrast to the LFS, the HFS magnetic
response and correlated global confinement impact is unchanged with plasma pressure, but is
strongly reduced in high collisionality conditions in both H- and L-mode. This experimentally
suggests the bootstrap current drives the HFS response through the kink-peeling mode drive,
though surprisingly weak or no dependence on the bootstrap current is seen in modeling.
Instead, modeling is revealed to be very sensitive to the details of the edge current profile
and equilibrium truncation. Holding truncation fixed, most HFS experimental trends are not
captured, thus demonstrating a stark contrast between the robustness of the HFS experimental
results and the sensitivity of its computation.
On the inward drift of runaway electrons in plateau regime
The well observed inward drift of current carrying runaway electrons during runaway plateau phase after disruption is studied by considering the phase space dynamic of runaways in a large aspect ratio toroidal system. We consider the case where the toroidal field is unperturbed and the toroidal symmetry of the system is preserved. The balance between the change in canonical angular momentum and the input of mechanical angular momentum in such a system requires runaways to drift horizontally in configuration space for any given change in momentum space. The dynamic of this drift can be obtained by integrating the modified Euler-Lagrange equation over one bounce time. It is then found that runaway electrons will always drift inward as long as they are decelerating. This drift motion is essentially non-linear, since the current is carried by runaways themselves, and any runaway drift relative to the magnetic axis will cause further displacement of the axis itself. A simplified analytical model is constructed to describe such inward drift both in the ideal wall case and no wall case, and the runaway current center displacement as a function of parallel momentum variation is obtained. The time scale of such displacement is estimated by considering effective radiation drag, which shows reasonable agreement with the observed displacement time scale. This indicates that the phase space dynamic studied here plays a major role in the horizontal displacement of runaway electrons during plateau phase.
Radially dependent large-scale dynamos in global cylindrical shear flows and the local cartesian limit
For cylindrical differentially rotating plasmas, we study large-scale magnetic field generation from finite amplitude non-axisymmetric perturbations by comparing numerical simulations with quasi-linear analytic theory. When initiated with a vertical magnetic field of either zero or finite net flux, our global cylindrical simulations exhibit the magnetorotational instability (MRI) and large-scale dynamo growth of radially alternating mean fields, averaged over height and azimuth. This dynamo growth is explained by our analytic calculations of a non-axisymmetric fluctuation-induced electromotive force that is sustained by azimuthal shear of the fluctuating fields. The standard ‘Ω effect’ (shear of the mean field by differential rotation) is unimportant. For the MRI case, we express the large-scale dynamo field as a function of differential rotation. The resulting radially alternating large-scale fields may have implications for angular momentum transport in discs and corona. To connect with previous work on large-scale dynamos with local linear shear and identify the minimum conditions needed for large-scale field growth, we also solve our equations in local Cartesian coordinates. We find that large-scale dynamo growth in a linear shear flow without rotation can be sustained by shear plus non-axisymmetric fluctuations – even if not helical, a seemingly previously unidentified distinction. The linear shear flow dynamo emerges as a more restricted version of our more general new global cylindrical calculations.
Pressure-driven amplification and penetration of resonant magnetic perturbations
We show that a resonant magnetic perturbation applied to the boundary of an ideal plasma screw-pinch equilibrium with nested surfaces can penetrate inside the resonant surface and into the core. The response is significantly amplified with increasing plasma pressure. We present a rigorous verification of nonlinear equilibrium codes against linear theory, showing excellent agreement.
Large-volume flux closure during plasmoid-mediated reconnection in Coaxial Helicity Injection
A large-volume flux closure during transient coaxial helicity injection (CHI) in NSTX-U is demonstrated through resistive magnetohydrodynamics (MHD) simulations. Several major improvements, including the improved positioning of the divertor poloidal field coils, are projected to improve the CHI start-up phase in NSTX-U. Simulations in the NSTX-U configuration with constant in time coil currents show that with strong flux shaping the injected open field lines (injector flux) rapidly reconnect and form large volume of closed flux surfaces. This is achieved by driving parallel current in the injector flux coil and oppositely directed currents in the flux shaping coils to form a narrow injector flux footprint and push the injector flux into the vessel. As the helicity and plasma are injected into the device, the oppositely directed field lines in the injector region are forced to reconnect through a local Sweet–Parker type reconnection, or to spontaneously reconnect when the elongated current sheet becomes MHD unstable to form plasmoids. In these simulations for the first time, it is found that the closed flux is over 70% of the initial injector flux used to initiate the discharge. These results could work well for the application of transient CHI in devices that employ super conducting coils to generate and sustain the plasma equilibrium.
The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo
A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed
and explored. The effect relies on the interaction of magnetic fluctuations with
a mean shear flow, meaning the saturated state of the small-scale dynamo can
drive a large-scale dynamo – in some sense the inverse of dynamo quenching. The
dynamo is non-helical, with the mean field α coefficient zero, and is caused by the
interaction between an off-diagonal component of the turbulent resistivity and the
stretching of the large-scale field by shear flow. Following up on previous numerical
and analytic work, this paper presents further details of the numerical evidence
for the effect, as well as an heuristic description of how magnetic fluctuations can
interact with shear flow to produce the required electromotive force. The pressure
response of the fluid is fundamental to this mechanism, which helps explain why the
magnetic effect is stronger than its kinematic cousin, and the basic idea is related
to the well-known lack of turbulent resistivity quenching by magnetic fluctuations.
As well as being interesting for its applications to general high Reynolds number
astrophysical turbulence, where strong small-scale magnetic fluctuations are expected
to be prevalent, the magnetic shear-current effect is a likely candidate for large-scale
dynamo in the unstratified regions of ionized accretion disks. Evidence for this is
discussed, as well as future research directions and the challenges involved with
understanding details of the effect in astrophysically relevant regimes.
The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes.
The linear growth rate and the wavenumber are found to scale as $S^{1/4}(1+P_{m})^{-5/8}$ and $S^{3/8}(1+P_{m})^{-3/16}$ with respect to the Lundquist number $S$ and the magnetic Prandtl number $P_m$.
Furthermore, the linear layer width is shown to scale as $S^{-1/8}(1+P_{m})^{1/16}$.
The growth of the plasmoids slows down from an exponential growth to an algebraic growth when they enter into the nonlinear regime.
In particular, the time-scale of the nonlinear growth of the plasmoids is found to be $\tau_{NL} \sim S^{-3/16}(1+P_{m})^{19/32}\tau_{A,L}$.
The nonlinear growth of the plasmoids is radically different from the linear one, and it is shown to be essential to understand the global current sheet disruption.
It is also discussed how the plasmoid instability enables fast magnetic reconnection in viscoresistive plasmas.
In particular, it is shown that the recursive plasmoid formation can trigger a collisionless reconnection regime if
$S \ge L_{cs} (\epsilon_C I_k)^{-1}(1+P_M)^{19/32}$, where $L_{cs}$ is the half-length of the global current sheet and $I_k$ is the relevant kinetic length scale.
On the other hand, if the current sheet remains in the collisional regime, the global (time-averaged) reconnection rate is shown to be $\langle \left.d\psi/dt\right|_X \rangle \approx \epsilon_c \nu_{A,u} B_u (1+P_m)^{-1/2}$, where $\epsilon_c$ is the critical inverse aspect ratio of the current sheet, while $\nu_{A,u}$ and $B_u$ are the Alfvén speed and the magnetic field upstream of the global reconnection layer.
Gyrokinetic-ion drift-kinetic-electron simulation of the (m=2, n=1) cylindrical tearing mode
Particle-in-cell simulations of (m=2,n=1) tearing mode in cylindrical plasmas are carried out with kinetic electrons using the split-weight control-variate algorithm [Y. Chen & S. E. Parker, J. Comput. Phys. 220, 839 (2007)].
Radially, global simulation shows global mode structure in agreement with reduced-magnetohydrodynamic eigenmode calculation.
Simulations of the tearing layer are verified with analytic results for the collisionless, semi-collisional, and drift-tearing mode.
Formation of current singularity in a topologically constrained plasma
Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.
Turbulent magnetohydrodynamic reconnection mediated by the plasmoid instability
It has been established that the Sweet–Parker current layer in high Lundquist number reconnection is unstable to the super-Alfvénic plasmoid instability. Past two-dimensional magnetohydrodynamic simulations have demonstrated that the plasmoid instability leads to a new regime where the Sweet–Parker current layer changes into a chain of plasmoids connected by secondary current sheets, and the averaged reconnection rate becomes nearly independent of the Lundquist number. In this work, a three-dimensional simulation with a guide field shows that the additional degree of freedom allows plasmoid instabilities to grow at oblique angles, which interact and lead to self-generated turbulent reconnection. The averaged reconnection rate in the self-generated turbulent state is of the order of a hundredth of the characteristic Alfvén speed, which is similar to the two-dimensional result but is an order of magnitude lower than the fastest reconnection rate reported in recent studies of externally driven three-dimensional turbulent reconnection. Kinematic and magnetic energy fluctuations both form elongated eddies along the direction of the local magnetic field, which is a signature of anisotropic magnetohydrodynamic turbulence. Both energy fluctuations satisfy power-law spectra in the inertial range, where the magnetic energy spectral index is in the range from −2.3 to −2.1, while the kinetic energy spectral index is slightly steeper, in the range from −2.5 to −2.3. The anisotropy of turbulence eddies is found to be nearly scale-independent, in contrast with the prediction of the Goldreich–Sridhar theory for anisotropic turbulence in a homogeneous plasma permeated by a uniform magnetic field.
Blob Structure and Motion in the Edge and SOL of NSTX
The structure and motion of discrete plasma blobs (a.k.a. filaments) in the edge and scrape-off layer of NSTX is studied for representative Ohmic and H-mode discharges. Individual blobs were tracked in the 2D radial versus poloidal plane using data from the gas puff imaging diagnostic taken at 400 000 frames $s^{−1}$. A database of blob amplitude, size, ellipticity, tilt, and velocity was obtained for ~45 000 individual blobs. Empirical relationships between various properties are described, e.g. blob speed versus amplitude and blob tilt versus ellipticity. The blob velocities are also compared with analytic models.
Particle-in-cell δf gyrokinetic simulations of the microtearing mode
The linear stability properties of the microtearing mode are investigated in the edge and core regimes of the National Spherical Torus Experiment (NSTX) using the particle-in-cell method based gyrokinetic code GEM. The dependence of the mode on various equilibrium quantities in both regions is compared. While the microtearing mode in the core depends upon the electron-ion collisions, in the edge region, it is found to be weakly dependent on the collisions and exists even when the collision frequency is zero. The electrostatic potential is non-negligible in each of the cases. It plays opposite roles in the core and edge of NSTX. While the microtearing mode is partially stabilized by the electrostatic potential in the core, it has substantial destabilizing effect in the edge. In addition to the spherical tokamak, we also study the microtearing mode for parameters relevant to the core of a standard tokamak. The fundamental characteristics of the mode remain the same; however, the electrostatic potential in this case is destabilizing as opposed to the core of NSTX. The velocity dependence of the collision frequency, which is crucial for the mode to grow in slab calculations, is not required to destabilize the mode in toroidal devices.
Post calibration of the two-dimensional electron cyclotron emission imaging instrument with electron temperature characteristics of the magnetohydrodynamic instabilities
The electron cyclotron emission imaging (ECEI) instrument is widely used to study the local electron temperature $(T_e)$ fluctuations by measuring the ECE intensity $I_{ECE} \propto T_e$ in tokamak plasmas.
The ECEI measurement is often processed in a normalized fluctuation quantity against the time averaged value due to complication in absolute calibration. In this paper, the ECEI channels are relatively calibrated using the flat $T_e$ assumption of the sawtooth crash or the tearing mode island and a proper extrapolation.
The 2-D relatively calibrated electron temperature $(T_{e,rel})$ images are reconstructed and the displacement amplitude of the magnetohydrodynamic modes can be measured for the accurate quantitative growth analysis.
Pushing particles with waves: Current Drive and alpha-Channeling
It can be advantageous to push particles with waves in tokamaks or other
magnetic confinement devices, relying on wave-particle resonances to
accomplish specific goals. Waves that damp on electrons or ions in
toroidal fusion devises can drive currents if the waves are launched
with toroidal asymmetry. Theses currents are important for tokamaks,
since they operate in the absence of an electric field with curl,
enabling steady state operation. The lower hybrid wave and the electron
cyclotron wave have been demonstrated to drive significant currents.
Non-inductive current also stabilizes deleterious tearing modes. Waves
can also be used to broker the energy transfer between energetic alpha
particles and the background plasma. Alpha particles born through fusion
reactions in a tokamak reactor tend to slow down on electrons, but that
could take up to hundreds of milliseconds. Before that happens, the
energy in these alpha particles can destabilize on collisionless
timescales toroidal Alfven modes and other waves, in a way deleterious
to energy confinement. However, it has been speculated that this energy
might be instead be channeled instead into useful energy, that heats
fuel ions or drives current. An important question is the extent to
which these effects can be accomplished together.
Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code
The VMEC nonlinear ideal MHD equilibrium code [S.P. Hirshman & J.C. Whitson, Phys. Fluids 26, 3553 (1983)] is compared against analytic linear ideal MHD theory in a screw-pinch-like configuration.
The focus of such analysis is to verify the ideal MHD response at magnetic surfaces which possess magnetic transform ($\iota$) which is resonant with spectral values of the perturbed boundary harmonics.
A large aspect ratio circular cross section zero-beta equilibrium is considered.
This equilibrium possess a rational surface with safety factor $q=2$ at a normalized flux value of $0.5$.
A small resonant boundary perturbation is introduced, exciting a response at the resonant rational surface.
The code is found to capture the plasma response as predicted by a newly developed analytic theory that ensures the existence of nested flux surfaces by allowing for a jump in rotational transform ($\iota=1/q$).
The VMEC code satisfactorily reproduces these theoretical results without the necessity of an explicit transform discontinuity ($\Delta \iota$) at the rational surface.
It is found that the response across the rational surfaces depends upon both radial grid resolution and local shear ($d\iota/d\Phi$), where $\iota$ is the rotational transform and $\Phi$ the enclosed toroidal flux).
Calculations of an implicit $\Delta\iota$ suggest that it does not arise due to numerical artifacts (attributed to radial finite differences in VMEC) or existence conditions for flux surfaces as predicted by linear theory (minimum values of $\Delta\iota$).
Scans of the rotational transform profile indicate that for experimentally relevant levels of transform shear the response becomes increasing localised.
Careful examination of a large experimental tokamak equilibrium, with applied resonant fields, indicates that this shielding response is present, suggesting the phenomena is not limited to this verification exercise.
Suppressed gross erosion of high-temperature lithium via rapid deuterium implantation
Lithium-coated high-Z substrates are planned for use in the NSTX-U divertor and are a candidate plasma facing component (PFC) for reactors, but it remains necessary to characterize the gross Li erosion rate under high plasma fluxes ($>10^{23} m^{−2} s^{−1}$), typical for the divertor region. In this work, a realistic model for the compositional evolution of a Li/D layer is developed that incorporates first principles molecular dynamics (MD) simulations of D diffusion in liquid Li. Predictions of Li erosion from a mixed Li/D material are also developed that include formation of lithium deuteride (LiD). The erosion rate of Li from LiD is predicted to be significantly lower than from pure Li. This prediction is tested in the Magnum-PSI linear plasma device at ion fluxes of $10^{23}–10^{24} m^{−2} s^{−1}$ and Li surface temperatures ≤800 °C. Li/LiD coatings ranging in thickness from 0.2 to 500 μm are studied. The dynamic D/Li concentrations are inferred via diffusion simulations. The pure Li erosion rate remains greater than Langmuir Law evaporation, as expected. For mixed-material Li/LiD surfaces, the erosion rates are reduced, in good agreement with modelling in almost all cases. These results imply that the temperature limit for a Li-coated PFC may be significantly higher than previously imagined.
Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov–Maxwell equations
Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov–Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. $10^9$, degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.
We demonstrate that in a 3D resistive magnetohydrodynamic simulation, for some parameters it is possible to form a stationary state in a tokamak where a saturated interchange mode in the center of the discharge drives a near helical flow pattern that acts to nonlinearly sustain the configuration by adjusting the central loop voltage through a dynamo action.
This could explain the physical mechanism for maintaining stationary nonsawtoothing “hybrid” discharges, often referred to as “flux pumping.”
Local wave particle resonant interaction causing energetic particle prompt loss in DIII-D plasmas
A new wave particle resonance mechanism is found explaining the first-orbit prompt neutral beam-ion losses induced by shear Alfvén Eigenmodes (AEs) in the DIII-D tokamak. Because of the large banana width, a typical trapped beam ion can only interact locally with a core localised Alfvén Eigenmode for a fraction of its orbit, i.e. part of its inner leg of the banana orbit. These trapped beam ions can experience substantial radial kick within one bounce as long as the phases of the wave seen by the particles are nearly constant during this local interaction. A wave particle resonant condition is found based on the locally averaged particle orbit frequencies over the interaction part of the particle orbit. It is further found that the frequency width of the local resonance is quite large because the interaction time is short. This implies that particles over a considerable region of phase space can interact effectively with the localised AEs and experience large radial kicks within one bounce orbit. The radial kick size is found numerically and analytically to scale linearly in AE amplitude and is about 5 cm for typical experimental parameters. These results are consistent with experimental measurement.
Higher order volume-preserving schemes for charged particle dynamics
A class of higher order numerical methods for advancing the charged particles in a general electromagnetic field is developed based on processing technique. By taking the volume-preserving methods as the kernel, the processed methods are still volume-preserving, and preserve the conservative quantities for the Lorenz force system. Moreover, this class of numerical methods are explicit and are more efficient compared with other higher order composition methods. Linear stability analysis is given by applying the numerical methods to the test equation. It is shown that the newly constructed higher order methods have the better stability property. This allows the use of larger step sizes in their implementation.
Mesh generation for confined fusion plasma simulation
ULF waves in the ion cyclotron frequency range waves are regul arly observed at Mercury’smagnetosphere. Although previous statistical studies have shown that ULF waves are primarily compressionalnear the equator and transverse with linear polarization at higher latitude, the underlying reaso n for thisdistribution of wave polarization has not been understood. In order to address this key question, we havedeveloped a two-dimensional, ﬁnite element code that solves the full wave equations in glob al magnetosphericgeom etry. Using this code, we show that (1) efﬁcien t mode conversion from the fast compressional wa ves to theion-ion hybrid resonance occurs at Mercury consistent with previous calculations; (2) such mode-convertedwaves globally oscillate similar to ﬁeld line resonance at Earth; and (3) compressional wave energy is primarilylocalized near the equator, while ﬁeld-aligned transverse, linearly polarized waves generated by modeconversion at the ion-ion hybrid resonance radiate to higher latitude. Based on these wave solutions, we suggestthat the stron g transverse component of observed ULF waves at Mercury in high magneti c latitu de can beexplained as excitation of the ﬁeld line resonant waves at the ion-ion hybrid resonance.