# Research Seminars

Our Theory Seminars are usually held on Thursdays at 10:45am in T169 (come a little early for coffee, tea and cookies!)

(All visitors to PPPL must have their host notify the Site Protection Division or the Departmental Administrator Jennifer Jones for entrance to the laboratory.)

### Upcoming

• Join Zoom Meeting
Thermal ion orbit loss in diverted tokamaks and its role in the radial current balance
(abstract)
Robert Brzozowski, UCLA
#s1213, Friday, 29 Jan 2021, 11:00am
Ion orbit loss has long been considered a potential player in triggering and/or sustaining the turbulence suppression necessary for the L-H transition. A loss cone model for the X-point mediated loss of thermal ions in diverted tokamaks finds that the loss plays a significant role in establishing the near-edge environment. The effective timescale of any one trajectory’s loss qualitatively changes if transit occurs faster than the ion would be scattered out of the loss region; above this threshold the rate of loss is driven by the rate of transport into the loss cone, while below this threshold the rate of loss is driven by the physical-space drift motions. The consideration of velocity-space relaxation processes along the loss region’s boundary serves both to demarcate the loss cone along this qualitative change in the effective timescale and to estimate the steady-state loss current across the resulting modified boundary. The orbit loss calculations are implemented into the transport code SOLPS as source terms, and the equilibrium radial current balance is investigated in L-mode plasmas near the L-H transition. Within the studied parameter space, the loss current is directly proportional to the ion temperature and exhibits low- and high-density branch behaviors for a given input power. Analysis indicates that the return current primarily consists of two components: an increased inward flow of ions associated with the perpendicular viscosity and a decreased outward diamagnetic flow of ions. The former drives the leading order plasma response, an increase in the shear of the electric field and plasma rotations in the vicinity of the separatrix, while the latter involves lower order poloidal redistributions of the pressure about a flux surface. Following these observations, experimental proposals on ASDEX Upgrade have been made to ascertain the role of ion orbit losses. [1] M. Laishram, D. Sharma, and P. K. Kaw, Phys. Rev. E 91, 063110 (2015). [2] M. Laishram, D. Sharma, P. K. Chattopdhyay, and P. K. Kaw, Phys. Rev. E 95, 033204 (2017). [3] M. Laishram, D. Sharma, and P. Zhu, Journal of Physics D: Applied Physics 53, 025204 (2019). [4] M. Laishram, Driven dust vortex characteristics in plasma with external transverse and weak magnetic field (2020), 2011.03237.

### Past

• Join Zoom Meeting
Modeling of experimentally observed driven dust vortex characteristics in laboratory plasma
Modhuchandra Laishram, Institute for Plasma Research, India, abstract, slides
[#s1192, 17 Dec 2020]
A two-dimensional (2D) hydrodynamic model is developed for characterizing dynamics of driven-dissipative dust cloud confined in an axisymmetric toroidal setup along with an unbounded sheared streaming plasma [1, 2]. This formulation brings out several sources of the dust vorticity due to the background sheared plasma flow fields. The numerical solutions confirm the analytical structure of the driven dust vortex flow in the linear limit [1], but also fairly predict experimentally observed nonlinear characteristics of the dust rotation such as threshold structural bifurcation, the emergence of uniform vorticity core region, recovered scaling law for estimates the kinematic viscosity from the experimentally measurable quantities, and formation of steady-state multiple counter-rotating and co-rotating vortices [2, 3]. The hydrodynamic model is extended for analysis of driven vortex characteristics in presence of external transverse and weak magnetic field (B) in a planner setup and parametric regimes motivated by recent magnetized dusty plasma (MDP) experiments [4]. This analysis has shown that shear in the B can produce a sheared internal field (Ea) in between electrons and ions due to the E × B and ∇B × B-drifts that causes rotation of the dust cloud levitated in the plasma. The flow solution demonstrates that neutral pressure decides the dominance between the ions-drag and the Ea-force. The shear ions-drag generates an anti-clockwise circular vortical structure, whereas the shear Ea-force is very localized and gives rise to a clockwise D-shaped elliptical structure which turns into a meridional structure with decreasing B. In the regime of high pressure and lower B, the Ea-force becomes comparable or dominant over the ion drag and peculiar counter-rotating vortex pairs are developed in the domain. [1] M. Laishram, D. Sharma, and P. K. Kaw, Phys. Rev. E 91, 063110 (2015). [2] M. Laishram, D. Sharma, P. K. Chattopdhyay, and P. K. Kaw, Phys. Rev. E 95, 033204 (2017). [3] M. Laishram, D. Sharma, and P. Zhu, Journal of Physics D: Applied Physics 53, 025204 (2019). [4] M. Laishram, Driven dust vortex characteristics in plasma with external transverse and weak magnetic field (2020), 2011.03237.
• Join Zoom Meeting
Extended neoclassical plasma rotation and transport theory
Cheonho Bae, Atlanta International School, abstract, slides
[#s1191, 15 Dec 2020]
Extended neoclassical plasma rotation theory has been developed based on the fluid moment equations with collisionality-extended Braginskii’s closure of the viscosity and the first-order poloidal asymmetries in velocities, densities, and electrostatic potential [1-3]. Major recent extensions [3,4] include rotation and transport calculations with generalized D-shaped flux surfaces using the Miller geometry [5] with the Shafranov shifts. Recent rotation calculations of DII-D and KSTAR discharges [3,4], using the nonlinear self-consistent neoclassical GTROTA code [6], indicated agreements to within <15% to the measurements except in the very edge (rho > .90), thus providing confidence on the related transport calculations such as the radial electric field and the poloidal asymmetries. Further extension efforts [7] are in progress with its major extension to Mikhailovskii-Tsypin’s closure of the viscosity and other edge physics to increase the accuracy on the edge rotation and transport calculations, and to include non-axisymmetric toroidal perturbations and develop a neoclassical toroidal viscosity formalism. Capabilities of the GTROTA code have also been extended to allow self-consistent rotation and transport calculations of up to four ion and electron species. Future plans on theory and code development, with its focus on edge rotation and transport, will be discussed. [1] W. M. Stacey, A. W. Bailey, D. J. Sigmar and K. C. Shaing, Nucl. Fusion 25 , 463 (1985). [2] W. M. Stacey and C. Bae, Phys. Plasmas 16, 082501 (2009). [3] C. Bae, W.M. Stacey, W.M. Solomon, Nucl. Fusion, 53 (2013) 043011. [4] C. Bae, W.M. Stacey, S.G. Lee, L. Terzolo, Phys. of Plasmas, 21 (2014). [5] R.L. Miller, M.S. Chu, J.M. Greene, et. al., Phys. of Plasmas, 5 (1998). [6] C. Bae, W.M. Stacey, T.D. Morley, Comp. Phys. Communications, 184 (2013). [7] W. M. Stacey and C. Bae, Phys. Plasmas 22, 062503 (2015).
• Jaeheon Ahn, abstract
[#s1189, 03 Dec 2020]
The plasma core is likely to be affected by 'sawteeth' playing significant role in core confinement and impurity transport. In particular, heavy impurities accumulated in the core plasma may lead to a radiative collapse. In order to understand and control their dynamics, the characteristics of compound sawteeth and the control of sawteeth relying on current or power deposition in the vicinity of the q=1 surface are explored by means of MHD simulations. In this work, the numerical tool used to simulate sawteeth is the XTOR-2F code, which is a non-linear tridimensional code solving two-fluid MHD equations. Neoclassical transport is shown to be important for heavy impurities in the core region. Meanwhile, ASDEX-U measurements show that the impurity dynamics in presence of sawteeth differ from the predictions made by transport codes. Fluid equations that model the transport of impurities in a highly collisional (Pfirsch-Schlüter) regime are implemented and coupled to the set of two-fluid MHD equations. The simulations show a difference between the impurity profiles with and without sawteeth, consistent with experimental observations. This results from a competition between neoclassical processes and sawtooth relaxations.
• Jervis Mendonca, abstract
[#s1188, 03 Dec 2020]
The effects of flow shear on the stability of a (2,1) tearing mode are examined using numerical and analytic studies on a number of model systems [1]. For a cylindrical reduced magnetohydrodynamic (MHD) model, linear computations using the CUTIE code show that sheared axial flows have a destabilizing effect, while sheared poloidal flows tend to reduce the growth rate of the mode. These effects are independent of the direction of the flow. For helical flows the sign of the shear in the flow matters. This symmetry breaking is also seen in the nonlinear regime where the island saturation level is found to depend on the sign of the flows. I have subsequently done this study for the visco resistive kink (m= 1, n= 1) mode in the RMHD regime [2].
• Comparative Heliophysics: Planetary Space Weather in Our Solar System and Beyond
Chuanfei Dong, abstract
[#s1190, 02 Dec 2020]
In the last two decades, the field of heliophysics has witnessed a tremendous surge. Research in heliophysics now encompasses a wide spectrum of fields ranging from space and magnetospheric physics to solar and stellar physics. One of the primary objectives of heliophysics is to understand the Sun and its interactions with planets (including Earth), where space weather plays an important role. In my presentation, I will begin with NASA’s Mars Atmosphere and Volatile EvolutioN (MAVEN) mission and delineate my study on the Martian responses to an interplanetary coronal mass ejection (ICME) - sometimes termed as solar storm - by using a sophisticated multifluid magnetohydrodynamic (MHD) code. I will then discuss how an active young Sun transformed Mars from an early warmer and wetter world to a desiccated and frigid planet with a tenuous atmosphere. In recent several years, it is well recognized that heliophysics plays an increasingly important role in the rapidly growing field of exoplanetary science. I will present my studies on exoplanetary atmospheric losses due to the impact of stellar winds and storms on planets residing within close-in habitable zones of M-type stars, which is a key factor that determines planetary habitability. Last but not least, I will introduce the ten- moment multifluid model developed at Princeton with its applications to the global magnetosphere of Mercury and discuss how this new model may enhance the science return from ESA-JAXA BepiColombo mission to Mercury where I serve as a Co-I.
• Extending M3D-C1 to stellarator geometry: preliminary results
Yao Zhou, PPPL, abstract, slides
[#s1177, 19 Nov 2020]
Stellarator plasmas have been observed to be nonlinearly stable even when driven beyond linear MHD stability thresholds. Hence, stellarator designs could employ nonlinear stability considerations to relax linear stability constraints, which can often be too restrictive and costly. However, this possibility has not been systematically investigated due to the lack of a state-of-the-art nonlinear initial-value MHD code for stellarators. We aim to fill this gap by extending the M3D-C1 code from tokamak to stellarator geometry. Our approach introduces a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework. The mapping from the logical to the physical (R, phi, Z) coordinates is then used to calculate derivatives in the latter, in terms of which the existing physics equations are written. This way, no significant changes to the extended MHD models within M3D-C1 are required. So far, we have successfully implemented this approach in 2D and verified its results against the existing code. Preliminary results in 3D will also be presented, including proof-of-principle resistive MHD simulations of simple stellarator plasmas such as a rotating ellipse.
• First Principles Modeling of Point Defects in Bandgap Materials
Bharat Medasani, PPPL, abstract, slides
[#s1176, 05 Nov 2020]
Point defects have a strong impact on the performance of semiconductor and insulator materials used in technological applications, spanning microelectronics to energy conversion and storage. They also play a critical role in the synthesis and growth of oxide films. The nature of the dominant defect types, how they vary with processing conditions, and their impact on materials properties are central aspects that determine the performance of a material in a certain application. This information is, however, difficult to access directly from experimental measurements. Consequently, computational methods, based on electronic density functional theory (DFT), have found widespread use in the calculation of point-defect properties. DFT based computational methods for point defects have inherent errors that require explicit corrections. In this talk I explain the DFT based modeling of point defects and the associated correction schemes using Cr2O3 as an example. Utilizing the points defect data, self-diffusion in Cr2O3 is evaluated.
• Peeling-ballooning modes in low aspect ratio - towards a predictive edge pedestal model for spherical tokamaks
Dr. Andreas Kleiner (PPPL), abstract, slides
[#s1131, 15 Oct 2020]
Edge-localized modes (ELMs) are a major concern for tokamak devices and their control is crucial for the operation of future reactor-scale machines. ELMs can be triggered when strong gradients are present in the edge transport barrier (edge pedestal). The width and height of the pedestal is often constrained by the occurrence of ideal-MHD peeling-ballooning modes [1] as well as kinetic ballooning modes (KBMs) in the pedestal region; this model has been successfully applied by the EPED model [2] to predict the pedestal height and width in conventional aspect ratio tokamaks. The predictions of the EPED model however often do not accurately describe observations in machines with low aspect ratio (e.g. spherical tokamaks). For ELMing discharges in NSTX the EPED model predicts stability. The reasons for this discrepancy might be associated with the limitation to ideal-MHD computations or the breakdown of the assumption that local ballooning theory well approximates the stability limit of kinetic ballooning modes in the edge of low aspect ratio plasmas. With the goal of obtaining a model to predict ELMs in spherical tokamaks and to find the limiting values for pedestal width and height, we model peeling-ballooning modes including non-ideal effects. The extended-MHD code M3D-C1 [3,4] is applied to determine the stability thresholds of peeling-ballooning modes in NSTX discharges. We mainly focus on the influence of plasma resistivity and rotation on edge stability, but also consider two-fluid effects. By varying pedestal parameters such as the pressure gradient and current density for given (ELMing) discharges, we are able to locate these discharges in parameter space relative to the stability boundary. In this context, we also identify the physics mechanisms that are important to describe these macroscopic edge modes in spherical tokamaks. We find robust resistive peeling-ballooning modes well before the ideal stability threshold is met. These modes thus extend the region of ideal peeling-ballooning instability in the investigated ELMing NSTX discharges. It is found that the actual NSTX plasmas are localized close to, or slightly within, the unstable side of the stability boundary calculated with our model. For large aspect ratio discharges the model is benchmarked with the ELITE code, which is employed in the frame of the EPED model. This study of macroscopic instabilities constitutes a first step towards a model to predict pedestal width and height in H-mode discharges in spherical tokamaks.
• Learning long division: weak operations in a discontinuous Galerkin kinetic solver
Mana Francisquez, MIT, abstract, slides
[#s1120, 08 Jul 2020]
The Gkeyll computational plasma physics code aims to provide a unified framework for fluid and kinetic studies using state-of-the-art discontinuous Galerkin (DG) methods. In developing Gkeyll we learned a number of lessons in DG theory and application, which are central to Gkeyll's algorithms and perhaps of interest to other DG workers. Some of these lessons stem from encountering operations as simple as division, so in this talk we will motivate DG division and how we have addressed that problem to deliver alias-free and conservative algorithms for, for example, kinetic collision operators. The concept of a weak equality, common to applied math and FEM communities, plays a central role. We will then discuss how weak equality has been leveraged in order to formulate and implement more complex operations, such as spectral transforms for piecewise discontinuous polynomial data and multigrid solutions of DG Poisson equations.
• An Improved Equation-Free Projective Integration Method for Gyrokinetic Profile Evolution of Tokamak Plasmas
Benjamin Sturdevant, PPPL, abstract, slides
[#s1105, 02 Mar 2020]
Cross-scale interactions between micro-scale transport processes and macro-scale profile evolution are difficult to study using brute-force long-time gyrokinetic simulations due to the large computational resources required and a possible accumulation of error. To address this, a multi-scale time integration method based on the equation-free projective integration method of Keverekidis and Gear [1] has been developed to accelerate kinetic simulations [2]. Previous attempts to use the equation-free method in kinetic plasma simulations were limited due to the appearance of spurious transient oscillations occurring after the lifting process, which are present when the kinetic simulations are initialized with a simplified model distribution function [3]. In this work, a kinetically-informed lifting algorithm has been added to the equation-free method to mitigate this issue. This scheme has been verified in the gyrokinetic particle-in-cell code XGCa. It has been demonstrated to accurately reproduce profile evolution due to collisional neoclassical orbital dynamics while achieving a computational speed up of over 4x compared to brute force time stepping.

References:

[1] I.G. Kevrekidis, C.W. Gear, J. Hyman, P. Kevrekidis, O. Runborg, and C. Theodoropoulos, Comm. Math. Sci. 1 (4) (2003) 715-762.
[2] B. Sturdevant, S.E. Parker, C.S. Chang, and R. Hager, submitted to Phys. Plasmas (2019).
[3] M. A. Shay, J.F. Drake, B. Dorland, J. Comput. Phys. 226 (2007) 571-585
• Global modelling of microinstabilities in stellarators and with electromagnetic effects using XGC
Michael Cole, PPPL, abstract, slides
[#s1104, 27 Feb 2020]
Global gyrokinetic simulations are an increasingly important tool for understanding and designing magnetic confinement fusion devices. The recent operation of the optimized stellarator Wendelstein 7-X in a turbulence-dominated regime gives renewed urgency to the need for stellarator gyrokinetics in general, while electromagnetic effects are likely to play an important role in turbulence transport in both tokamaks and stellarators. In this talk, we report developments and deployment of the full volume gyrokinetic code XGC for stellarator physics and electromagnetic physics. XGC has been extended to treat general 3D toroidal equilibria with modifications to permit efficient electrostatic field solve. The code has then been used to reproduce linear electrostatic ITG calculations in Wendelstein 7-X and PPPL's QUASAR, followed by the first global turbulence transport simulations in QUASAR geometry. In addition, implementation of improved explicit electromagnetic techniques has allowed XGC to reproduce the transition from ion temperature gradient (ITG) to kinetic balloon mode (KBM) dominated microinstability regimes in tokamak cyclone base case geometry. This has then been extended to simulations of KBM in test geometry similar to NSTX-U. Recent flux tube simulations with the GENE code (Aleynikova 2018) show a similar transition from an ITG to a KBM dominated regime at beta values lower than those envisioned for peak Wendelstein 7-X performance and future reactors. One future use of the combined global electromagnetic stellarator gyrokinetic code will be to investigate this and predict turbulence transport in optimized stellarators.
• Simulations, High Throughput Workflows, and Machine Learning in Materials Science
Bharat Medasani, University of Delaware, abstract
[#s1103, 25 Feb 2020]
In the first part of talk, a classical density functional theory for modeling the ionic environment surrounding macromolecules in aqueous suspensions is presented. Our approach extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, excluded volume correlations, and size asymmetry. I explain the computational schemes for 1d systems (obtained after applying symmetry) and 3d systems. Results for spherical and cylindrical models representing nanoparticles and proteins respectively are presented.
In the second part, Fireworks, a popular workflow software for running simulations in high throughput at supercomputing centers is presented. Fireworks has been used to run more than 100 million CPU-hours worth of materials science and computational chemistry simulations at National Energy Research Supercomputing Center (NERSC). It supports many features relevant to enabling modern data-driven and high-throughput science applications. I also discuss my work in optimizing the performance of Fireworks.
In the final part, I present a novel use of machine learning to predict defects in B2 intermetallics, a class of intermetallics containing two elements and with a specific crystal structure. Data on defects in materials is scarce due to the complexities involved in both experiments and simulations. Computational data for defects was generated using Fireworks based workflows. Using the generated data and by applying gradient boosting classification (which was then an innovative machine learning technique) defects in B2 intermetallics were predicted with a high accuracy.
• Progress in theoretical understanding of the Dimits shift and the tertiary instability in drift-wave turbulence
Hongxuan Zhu, PPPL, abstract, slides
[#s1102, 20 Feb 2020]
A generic understanding of the well-known Dimits shift in electrostatic drift-wave turbulence is obtained, for the first time, by studying the tertiary instability of a zonal flow within reduced turbulence models [Phys. Rev. Lett. 124, 055002 (2020)]. We show that tertiary modes are localized near extrema of the zonal velocity U(x) with respect to the radial coordinate x. These modes can be described as quantum harmonic oscillators with complex frequencies, so their spectrum can be readily calculated. The corresponding growth rate is derived within the modified Hasegawa-Wakatani model. We show that the growth rate equals the primary-instability growth rate plus a term that depends on the local flow "curvature", i.e., the second radial derivative of U; hence, the instability threshold is shifted compared to that in homogeneous turbulence. This shift is the Dimits shift, which we find explicitly in the Terry-Horton limit, and our analytic predictions agree well with results from numerical simulations. Our theory of the tertiary instability also extends to other turbulence models. For example, the key features of the tertiary instability of ion-temperature-gradient drift waves are reproduced by our theory and verified by gyrokinetic simulations using the code GS2.

Remote participation: https://zoom.us/j/832071905
• Towards a quasi-dynamic model for 3D MHD based on energy minimisation and relaxation
Adelle Wright, Australian National University, abstract, slides
[#s1100, 13 Feb 2020]
Recent experiments have found evidence of MHD activity in stellarators, including the observation of sawtooth-like oscillations during electron cyclotron current drive (ECCD) experiments in the second Wendelstein 7-X campaign [1]. In this talk, we present our approach to developing a quasi-dynamical model for 3D MHD that is based on energy minimisation and relaxation, and motivated by the need for predictive and computationally efficient global modelling of macroscopic dynamics in stellarators.

We propose to approximate plasma evolution by a sequence of MHD equilibria which are connected via re-equilibrating relaxation events and consistent with broader physics setting of extended-MHD. A particular challenge, compared to previous cognate approaches [2], is to accommodate the variety of topological structures (e.g. magnetic islands and stochastic field regions) which can be supported in 3D MHD equilibria.

For our equilibria we use the Multi-Region Relaxed MHD (MRxMHD) model, proposed by Dewar et al. [3], wherein a plasma is partitioned into a finite number of Taylor-relaxed, force-free (i.e. constant pressure) volumes. The volumes are separated by current sheet interfaces across which a pressure jump is supported leading to equilibria with discontinuous, stepped pressure profiles. We discuss an a priori prescription for determining the sequence of equilibria which is based on the successive break up of MRxMHD interfaces and exploits the Hamiltonian nature of magnetic fields.

Next, we consider dynamical accessibility, i.e. whether successive equilibria in a quasi-dynamical sequence can be reached by the plasma in a way that is consistent with both MRxMHD and extend-MHD. Since MRxMHD states are hypothesised to form via volume-localised Taylor relaxation, we examine in detail the nonlinear dynamics of relaxation. Using a simple force-free model as a testbed, we discuss the development of diagnostics and analysis tools, with a view to quantitatively constraining the timescale and parameter regime in which such a quasi-dynamical model may be valid.

[1] M. Zanini et al., EPJ Web of Conferences 203, 02013 (2019).
[2] R. Clemente et al., Plasma physics and controlled nuclear fusion 1988 V.2 (1989).
[3] R. L. Dewar et al., Journal of Plasma Physics 81.6 (2015).

Remote participation: https://zoom.us/j/832071905
• DCON for SPEC
Alan H. Glasser, Fusion Theory and Computation , Inc. (FTCI), abstract, slides
[#s1101, 12 Feb 2020]
DCON is a widely-used ideal MHD stability code for axisymmetric toroidal plasmas, based on a generalization of Newcomb’s criterion for a cylindrical plasma. This presentation describes a further generalization to non-axisymmetric toroidal plasmas with toroidal periodicity and stellarator symmetry.

This work was originally formulated for equilibria computed by the VMEC code, but that has encountered several problems. One is that VMEC imposes nested flux surfaces on the solution, which is unrealistic and fails to find a true energy minimum. A second is that it uses radial finite differences, uniformly spaced in toroidal magnetic flux, to solve for the magnetic field B, resulting in very poor resolution near the magnetic. A third is a failure to maintain div B = 0. These problems have proved fatal to the DCON approach.

The current approach is based on equilibria computed by the more recent SPEC code, developed by Dewar, Hudson, et al. SPEC (Stepwise Pressure Equilibrium Code) partitions the plasma into infinitesimal interfaces with finite plasma pressure discontinuities but [[P + B2/2]] = 0; and volumes between the interfaces where the plasma relaxes to a Taylor state and may have regions of multiple small islands and stochasticity. Radial discretization uses Chebyshev polynomials, with regularization in the innermost volume near the axis of the coordinate system. It solves for the vector potential A rather than the magnetic field B, ensuring div B = 0.

DCON for SPEC treats the interfaces as having finite width d and then takes the limit as δ -> 0.It derives a sequence of Euler-Lagrange equations for complex vectors of poloidal and toroidal Fourier components in successive interfaces and volumes, coupled together to produce a global solution and a generalized necessary and sufficient condition for ideal MHD stability. The derivation is complete and is being implemented in a new code.

Remote participation: https://zoom.us/j/832071905
• Stochastic electron acceleration in laser-plasma interactions
Yanzeng Zhang, University of California San Diego, USA, abstract, slides
[#s1099, 11 Feb 2020]
The generation of energetic electron beams via the interaction of an intense laser pulse with underdense plasma is of great interest for many different applications, where the mechanisms of electron acceleration have been suggested and studied analytically, numerically, and experimentally over many years. It was revealed that the presence of self-generated (or externally applied) quasi-static electric and magnetic fields or a second counter-propagating weak laser pulse could significantly increase the electron energy well beyond the ponderomotive energy scaling (the maximum energy of an electron in the dominant laser only). However, due to the multidimensional spatio-temporal characteristics of the laser waves and strong nonlinearity of relativistic electron in these fields, the analytic investigations of the mechanism of electron acceleration in the earlier studies are quite limited, whereas the numerical simulations, which could also provide information of electron dynamics, are only valid within simulated parameter range. In this talk, I will introduce a novel approach to investigating the electron dynamics, especially paying attention to the stochastic electron acceleration, in different configurations of laser beams and quasi-static EM fields. The main idea of this method is to find proper canonical variables so that the new Hamiltonian describing the electron dynamics is time-independent without the appreciated perturbation. It can significantly simplify the analysis of the electron dynamics and allow us to utilize the fundamental results of previous studies on regular and stochastic motion in Hamiltonian systems. The physics underlying stochastic electron acceleration are revealed and the stochastic conditions are found by deriving the Chirikov-like mappings, which introduce the upper limit of the electron energy gained from the stochastic electron acceleration.

Remote participation: https://zoom.us/j/832071905
• Collective Thomson Scattering Diagnostic on Wendelstein 7-X
Ivana Abramovic, Eindhoven University of Technology, The Netherlands, abstract, slides
[#s1098, 27 Jan 2020]
The most advanced and the World’s only optimized stellarator, the Wendelstein 7-X (W7-X) experiment in Greifswald (Germany), came into operation in 2015 with the goal to explore the viability of the optimized stellarator concept as a fusion reactor. Adequate diagnostics of the key plasma parameters are of crucial importance for fulfilling this goal. The research conducted over the course of this project concerns the development of theory and modelling of collective Thomson scattering diagnostic on W7-X. Collective Thomson scattering (CTS) is a powerful microwave diagnostic sensitive primarily to ion dynamics and capable of simultaneously measuring a number of important parameters such as: ion temperature, plasma composition, drift velocities and fast ion population. A CTS measurement results in a spectrum from which values of desired plasma parameters can be inferred. To this end a forward model, eCTS, of the scattering was developed which allows calculation of synthetic CTS spectra based on a set of input parameters. The forward model was integrated into a Bayesian scientific framework which allows one to solve the inverse problem of inferring posterior probability distributions of input parameters of the forward model given the measured spectra. eCTS has successfully been used to analyze the first CTS spectra obtained on W7-X. Additionally neural networks were trained on databases produced by eCTS in a relevant parameter space in order to provide fast inference of bulk ion temperatures as an alternative for Bayesian inference.
The work also furthers CTS theory by extending the set of parameters measurable by the CTS diagnostic to include the radial electric field and enables exploration of anisotropic temperature effects. Finally, the work explores experimental challenges hindering optimal performance of CTS as well as data analysis related challenges which stand in the way of using this diagnostic to its full potential.

Remote participation: https://zoom.us/j/832071905
• Excitation and Damping Mechanisms of Geodesic Acoustic Modes in Tokamaks
Ivan Novikau, Max-Planck-Institut for Plasma Physics (IPP), Garching, Germany, abstract, slides
[#s1097, 23 Jan 2020]
Turbulence in tokamaks generates radially sheared zonal flows (ZFs). Their oscil- latory counterparts, geodesic acoustic modes (GAMs), appear due to the action of the magnetic field curvature. The zonal structures can reduce the radial transport in toka- mak plasma acting as a sink for the turbulence energy through the inverse energy cascad- ing. The GAMs can also be driven by an anisotropic energetic particle (EP) population leading to the formation of global radial structures, called EGAMs. The EGAMs play a role of an intermediate agent between the EPs and thermal plasma, by redistributing EP energy to the bulk plasma through the collisionless wave-particle interaction. In such a way, the EGAMs might contribute to the plasma heating. Thus, investigation of EGAM characteristics, especially in the velocity space, is necessary for precise understanding of the transport phenomena in tokamak plasmas. In addition to ion Landau damping, both the GAMs and EGAMs have been found to be subject to the electron Landau damping. To investigate the influence of the electron damping on the GAMs and EGAMs, a Mode-Particle-Resonance (MPR) diagnostic has been implemented in the global gyrokinetic particle-in-cell code ORB5. This enables to investigate the relative importance and the evolution of wave-particle resonances responsible for the ion and electron Landau damping, and of the EP drive. An ASDEX upgrade (AUG) discharge #31213 is chosen as a reference case for this investigation due to its rich EP nonlinear dynamics.
Nonlinear GAM excitation by turbulence is also considered. Using realistic temper- ature and density profiles as well as magnetic equilibrium of AUG shot #20787, GAM excitation by ITG instabilities is shown with comparison between numerical and exper- imental GAM frequency spectra. Finally, excitation of a global GAM-like structure in a TCV magnetic configuration is presented as well.

Remote participation via Zoom: https://zoom.us/j/4634811292
• Electron Modeling for MHD Simulation in Fusion Plasmas
Dongjian Liu, Sichuan University, Chengdu, China, abstract, slides
[#s1096, 22 Jan 2020]
A series of electron model has been developed to study the low frequency electromagnetic modes in magnetized plasmas[1] [2]. Coupled to the gyrokinetic ions, the global gyrokinetic particle simulation of tearing modes have been developed and verified in the gyrokinetic toroidal code (GTC). GTC linear simulations in the fluid limit of the kink-tearing, resistive tearing modes and collisonless tearing mode in the cylindrical geometry agree well with the magnetohydrodynamic eigenvalue and initial value codes.

References:
[1] Dongjian Liu and Liu Chen, Plasma Physics and Controlled Fusion, 53 062002 (2011)
[2] Dongjian Liu, Wenlu Zhang, Joseph McClenaghan, Jiaqi Wang and Zhihong Lin, Physics of Plasmas 21,122520 (2014).

Remote participation via Zoom: https://zoom.us/j/4634811292
• Generation of suprathermal electrons by collective processes in Maxwellian plasmas
Sabrina F. Tigik, Instituto de Física, Universidade Federal do Rio Grande do Sul,Brazil , abstract
[#s1095, 06 Jan 2020]
Weak turbulence theory is the standard formalism for treating nonlinear, low amplitude, kinetic instabilities in collisionless plasmas; therefore, it is concerned only with the description of collective plasma oscillations. However, the long-lasting timescale of nonlinear processes suggests that collisions might affect the late plasma dynamics, acting alongside nonlinear oscillatory effects [1]. Such cases, where collective and collisional processes coexist in the plasma dynamics, have been rigorously addressed only recently [2]. One of the outcomes of this extended formulation is a then-unknown mechanism named electrostatic bremsstrahlung emission. The electrostatic bremsstrahlung is a kind of transient radiation, emitted in all spectrum, caused by continuous interparticle interactions. The portion irradiated in the eigenmode frequency range is capable of altering the wave spectrum, which will then modify the velocity distribution through wave-particle resonance. Considering emissions in the Langmuir wave frequency range, and Maxwellian electrons as the initial state, I have analyzed the time evolution of the system. The result was the scattering off of a small fraction of the thermal electrons in the resonance region, to high velocities, creating a suprathermal population. The tail grows consistently in the beginning, but after long integration time, the growth rate slows down, indicating that the system is arriving at a new asymptotic equilibrium state [3].

References: [1] S. F. Tigik, L. F. Ziebell, P. H. Yoon, and E. P. Kontar. Two-dimensional time evolution of beam-plasma instability in the presence of binary collisions. Astronomy & Astrophysics, 586:A19, February 2016.
[2] P. H. Yoon, L. F. Ziebell, E. P. Kontar, and R. Schlickeiser. Weak turbulence theory for collisional plasmas. Physical Review E, 93:033203, Mar 2016.
[3] S. F. Tigik, L. F. Ziebell, and P. H. Yoon. Generation of suprathermal electrons by collective processes in collisional plasma. The Astrophysical Journal Letters, 849(2):L30, 2017.

Remote participation via Zoom: https://zoom.us/j/8320719053
• Flow effects on visco-resistive MHD in a periodic cylindrical tokamak
Jervis Mendonca, Institute for Plasma Research, HBNI, India , abstract
[#s1094, 03 Jan 2020]
Flow and viscosity significantly modify resistive modes in a tokamak, and I have investigated these using the CUTIE code. These studies indicate that flow can be used to improve plasma duration and quality in a tokamak, and this has motivated my investigation. In this presentation, I have begun by studying the (2,1) tearing mode and found several new results, namely, that nature of stabilisation depended on whether axial or poloidal flows were used. I also observed that the sign of shear in helical flow mattered. This symmetry breaking is also seen in the nonlinear regime where the island saturation level is found to depend on the sign of the flows. I have proceeded to study the (1,1) internal kink mode using a Visco-Resistive MHD(V-RMHD) model. I have observed here that stabilisation due to axial flows in particular are affected by the viscosity regime. Symmetry breaking at higher viscosity in linear growth rates and nonlinear saturation levels as well is observed. In summary, for axial, poloidal, and most helical flow cases, there is flow induced stabilisation of the nonlinear saturation level in the high viscosity regime and destabilisation in the low viscosity regime. I have continued my studies in the two fluid regime. In the linear regime, we have studied how the growth rate as well as diamagnetic flow frequency of the modes changes due to fluid effects for a range of viscosity and resistivity values. I have also found diamagnetic drift stabilisation of the (1,1) mode in the two fluid case, that is, we have seen the growth rate of the (1,1) mode reduces with an increase in density gradient. In the nonlinear case, I investigate the evolution of the mode with imposed axial flow, poloidal and helical flows. I find the viscosity regime affects the nonlinear saturation regime.

Remote participation via Zoom: https://zoom.us/j/8320719053
• Wide q95 Windows for Edge-Localized-Mode Suppression by Resonant Magnetic Perturbations in the DIII-D Tokamak
Qiming Hu, PPPL, abstract, slides
[#s1075, 12 Dec 2019]
Edge-Localized-Mode (ELM) suppression by resonant magnetic perturbations (RMPs) typically occurs over narrow ranges in the plasma magnetic safety factor q95, however wide q95 windows of ELM suppression are favourable for the robust avoidance of ELMs in ITER and future reactors. Here we show from experiment and nonlinear two-fluid MHD simulation that wide q95 windows for ELM suppression are accessible in low-collisionality DIII-D plasmas relevant to ITER high power mission so long as the applied RMP strength exceeds the threshold for resonant field penetration at the pedestal top by ~1.5X. When the applied RMP is close to the threshold for resonant field penetration at the top of the pedestal, only isolated magnetic islands form near the pedestal top, producing narrow q95 windows of ELM suppression (dq95 ~ 0.1). However, as the threshold for field penetration decreases relative to the RMP amplitude, then multiple magnetic islands can be driven on adjacent rational surfaces near the pedestal top. Multiple magnetic islands lead to q95 window merging and wide regions of ELM suppression (up to dq95 ~ 0.7 seen in DIII-D). Nonlinear MHD simulations are in quantitative agreement with experiment and predict improved access to wide windows of ELM suppression in DIII-D by using n = 4 RMPs, due to the denser rational surfaces and the weak dependence of the penetration threshold and island width on toroidal mode number.
• Regimes of weak ITG/TEM modes for transport barriers without velocity shear
Mike Kotschenreuther, University of Texas, Austin , abstract, slides
[#s1093, 11 Dec 2019]
TBD
• A deep dive into the distribution function: understanding phase space dynamics using continuum Vlasov-Maxwell simulations
J. Juno, University of Maryland , abstract, slides
[#s1091, 05 Dec 2019]
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly collisional plasma is challenging. The equation system of relevance, the Vlasov-Maxwell system of equations, is difficult to numerically integrate, and traditional methods such as the particle-in-cell method introduce counting noise into the distribution function.
But motivated by the physics contained in the distribution function, we have implemented a novel continuum Vlasov-Maxwell method in the Gkeyll framework [1,2]. The algorithm uses the discontinuous Galerkin finite element method to produce a high order accurate solution, and a number of algorithmic breakthroughs have been made to produce a robust, cost efficient solver for the Vlasov-Maxwell system of equations.
In this talk, I will present both our algorithmic work and the phase space dynamics of a number of plasma processes, focusing on two applications which make manifest the power and utility of a continuum Vlasov-Maxwell method. I will demonstrate how the high fidelity representation of the distribution function, combined with novel diagnostics, permits detailed analysis of the energization processes in a perpendicular collisionless shock. In addition, I will show a set of recent results on the evolution of kinetic instabilities driven by unstable beams of plasma, where the generation of small scale structures in velocity space has dramatic consequences for the overall macroscopic evolution of the plasma[3]. To further motivate the development of the continuum Vlasov-Maxwell method, I will also show how particle noise can modify the dynamics of the latter set of simulations with analogous particle-in-cell simulations.

[1] J. Juno, A. Hakim, J. TenBarge, E. Shi, W. Dorland (2018). Discontinuous Galerkin algorithms for fully kinetic plasmas. Journal of Computational Physics, 353, 110—147.
[2] A. Hakim, M. Francisquez, J. Juno, G. Hammett. “Conservative Discontinuous Galerkin Discretizations of Fokker-Planck Operators.” submitted to Journal of Plasma Physics, 2019
[3] V. Skoutnev, A. Hakim, J. Juno, J. TenBarge. “Temperature-dependent Saturation of Weibel-type Instabilities in Counter-streaming Plasmas.” Astrophysical Journal Letters, 872, 2. (2019)
• More Intelligent Execution of Ensembles of Nonlinear Kinetic Simulations: learning and improving efficiency and accuracy as we go - BARS, SHAD BARS and mini-BARS
Bedros Afeyan, Polymath Research Inc.
[#s1092, 04 Dec 2019]
• Machine learning of equivariant functions inspired by atomistic modelling with a special view towards fusion materials simulations
Bastiaan J. Braams, Centrum Wiskunde & Informatica (CWI),The Netherlands , abstract, slides
[#s1089, 27 Nov 2019]
Over the past several years big data methods, including but not limited to use of deep convolutional neural networks, have been very successful in computer science applications and there is increasing effort to apply big data or machine learning methods to problems in physical science and engineering. Conversely we are seeing that problems from physical science are influencing machine learning research done in computer science environments. A very important application of big data methods in physical science where we see this mutual influence is the construction of effective interatomic potentials and force fields for atomistic modelling of molecular and condensed phase systems (e.g. [1]). This application shares features with certain applications in three-dimensional image processing in having data associated with point clouds and in seeking to represent functions that are invariant or covariant with respect to a permutation group (applied to the labelling of points in the cloud) and with respect to spatial groups of translations, rotations and inversion. Some by now almost classical big data approaches to the atomistic problem include use of Gaussian process approximation (kernel ridge regression) [2] and use of spherical wavelet expansions [3]. In addition deep neural networks are being applied (e.g. [4], [5]) and here we see the closest link to machine learning research with key words such as Point Cloud Convolutional Networks, Deep Sets, Spherical CNNs, Tensor Field Networks and Gauge Equivariant Neural Networks [6]. The presentation will provide a survey of these machine learning developments in the context of the application in physical science with a special view towards radiation damage simulations for fusion.

References:
[1] Ceriotti, Michele. "Atomistic machine learning between predictions and understanding." arXiv preprint arXiv:1902.05158 (2019).
[2] Bartók, Albert P., and Gábor Csányi. "Gaussian approximation potentials: A brief tutorial introduction." International Journal of Quantum Chemistry 115, no. 16 (2015): 1051-1057.
[3] Eickenberg, Michael, Georgios Exarchakis, Matthew Hirn, Stéphane Mallat, and Louis Thiry. "Solid harmonic wavelet scattering for predictions of molecule properties." The Journal of chemical physics 148, no. 24 (2018): 241732.
[4] Schütt, Kristof T., Huziel E. Sauceda, P-J. Kindermans, Alexandre Tkatchenko, and K-R. Müller. "SchNet–A deep learning architecture for molecules and materials." The Journal of Chemical Physics 148, no. 24 (2018): 241722.
[5] Zhang, Linfeng, Jiequn Han, Han Wang, Wissam Saidi, Roberto Car, and Weinan E. "End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems." In Advances in Neural Information Processing Systems, pp. 4441-4451. 2018.
[6] Extensive further references to be provided in the presentation.
• An adjoint approach for the shape gradients of 3D MHD equilibria
Elizabeth Paul, University of Maryland , abstract, slides
[#s1090, 25 Nov 2019]
The design of modern stellarators often employs gradient-based optimization to navigate the high-dimensional spaces used to describe their geometry. However, computing the numerical gradient of a target function with respect to many parameters can be expensive. The adjoint method allows these gradients to be computed at a much lower cost and without the noise associated with finite differences. In addition to gradient-based optimization, the derivatives obtained from the adjoint method are valuable for local sensitivity analysis and tolerance quantification.

[1] Antonsen, T.M., Paul, E.J. & Landreman, M. 2019 Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria. Journal of Plasma Physics 85 (2).
[2] Hirshman, S.P. & Whitson, J.C. 1983 Steepest descent moment method for three-dimensional magnetohydrodynamic equilibria. Physics of Fluids 26 (12), 3553.
[3] Cooper, W.A., Hirshman, S.P., Merazzi, S. & Gruber, R. 1992 3D magnetohydrodynamic equilibria with anisotropic pressure. Computer Physics Communications 72 (1),1–13.
[4] Paul, E.J., Antonsen, T.M., Landreman, M., Cooper, W.A. Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria, Part II: Applications. Submitted to Journal of Plasma Physics.
• Learning data driven discretizations for partial differential equations
[#s1077, 14 Nov 2019]
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small scale physics. Deriving such coarse grained equations is notoriously difficult, and often ad hoc. Here we introduce data driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end-to-end to best satisfy the equations on a low resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in one spatial dimension at resolutions 4-8x coarser than is possible with standard finite difference methods.
• Variational Principles and Applications of Local Topological Constants of Motion for Non-Barotropic Magnetohydrodynamics
Asher Yaholom, Ariel University, Israel, abstract, slides
[#s1076, 12 Nov 2019]
Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this presentation we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic MHD can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary non-barotropic flows. This is less than the eight variables which appear in the standard equations of barotropic MHD which are the magnetic field B ⃗ the velocity field v ⃗, the entropy s and the density ρ. The case of non-barotropic MHD in which the internal energy is a function of both entropy and density was not discussed in previous works which were concerned with the simplistic barotropic case. It is important to understand the rule of entropy and temperature for the variational analysis of MHD. Thus we introduce a variational principle of non-barotropic MHD and show that five functions will suffice to describe this physical system.
We will also discuss the implications of the above analysis for topological constants. It will be shown that while cross helicity is not conserved for non-barotropic MHD a variant of this quantity is. The implications of this to non-barotropic MHD stability is discussed.

[1] Asher Yahalom, “Simplified Variational Principles for non-Barotropic Magnetohydrodynamics,” J. Plasma Phys. (2016), vol. 82, 905820204.
[2] Asher Yahalom, “Non-Barotropic Magnetohydrodynamics as a Five Function Field Theory,” International Journal of Geometric Methods in Modern Physics, No. 10 (November 2016), Vol. 13 1650130.
[3] Asher Yahalom, “A Conserved Local Cross Helicity for Non-Barotropic MHD,” Journal of Geophysical & Astrophysical Fluid Dynamics (2017), Vol. 111, No. 2, 131–137.
[4] Asher Yahalom, “Non-Barotropic Cross-helicity Conservation Applications in Magnetohydrodynamics and the Aharanov - Bohm effect," Fluid Dynamics Research (2017), Volume 50, Number 1, 011406.
• First-principle formulation of resonance broadened quasilinear theory near an instability threshold
Vinícius Duarte, PPPL, abstract, slides
[#s1069, 19 Sep 2019]
A method is developed to analytically determine the resonance broadening function in quasilinear theory, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the nonlinear growth rate and mode saturation levels for near-threshold plasmas previously calculated from kinetic theory. The distribution function is also calculated, which enables precise determination of the characteristic collisional resonance width.
[Based on preprint V. Duarte, N. Gorelenkov, R. White and H. Berk, The collisional resonance function in discrete-resonance quasilinear plasma systems, arXiv:1906.01780v1 (2019)]
• Global gyrokinetic PIC simulations of electromagnetic perturbations in fusion plasmas
Alexey Mishchenko, IPP, abstract, slides
[#s1068, 12 Sep 2019]
An overview of European gyrokinetic PIC codes will be presented with a focus on numerical schemes used in the electromagnetic regime. Simulations of Alfven modes destabilized by the fast particles and of the zonal flows generated by the unstable Alfven waves will be discussed. Gyrokinetic PIC simulations of the MHD-type instabilities will be addressed on example of the internal kink modes. Simulations of the transition from the ITG-dominated regime to the KBM regime and finally to the microtearing instabilities with plasma beta increasing will be shown.
• Next-gen distributed computing networks in support of research, discovery and innovation
Dan Desjardin, Royal Military College of Canada/Distributed Compute Labs, abstract
[#s1065, 15 Aug 2019]
Distributed Compute Labs (DCL) is a Canadian educational nonprofit organization responsible for developing and deploying the Distributed Compute Protocol (DCP), a lightweight, easy-to-use, idiomatic, and powerful computing framework built on modern web technology, that allows any device — from smartphones to enterprise web servers — to contribute otherwise idle CPU and GPU capacity to secure and configurable general-purpose computing networks. By leveraging existing devices and infrastructure — a university’s desktop fleet, for example — a large supply of latent computational resources becomes available at no additional capital cost. DCP makes it possible for everyone — from a student in Santa Barbara to a large enterprise in New York City — to have access to large quantities of cost-effective computing resources. In summary, the Distributed Compute Protocol democratizes access to digital infrastructure, reduces barriers, and unleashes innovation.
• Phase-space theory of the Dimits shift and cross-scale interactions in drift-wave turbulence
Ilya Dodin, PPPL, abstract, slides
[#s1066, 08 Aug 2019]
Interactions of drift-wave turbulence with zonal flows, which are of interest due to their effect on fusion-plasma confinement, can be elucidated by using phase-space methods from quantum theory [1-7]. In this talk, I will show how applying these methods: (i) helps explain the cross-scale interactions between ITG and ETG turbulence seen in gyrokinetic simulations and also (ii) leads to a semi-quantitative analytic theory of the zonal-flow stability and the Dimits shift within the Terry-Horton model of drift-wave turbulence.

[1] H. Zhu, Y. Zhou, and I. Y. Dodin, Nonlinear saturation and oscillations of collisionless zonal flows, New J. Phys. 21, 063009 (2019).
[2] Y. Zhou, H. Zhu, and I. Y Dodin, Formation of solitary zonal structures via the modulational instability of drift waves, Plasma Phys. Control. Fusion 61, 075003 (2019).
[3] D. E. Ruiz, M. E. Glinsky, and I. Y. Dodin, Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation, J. Plasma Phys. 85, 905850101 (2019).
[4] H. Zhu, Y. Zhou, and I. Y. Dodin, On the Rayleigh-Kuo criterion for the tertiary instability of zonal flows, Phys. Plasmas 25, 082121 (2018).
[5] H. Zhu, Y. Zhou, and I. Y. Dodin, On the structure of the drifton phase space and its relation to the Rayleigh-Kuo criterion of the zonal-flow stability, Phys. Plasmas 25, 072121 (2018).
[6] H. Zhu, Y. Zhou et al., Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation, Phys. Rev. E 97, 053210 (2018).
[7] D. E. Ruiz, J. B. Parker et al., Zonal-flow dynamics from a phase-space perspective, Phys. Plasmas 23, 122304 (2016).
• Gyrokinetic study of RMP-driven plasma density and heat transport in tokamak edge plasma using MHD screened RMP field
Robert Hager, PPPL, abstract, slides
[#s1064, 01 Aug 2019]
ITER plans to rely on RMP coils as the primary means for ELM control. However, puzzling observations on present-day experiments complicate understanding the underlying physics: plasma density is pumped out, which can lower the fusion efficiency in ITER, while the electron heat transport is still low in the pedestal. Kinetic level understanding including most of the important physics is needed but has not been available. Gyrokinetic total-f simulation of the plasma transport driven by n=3 resonant magnetic perturbations (RMPs) in a DIII-D H-mode plasma is performed using the gyrokinetic code XGC. The RMP field is calculated in M3D-C1 and coupled into XGC in realistic divertor geometry with neutral particle recycling. The RMP field is stochastic around the pedestal foot but exhibits good KAM surfaces at pedestal top and steep-slope. The simulation qualitatively reproduces the experimental phenomena: plasma density is pumped-out due to enhanced electrostatic turbulence while electron heat transport is low. Different from earlier gyrokinetic studies, the present simulation consistently combines neoclassical and turbulent transport, a fully nonlinear Fokker-Planck collision, neutral particle recycling, and the full 3-D electric field. Density pump-out is not seen without turbulence effects. Reduction of the ExB shearing rate is likely to be responsible, mostly, for the enhanced edge turbulence, which is found to be from trapped electron modes.
• Velocimetry and the aperture problem for 2D incompressible flows
Tim Stoltzfus-Dueck, abstract, slides
[#s1028, 16 May 2019]
The inference of velocity fields from 2D movies evolving conserved scalars (optical flow) is fundamentally ambiguous due to the well-known “aperture problem”: velocities along isocontours of the scalar are not visible. This may even corrupt the inference of velocity fields averaged at scales longer than the typical length scale of features in the scalar field, as in the drift wave. However, for divergence-free flows, a stream-function formulation allows us to show that the "invisible velocity" vanishes in the surface average inside any closed scalar isocontour. This error-free averaged velocity may be used as an “anchor” for a more reliable inference of the larger-scale velocity field, or to test model-based optical-flow schemes. We have also used the stream-function formulation to derive a new method of optical flow for divergence-free flows. We discuss the new algorithm, including details of discretization, boundary conditions, and image preprocessing that can significantly affect its performance. A simple implementation of the new method is shown to work well for a number of synthetic movies, and is also applied to a GPI movie of edge turbulence in NSTX.
• Realisability of discontinuous MHD equilibria
Adelle Wright, Australian National University, Canberra, abstract, slides
[#s1034, 14 May 2019]
Smooth 3D MHD equilibria with non-uniform pressure may not exist but, mathematically, there exist 3D MHD equilibria with non-uniform, stepped pressure profiles. The pressure jumps occur at surfaces with highly irrational values of rotational transform and generate singular current sheets. If physically realisable, how such states form dynamically remains to be understood. To be physically realisable states, MHD equilibria must exist for some non-trivial timescale, meaning they must be at least be ideally stable and sufficiently stable to the fastest growing resistive instabilities. This presentation will discuss recent progress towards understanding discontinuous MHD equilibria via a stability analysis of a continuous cylindrical equilibrium model with radially localised pressure gradients, which examines how the resistive stability characteristics of the model change as the localisation of pressure gradients is increased to approach a discontinuous pressure profile in the zero-width limit.
• Kinetic Effects on Adiabatic Index via Geodesic Acoustic Continuum Calculations
Fabio Camilo de Souza, University of Sao Paulo, Brazil, abstract, slides
[#s1027, 08 May 2019]
Geodesic Acoustic Mode (GAM) is primarily an electrostatic oscillation with the dominant toroidal N=0 and poloidal M=0,1 mode numbers. First predicted within the magnetohydrodynamic (MHD) theory [1], it's frequency is proportional to the square root of the adiabatic index gamma. GAMs can be treated by the kinetic theory, to include such parameters as the plasma rotation of different species [2], fast ions with bump-on-tail like [3] or slowing down [4] distribution function, and other models, to investigate the plasma equilibrium conditions.
NOVA [5] is an ideal MHD code that computes the Alfvénic and acoustic continua and eigenmodes. The adiabatic index in NOVA is a fixed parameter, typically 5/3. The acoustic oscillations are calculated using the prescribed gamma value and its coupling with others continua.
As in kinetic calculations it is possible to include other effects for more accuracy of the GAM continuum. We modified NOVA to include a profile for gamma, given as a function of the magnetic surfaces. This modification makes the MHD acoustic continuum to match the Kinetic one. This kinetic gamma allows to compute more accurate eigenmodes which are strongly coupled to GAM continuum structure. This conclusion is similar to all low frequency oscillations including GAMs, the Alfvén-acoustic BAAE modes and others. The understanding of the impact of discharge parameters in these modes can improve the plasma transport control.
Simulation results for DIII-D will be presented, an Energetic Particle induced GAM appears in the maximum of the modified GAM continuum, the result matches the observed frequency for N=0 oscillation. Implications to the experiments in NSTX will be discussed.

[1] N. Winsor, et. al., Phys. Fluids 11, 2448 (1968)
[2] A.G. Elfimov, et. al., Phys. Plasmas 22, 114503 (2015)
[3] F. Camilo de Souza, et. al, Phys. Lett. A 381, 3066 (2017)
[4] Z. Qiu, et. al., Plasma Phys. Controlled Fusion 52, 095003 (2010)
[5] C. Z. Cheng and M. S. Chance, Journal of Computational Phys., 71, 124-146 (1987)
• Mapping the Sawtooth
Chris Smiet, PPPL, abstract
[#s1025, 02 May 2019]
The magnetic field in a tokamak defines a field line map: a mapping from a poloidal cross-section to that same cross-section by following magnetic field lines. Such a map must necessarily contain fixed points, of which the magnetic axis is an example. The jacobian (the matrix of partial derivatives) $\mathsf{M}$ describes the mapping around such a fixed point to first order, and is part of the Lie group $SL(2,\mathbb{R})$. Different elements of this group act on the euclidean plane as rotations, shear mappings or hyperbolic fixed points. We look at a transition from an ellpitic fixed point (field lines lie on nested surfaces around the fixed point) to an alternating hyperbolic fixed point (field lines map to opposite branches of hyberbolic surfaces) that can occur at $q=2, 2/3, 2/5, 2/7 ...$. Using the NOVA-K code we identify an ideally unstable mode that is localized on the axis and has a high growth rate when the safety factor is close to 2/3. This mode drives the fixed point into the alternating hyperbolic regime. The nonlinear evolution of this instability can lead to complete stochastization of a region near the axis. Though the Sawtooth oscillation has long been observed, there is still disagreement between theoretical models and observations, and no model can reconcile all observations. We speculate that the above transition could explain some of the observations that do not fit other models, such as measurements of q below 1, snakes, and persistent Alfven Eigenmodes.
• Hyper-Resistive Model of UHE Cosmic Ray Acceleration by AGNs
Ken Fowler, UC Berkeley, abstract, slides
[#s1024, 25 Apr 2019]
Ultra High Energy (UHE) cosmic rays (~ 10^20 eV) may be produced by known processes of acceleration by plasma turbulence in magnetized jets produced by Active Galactic Nuclei (AGNs). A simple model in which turbulence is represented as hyper-resistivity in Ohm’s Law yields several predictions in sufficient agreement with observations to motivate further investigation. Besides jet dimensions, these predictions include the unique extra-galactic cosmic ray energy spectrum (\propto 1/E^3 ) and a different interpretation of the synchrotron radiation by which AGN jets are observed. Crucial to the model is a new theory of jet propagation whereby un-collimated jets generated by General Relativistic MHD simulations evolve to a highly collimated structure, finally evolving at speed 0.01c that explains jet dimensions, while relativistic acceleration parallel to field lines yields both cosmic rays and synchrotron radiation.

References:
[1] S. A. Colgate, T. K. Fowler, H. Li & J.Pino, 2014 ApJ 789, 144, on AGN jets
[2] S. A. Colgate, T. K. Fowler, H. Li et al. 2015 ApJ 813, 136, on jet stability
[3] T. K. Fowler & H. Li, 2016 J. Plas. Phys. 82, 595820513, on UHE acceleration
[4] T. K. Fowler, H. Li, R. Anantua, 2019 ArXiV 2615445
• Realistic 2D quasilinear modeling of fast ion relaxation
Vinicius Duarte, PPPL, slides
[#s1071, 19 Apr 2019]
• Fishbone instability and transport of energetic particles
Guillaume Brochard, CEA, IRFM, abstract, slides
[#s1023, 18 Apr 2019]
Analytical and numerical studies have been carried out to verify linearly the newly implemented 6D PIC module into the nonlinear hybrid code XTOR-K [1],[2]. This code solves the two-fluid extended MHD equations in toroidal geometry while taking into account, self-consistently, kinetic ion populations. The verification has been performed by a linear model [3], developed from [4],[5],[6]. It solves non-perturbatively the kinetic internal kink dispersion relation, with the particularity to take into account non-resonant kinetic terms and passing particles, which have revealed to be crucial features of the fishbone instability. A verification between the model and XTOR-K in its linear phase is presented, regarding the pulsation and growth rate (ω, γ) of the internal kink, and the position in phase space of resonant planes. As expected, the instability is stabilized on the kink branch and then destabilized on the fishbone branch. On the basis of this verification, a series of linear and nonlinear runs have been performed with XTOR-K. Firstly a linear study of the alpha-induced fishbone instability on the ITER 15 MA equilibrium has been done. It highlights the linear thresholds of the instability in the diagram (q0, βh,0), with q0 the on-axis safety factor and βh,0 the on-axis kinetic beta. The fishbone mode is found to be unstable for ITER relevant (q0, βh) couples. Secondly, a first nonlinear simulation has been performed to study the nonlinear evolution of the wave-particle interaction between the kink rotation and the alpha particle precessional motion on the fishbone branch. The equilibrium is taken to have circular ITER-like flux surfaces and alpha particles at peak energy of 1MeV. Such a simulation explores one limit described in [7] where particles non-linearities dominate, far above the linear threshold in βh,0. Results show strong chirping of the fishbone mode associated with the transport of resonant particles. It is found that, for this configuration, the fishbone instability transports 5% of the core’s alphas toward q = 1. Once the resonant particles have reached q = 1, a classical internal kink grows.

References
[1] H. L ̈utjens, J-F. Luciani, JCP, (2010), 229, 8130-8143
[2] D. Leblond, PhD thesis, (2011)
[3] G. Brochard et al 2018 J. Phys.: Conf. Ser. 1125 012003
[4] D.Edery, X.Garbet, J-P.Roubin, A.Samain (1992), PPCF, 34, 6, 1089-1112
[5] F. Porcelli et al, Phys. FLuid B 4 (10), 1992
[6] F. Zonca, L. Chen, Physics of Plasmas 21, 072121 (2014) 1
[7] F.Zonca et al, New J. Phys. 17 (2015) 013052
• Improving computational efficiency of kinetic simulations with physics, mathematics, and machine learning
George Wilkie, Centrum Wiskunde & Informatica (CWI), abstract, slides
[#s1022, 11 Apr 2019]
Kinetic theory has made tremendous progress in recent decades thanks to reduced models and improved computational capacity. Some problems, especially in the non-Maxwellian regime, remain difficult even for large supercomputing clusters. In this talk, I will discuss how such problems can be solved on laptops with the right tools applied. Physical approximations can be made to reduce the burden of predicting the interaction between turbulence and energetic particles. To complement well-established physical reductions of the nonlinear Boltzmann equation, recent advances in applied mathematics are utilized for direct efficient solution. Throughout, I will discuss ongoing and potential applications of machine learning to improve efficiency even further.
• Simulating Relativistic Astroplasmas from Microphysics to Global Dynamics
Kyle Parfrey, NASA Goddard Space Flight Center, abstract, slides
[#s1007, 19 Mar 2019]
The most extreme and surprising behaviors of black holes and neutron stars are driven by their surrounding magnetic fields and plasmas. Numerical simulations of these systems are complicated by the exotic physical conditions, requiring new approaches. I will present a range of computational methods which are well adapted to challenges such as strongly curved spacetime, energetically dominant electromagnetic fields, and pathological current sheets. In particular, I will describe how a new technique for general-relativistic plasma kinetics will aid in understanding black holes' particle acceleration and jet launching, and in interpreting future observations with the Earth-spanning Event Horizon Telescope.
• Effects of zonal flows on transport crossphase in Dissipative Trapped-Electron Mode turbulence
Michael Leconte, National Fusion Research Institute, Korea, abstract, slides
[#s992, 14 Mar 2019]
Confinement regimes with edge transport barriers occur through the suppression of turbulent (convective) fluxes in the particle and/or thermal channels, i.e. $Γ = \sum{\sqrt{|n_k|^2}\sqrt{|φ_k|^2} sin δ^{n,φ}_k}$ and $Q = \sum{\sqrt{|T_k|^2}\sqrt{|φ_k|^2} sin δ^{T,φ}_k}$, respectively, for drift-wave turbulence. The quantity $|φ_k|^2$ is the turbulence intensity, while $δ^{n,φ}_k$ and $δ^{T,φ}_k$ are the crossphases. For H-mode, a decorrelation theory predicts that it is the turbulence intensity $|φ_k|^2$ that is mainly affected via flow-induced shearing of turbulent eddies [1]. However, for other regimes (e.g. I-mode), characterized by high energy confinement but low particle confinement, this decrease of turbulence amplitude cannot explain the decoupling of particle v.s. thermal flux, since a suppression of turbulence intensity $|φ_k|^2$ would necessarily affect both fluxes the same way. Here, we explore a possible new stabilizing mechanism: zonal flows may directly affect the transport crossphase. We show the effect of this novel mechanism on the turbulent particle flux, by using a simple fluid model [2,3] for dissipative trapped-electron mode (DTEM), including zonal flows. We first derive the evolution equation for the transport crossphase $δ_k$ between density and potential fluctuations, including contributions from the E × B nonlinearity [4]. By using a parametric interaction analysis including the back-reaction on the pump, we obtain a predator-prey like system of equations for the pump amplitude $φ_p$, the pump crossphase $δ_p$, the zonal amplitude $φ_z$ and the triad phase-mismatch ∆δ. The system displays limit-cycle oscillations where the instantaneous DTEM growth rate - proportional to the crossphase - shows quasi-periodic relaxations where it departs from that predicted by a linear theory. This implies that the crossphase does not respond instantaneously to the driving gradient, instead there is a finite response time, which for DTEM corresponds to the inverse of the de-trapping rate $ν = ν_{ei}/\sqrt{\epsilon}$ with $ν_{ei}$ the electron-ion collisionality and $\epsilon$ the inverse aspect ratio.

[1] H. Biglari, P.H. Diamond, P.W. Terry, Phys. Fluids B 2, 1 (1990).
[2] D. A. Baver, P.W. Terry, R. Gatto and E. Fernandez, Phys. Plasmas 9, 3318 (2002).
[3] F.Y. Gang, P.H. Diamond, J.A. Crotinger and A.E. Koniges, Phys. Fluids 3, 955 (1991).
[4] C.Y. An, B. Min and C.B. Kim, Plasma Phys. Controlled Fusion 59, 115006 (2017).
• Astrophysical Collisionless Shock and Current Sheet Instabilities: Particle Modeling and Laboratory Study
Zhenyu Wang, Princeton University, abstract, slides
[#s993, 13 Mar 2019]
In the first part of this talk, I will present the modelling and interpretation of a campaign of laser experiments designed to generate high Mach number magnetized collisionless shocks on OMEGA-EP. We compare the data to the results of 3-D PIC simulations, and describe the signatures of magnetized shock formation, including the early contact discontinuity formation stage, and a later magnetic reflection with magnetic overshoots. We explain the geometrical effects on the radiography introduced by density gradient in expanding plasma and by the curvature of the imposed magnetic field. We conclude that our experiments have reproducibly achieved magnetized shocks with Alfvenic Mach number 3 to 9 in laboratory conditions. In the second part, I will describe the gyrokinetic (GK) electron and fully kinetic (FK) ion particle (GeFi) simulation model and the particle simulation results of waves and current sheet instabilities. In the GeFi model, the GK electron approximation removes the high frequency electron gyromotion and plasma oscillation, but the electron finite Lamor radii effects are retained. For lower-hybrid waves, the GeFi results agree well with the fully kinetic explicit delta-f particle code and the fully kinetic Darwin particle code. Our 3-D GeFi and FK simulation results demonstrate the existence of the lower-hybrid-drift, kink and sausage instability in current sheet under finite guide magnetic fields with the realistic proton-to-electron mass ratio.
• Kinetic Simulations of Collisionless Plasmas
Rahul Kumar, Princeton University, abstract, slides
[#s989, 05 Mar 2019]
The particle-in-cell method has been remarkably successful in understanding physical processes occurring at the kinetic scales. I will discuss the implementation of the electromagnetic particle-in-cell method for collisionless plasmas in a self-developed code called PICTOR. I will focus on a few techniques employed to improve performance, diagnostic, and scalability of the code. I will then briefly discuss two physics problems to illustrate the efficacy of PIC simulations in addressing a few outstanding problems in plasma physics. First, I will discuss preferential heating and acceleration of heavy ion in Alfvenic turbulence. Then, I'll discuss how self-consistent PIC simulations, combined with the measurements from Voyager spacecraft, could be used to obtain a comprehensive understanding of the dynamics of solar wind termination shock.
• Available energy of magnetically confined plasmas
Per Helander, Max Planck Institute for Plasma Physics, Greifswald, Germany, abstract, slides
[#s990, 28 Feb 2019]
In this talk, the energy budget of a collisionless plasma subject to electrostatic fluctuations is studied. In particular, the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is considered. This excess measures how much thermal energy is “available” for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. The “available energy” defined in this way becomes an interesting and useful quantity in situations where adiabatic invariants impose non-trivial constraints on the plasma motion. For instance, microstability properties of certain stellarators can be inferred directly from the available energy, without the need to solve the gyrokinetic equation. The technique also suggests that an electron-positron plasma confined by a dipole magnetic field could be entirely free from turbulence.
• Finite Larmor Radius effects at the high confinement mode pedestal and the related force-free steady state
Wei-li Lee, PPPL, abstract, slides
[#s988, 19 Feb 2019]
For this talk, we will first relate our previous calculations on the radial electric field at the high confinement H-mode pedestal [W. W. Lee and R. B. White, Phys. Plasmas 24, 081204 (2017)] with the actual magnetic fusion experimental measurements. We will then discuss the new pressure balance due to the E x B current, which is induced by the resulting radial electric field, and its impact on the gyrokinetic MHD equations as well as their conservation properties in the force-free steady state.
• Impurity transport in stellarator plasmas
Albert Mollén, IPP Greifswald, abstract, slides
[#s985, 13 Feb 2019]
In contrast to tokamaks where turbulence typically dominates, a substantial fraction of the radial energy and particle transport in stellarators can often be attributed to collisional processes. The kinetic calculation of collisional transport has for a long time relied on simplified models which use the “mono-energetic” approximation, the simple pitch-angle scattering collision operator and are radially local. But not all experimental observations have been satisfactorily explained, and in recent years more advanced numerical tools have appeared which relax some of the approximations. These improvements in the modelling can be of particular importance when analyzing the impurity transport. I will discuss how the calculation of the impurity transport has advanced in recent years, and what the latest observations in the Wendelstein 7-X stellarator are.
• Black Aurora, Bohm Diffusions, Quasi-Neutrality Mysteries Explained
Kwan Chul Lee, NFRI, abstract, slides
[#s949, 07 Feb 2019]
Gyrocenter-Shift Analysis has been developed based on the momentum exchange of ion-neutral interaction in the magnetized plasmas. Recent 7 years, after the last PPPL theory seminar held on January 10, 2012, 3 papers on GCS analysis have been published [1-3]. This presentation will focus on the quasi-neutrality controversy after revisiting the basis of GCS analysis. The explanations on the satellite measurement of the black aurora and the transport phenomena named as Bohm diffusions will be presented as well as a related KSTAR experimental proposal.
[1] K. C. Lee, “Violation of Quasi-neutrality for Ion-neutral Charge-exchange Reactions in Magnetized Plasmas”, J. of Korean Phys. Soc., Vol. 63, No.10, 1944 (2013)
[2] Kwan Chul Lee, “Analysis of Bohm Diffusions Based on the Ion-Neutral Collisions”, IEEE Trans. on Plasma Science, Vol. 43 No. 2, 494 (2015)
[3] Kwan Chul Lee, “Electric field formation in three different plasmas: A fusion reactor, arc discharge, and the ionosphere”, Phys. of Plasmas, Vol. 24, 112505 (2017)
• Bringing the golden standard into the silicon age
Francesca Poli, PPPL, abstract, slides
[#s975, 31 Jan 2019]
A lot happened since TRANSP made its first appearance about thirty years ago. The 'golden standard' for tokamak discharge analysis has evolved to a code that is capable of predicting heating and current drive, thermal and particle transport. Its pool of users has expanded internationally to cover almost every tokamak operating nowadays, demanding modernization, increasing support and additional capabilities. This talk will review the strength and weaknesses of TRANSP, the plans for implementation of new physics modules targeting (as close as possible to) a Whole Device Model. It will discuss areas for partnership with the theory department and ongoing activities and plans in collaboration with the SciDAC projects, for extension of the transport outside the plasma boundary and for self-consistent calculations of transport and stability, including transport induced by energetic particles.
• Compressional Alfvén eigenmodes excited by runaway electrons
Chang Liu, PPPL, abstract, slides
[#s960, 25 Jan 2019]
Runaway electron phenomena is an important topic in general, and critically important in tokamak disruption studies. Given its high potential for damaging effects, it is critical to understand the physics of their generation and find a mitigation strategy for ITER. Kinetic instabilities associated with high-energy runaway electrons have been shown to play an important role in the behavior of runaway electrons Recently, a new kind of instability with magnetic signals in the Alfvén frequency range have been observed in disruption experiments in DIII-D, which is found to be related to the dissipation of the runaway electron current. In this talk, a candidate explanation for this phenomena is presented, namely resonant interaction with compressional Alfvén eigenmodes (CAE). CAEs driven by energetic ions have been well studied in spherical tokamaks like NSTX. For CAEs driven by resonances with runaway electrons, the damping rate of the modes due to electron-ion collisions are calculated. The model is applied to a time-dependent kinetic simulation of runaway electrons, which includes the bounce-average effect and the enhanced ion pitch-angle scattering due to partial screening. The results match with experiments qualitatively, and provide a promising way to diffuse runaway electrons before their energization. A brief overview of related research into runaway electrons is also given, indicating how this work fits into the wider effort to find mitigation strategies.
• Magnetohydrodynamical equilibria with current singularities and continuous rotational transform
Yao Zhou, abstract, slides
[#s967, 23 Jan 2019]
We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal m=1 kink instability, while addressing the subtle difference in the matching procedure for the HKT problem. Pedagogically, the essence of RDR's approach becomes more transparent in the reduced slab geometry of the HKT problem. We then compare the boundary-layer solution, which yields a current singularity at the resonant surface, to the numerical solution obtained using a flux-preserving Grad-Shafranov solver. The remarkable agreement between the solutions demonstrates the validity and universality of RDR's approach. In addition, we show that RDR's approach consistently preserves the rotational transform, which hence stays continuous, contrary to a recent claim that RDR's solution contains a discontinuity in the rotational transform.
• Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak
Tess Bernard, University of Texas - Austin, abstract
[#s942, 13 Dec 2018]
The first gyrokinetic simulations of plasma turbulence in the Texas Helimak device are presented. These have been performed using the Gkeyll (http://gkyl.readthedocs.io/) computational framework. The Helimak is a simple magnetized torus with a toroidal and vertical magnetic field and open field lines that terminate on conducting plates at the top and bottom of the device. It has features similar to the scrape-off layer region of tokamaks, such as bad curvature-driven instabilities and sheath boundary conditions on the end plates, which are included in these initial gyrokinetic simulations. A bias voltage can be applied across conducting plates to drive E x B flow and study the effect of velocity shear on turbulence suppression. Comparisons are presented between simulations and measurements from the experiment, showing qualitative similarities, including fluctuation amplitudes and equilibrium profiles that approach experimental values. There are also some important quantitative differences, and I discuss how certain physical and geometric effects may improve agreement in future results.
• Machine Learning Techniques for Analysis of High-Dimensional Chaotic Spatiotemporal Dynamics
Jaideep Pathak, University of Maryland, abstract, slides
[#s927, 06 Dec 2018]
High-dimensional chaos is a commonly observed feature of many interesting natural systems such as fluid flows or atmospheric dynamics. We formulate a machine learning approach for short-term prediction [1] and for understanding the long-term ergodic properties of the underlying dynamical processes of high-dimensional chaotic spatiotemporal dynamical systems. Specifically, we consider a situation in which limited duration time series data from some dynamical process is available, but a mechanistic, knowledge-based model of how that data is produced is either unavailable or too inaccurate to be useful. Our proposed approach, using a particular kind of recurrent neural network called a Reservoir Computer [2], is computationally efficient and scalable through parallelization to dynamical systems with arbitrarily high-dimensional chaotic attractors. Further, in the context of chaotic dynamical systems, machine learning can also be used in conjunction with an imperfect knowledge-based model for filling in gaps in our underlying mechanistic knowledge that can cause the model to be inaccurate. We demonstrate this technique using simulated data from the Kuramoto-Sivashinsky partial differential equation as well as the Lorenz ‘96 toy model of atmospheric dynamics [3].
[1] J. Pathak, B. Hunt, M. Girvan, Z. Lu, E. Ott, Phys. Rev. Lett. 120 (2018) 024102.
[2] H. Jaeger, H. Haa, Science 304 (2004) 78–80.
[3] E.N. Lorenz, in:, T. Palmer, R. Hagedorn, Predict. Weather Clim., Cambridge University Press, Cambridge, 2006, pp. 40–58.
• From SOL turbulence to planetary magnetospheres: computational plasma physics at (almost) all scales using the Gkeyll code
Ammar Hakim, PPPL, abstract, slides
[#s928, 05 Dec 2018]
Gkeyll is a computational plasma physics package that aims to simulate plasmas at all scales. At present, the code contains solvers for three major equation systems: Vlasov-Maxwell equations, electromagnetic gyrokinetic equations and multi-fluid moment equations. These span the complete range of plasma physics; electromagnetic shocks, turbulence and first-principles sheath physics, requiring full kinetic treatment; turbulence in tokamak core and SOL, requiring EM gyrokinetics; and planetary magnetospheres, requiring fluid treatment with proper accounting of kinetic effects to capture reconnection and current sheet dynamics. In this talk I will present the status of each of the major solvers implemented in the code, with emphasis on the features of the algorithms as well as the physics being studied. In particular, I will focus on recent progress in implementing a conservative algorithm for collisions; details of a novel algorithm for EM gyrokinetic in the symplectic formulation; and recent progress in developing a robust semi-implicit algorithm for multi-fluid moment equations. I will conclude with the short- and medium-term plans for the project as well as some ideas on strengthening advanced computing at PPPL, leveraging on the work done in Gkeyll as well as other projects.
• Coupled core-edge gyrokinetic simulation and Tungsten impurity transport in JET with XGC
Julien Dominski, abstract, slides
[#s929, 04 Dec 2018]
Incoming Exascale capabilities of super computers will enable whole-device simulations based on first principles plasma physics. To take full advantage of these new capabilities, new numerical schemes and more complete physical models are developed in XGC. XGC is a whole-volume total-f gyrokinetic code optimized for simulation of edge plasma in magnetic fusion devices. One goal of the ECP project is to couple XGC with a core code, such as GENE, to optimize the efficiency of whole-device simulations. The current status of this core-edge coupling project will be presented, including the presentation of the core-edge coupling scheme and of the coupled GENE-XGC simulations. Another goal is to study the influence of tungsten and beryllium on the performance of ITER. The Total-f gyrokinetic XGC is thus being upgraded to simulate the physics of many-species impurities in the whole-volume including SOL. First multi-species simulation of a JET plasma under tungsten contamination will be demonstrated, showing that the lower charge state W can move inward from into core, but the higher charge state W will move outward toward the pedestal top and accumulate, as seen in ASDEX-U.
• KBM nonlinear dynamics and first-principles-based classifiers with Machine Learning predictions for disruptions
Ge Dong, Princeton University, abstract, slides
[#s923, 20 Nov 2018]
Kinetic ballooning modes (KBM) are widely believed to play a critical role in disruptive dynamics as well as turbulent transport in tokamaks. While the nonlinear evolution of ballooning modes has been proposed as a mechanism for “detonation” in tokamak plasmas, the role of kinetic effects in such nonlinear dynamics remains largely unexplored. In this study saturation mechanism and nonlinear dynamics of KBM is presented, with global gyrokinetic simulation results of KBM nonlinear behavior. Instead of the finite-time singularity predicted by ideal MHD theory, the kinetic instability is shown to develop into an intermediate non-linear regime of exponential growth, followed by a nonlinear saturation regulated by spontaneously generated zonal fields. In the intermediate nonlinear regime, rapid growth of localized current sheet, which can mediate reconnection, is observed. In the future, the linear properties as well as nonlinear mode structures from the simulations could be incorporated into the deep learning models for disruption predictions in the form of a new parameter/channel, as a first-principles physics guide to the AI. The deep learning model could in turn provide feedback on the sensitivity of the parameters, including the linear stability properties of various modes, and nonlinear dynamics of these instabilities, and thus automatically select new inputs for the first-principles codes.
• Electron-impact excitation of molecular hydrogen: dissociation and vibrationally resolved cross sections
Dmitry Fursa, Curtin University, abstract
[#s922, 16 Nov 2018]
Molecular hydrogen and its isotopologues are present in a range of vibrationally excited states in fusion, atmospheric, and interstellar plasmas. Electron-impact excitation cross sections resolved in both final and initial vibrational levels of the target are required for modeling the properties and dynamics, and controlling the conditions of many low-temperature plasmas. Recently, the convergent close-coupling (CCC) method has been utilized to provide a comprehensive set of accurate excitation, ionization, and grand total cross sections for electrons scattering on H2 in the ground (electronic and vibrational) state, and calculations are being conducted to extend this data set to include cross sections resolved in all initial and final vibrational levels. In this talk I will review the available e-H2 collision data, discuss the resolution of a significant discrepancy between theory and experiment for excitation of the b3Su+ state, and present estimates for dissociation of H2.
• Strong-flow gyrokinetics with a unified treatment of all length scales
Amil Sharma, University of Warwick, abstract, slides
[#s921, 14 Nov 2018]
Tokamak turbulence exhibits interaction on all length scales, but standard gyrokinetic treatments consider global scale ﬂows and gyroscale ﬂows separately, and assume a separation between these length scales. However, the use of a small-vorticity ordering (Dimits, 2010) allows for the presence of large, time-varying ﬂows on large length scales, whilst providing a uniﬁed treatment including shorter length scales near and below the gyroradius. Some examples of strong-flow generalisations of gyrokinetics are presented, followed by a description of the nuances of the equations and numerical implementation that use the ordering of Dimits (2010). Our Euler-Lagrange and Poisson equations contain an implicit dependence that appears as a partial time derivative of the E × B ﬂow. This implicit dependence is analogous to the v||-formulation of gyrokinetics. However, as these implicit terms are small, we use an iterative scheme to resolve this. Additionally, we have developed a stand-alone Poisson solver based on that from the ORB5 code, and use this to simulate certain flow and density gradient driven instabilities in cylindrical geometry.
• Some Novel Features of Three Dimensional MagnetoHydroDynamic Plasma
Rupak Mukherjee, Institute for Plasma Research, abstract, slides
[#s920, 12 Nov 2018]
Within the framework of MagnetoHydroDynamics, a strong interplay exists between flow and magnetic fields leading to several interesting pathways for energy cascade. In this talk I numerically demonstrate three examples of such interplay using our in-house developed DNS code G-MHD3D which simulates three dimensional single fluid MHD equations. I also suggest analytical arguments in some of our numerical observations. The first problem discusses the phenomena of nonlinear interaction of magnetic and kinetic energies within the premise of two and three dimensional MHD equations leading to periodic exchange of energy. Scaling of the energy exchange frequency with deviation from Alfven resonance and initial wave number of excitation is numerically determined. Results are qualitatively reproduced by analysing the set of single fluid MHD equations through low degrees of freedom coupled ODEs obtained via a Galerkin procedure. Secondly, in three dimensions, at Alfven resonance, for some chaotic flows, the initial flow profile is found to “recur” periodically with the time evolution of the plasma. Such recurrence is unexpected in systems with high degree of freedom (e.g. 3D MHD). The primary cause of such phenomena is analysed using an effective number of active degrees of freedom present in the system. Finally we observe some preliminary results of large and intermediate scale magnetic field generation in plasmas often called as “dynamo” using our code. The growth rate of such ‘fast’ dynamos are compared for different parameters of the system and the fastest dynamos for the parameter set is identified. Physics details and numerical aspects of the development of the code, numerical protocols followed, direct numerical simulations results, numerical tools to diagnose the three dimensional grid data and the analytical arguments in support of the numerical observations will be presented in the talk.
• A gyrokinetic model for the tokamak periphery
Rogerio Jorge, EPFL, abstract, slides
[#s894, 01 Nov 2018]
We present a new gyrokinetic model that retains the fundamental elements of the plasma dynamics at the tokamak periphery, namely electromagnetic fluctuations at all scales, comparable amplitudes of background and fluctuating components, and a large range of collisionality regimes. Such model is derived within a gyrokinetic full-F approach, describing distribution functions arbitrarily far from equilibrium, and projecting the gyrokinetic equation onto a Hermite-Laguerre velocity space polynomial basis, obtaining a gyrokinetic moment hierarchy. The treatment of arbitrary collisionalities is performed by expressing the full Coulomb collision operator in gyrocentre phase space coordinates, and providing a closed formula for its gyroaverage in terms of the gyrokinetic moments. In the electrostatic regime and long-wavelength limit, the novel gyrokinetic hierarchy reduces to a drift-kinetic moment hierarchy that in the high collisionality regime further reduces to an improved set of drift-reduced Braginskii equations, which are widely used in scrape-off layer simulations. First insights on the linear modes described by our novel gyrokinetic model will be presented.
• APS Invited dry run - Quasi-linear resonance broadened model for fast ion relaxation in the presence of Alfvénic instabilities
Nikolai Gorelenkov, PPPL, abstract, slides
[#s883, 25 Oct 2018]
The resonance broadened quasi-linear (RBQ) model is developed for the problem of relaxing the fast energetic particle distribution function in constant-of-motion (COM) 3D space [N.N. Gorelenkov et al., Nucl. Fusion 58 (2018) 082016]. The model is generalized by using the QL theory [H. Berk et al., Phys. Plasmas'96] and carefully reexamining the wave particle interaction (WPI) in the presence of realistic AE mode structures and pitch angle scattering with the help of the guiding center code ORBIT. The RBQ model applied in realistic plasma conditions is improved by going beyond the perturbative-pendulum-like approximation for the wave particle dynamics near the resonance. The resonance region is broadened but remains 2-3 times smaller than predicted by an earlier bump-on-tail QL model. In addition the resonance broadening includes the Coulomb collisional or anomalous pitch angle scattering. The RBQ code takes into account the beam ion diffusion in the direction of the canonical toroidal momentum. The wave particle interaction is reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. The diffusion equation is solved simultaneously for all particles together with the evolution equation for the mode amplitudes. We apply the RBQ code to a DIII-D plasma with elevated q -profile where the beam ion profiles show stiff transport properties [C. Collins et al. PRL'16]. The sources and sinks are included via the Krook operator. The properties of AE driven fast ion distribution relaxation are studied for validations of the applied QL model to DIII-D discharges. Initial results show that the model is robust, numerically efficient, and can predict intermittent fast ion relaxation in present and future burning plasmas.
• Nonlinear interaction between toroidal Alfvén eigenmodes and tearing modes
Z. W. Ma, Zhejiang University, abstract, slides
[#s809, 15 Aug 2018]
Nonlinear interaction between toroidal Alfvén eigenmodes (TAEs) and the tearing mode is investigated by using the hybrid code CLT-K. It is found that the $n=1$ TAE is first excited by isotropic energetic particles at the linear stage and reaches the first steady state due to wave- particle interaction. After the saturation of the $n=1$ TAE, the $m/n=2/1$ tearing mode grows continuously and reaches its steady state due to nonlinear mode-mode coupling, especially, the $n=0$ component plays a very important role in the tearing mode saturation. The results suggest that the enhancement of the tearing mode activity with increase of the resistivity could weaken the TAE frequency chirping through the interaction between the $p=1$ TAE resonance and the $p=2$ tearing mode resonance for passing particles in the phase space, which is opposite to the classical physical picture of the TAE frequency chirping that is enhanced with increase of dissipation.
• Understanding coronal structures on the Sun
Hardi Peter, Max Planck Institute for Solar System Research, Germany, abstract, slides
[#s799, 17 Jul 2018]
Since decades coronal heating is a buzzword that is used as a motivation on coronal research. Depending on the level of detail one is interested in, one could define this question anything ranging from answered to not understood at all. 3D MHD models can now produce a corona in a numerical experiment that comes close to the real Sun in complexity. And the fact alone that in these models a three-dimensional loop-dominated time-variable corona is produced could be used as an argument that the problem of coronal heating is solved. However, careful inspection of these model results shows that despite their success they leave many fundamental questions unanswered. In this talk I will address some of these aspects, including the mass and energy exchange between chromosphere and corona, the apparent width of coronal loops, the energy source of hot active region core loops, or the internal structure of loops. In this sense this talk will pose more questions that it provide answers.
• Machine-learning driven correlation studies: multi-band frequency chirping at NSTX
Ben Woods, University of York, abstract, slides
[#s777, 28 Jun 2018]
Magnetic perturbations in a very broadband range (<30 kHz to >1 GHz) are commonly measured on tokamaks such as NSTX by using Mirnov coils. The spectral behaviour of the perturbations can be categorised as quiescent, fixed-frequency, chirping, or avalanching. Here, ‘chirping’ modes experience a time-dependent frequency shift due to non-linear effects – in some cases, multiple plasma modes chirp in a near-concurrent fashion (mode 'avalanching'). Mode avalanching in the Alfvénic and super-Alfvénic frequency bands is typically correlated with fast-ion loss. However, transition to this phase of mode behaviour is not fully understood. Traditional methods for characterising mode behaviour are highly labour intensive for human characterisation - studying parametric dependences of plasma parameters on mode character proves difficult. Here, preliminary results are presented from machine-learning driven studies of correlations between different mode character (quiescent, fixed-frequency, chirping, avalanching) and weighted averages of plasma parameters obtained from TRANSP (v-fast/v-Alfvén, Q-profile, β-fast/β-Alfvén). The weighted averages form insightful metrics of the stability of plasma modes, allowing for correlations to be drawn (i.e. magnetic shear versus mode character). These results yield similar correlations to previous work by Fredrickson et al. [1] in both the kink/tearing/fishbone frequency band (~1-30 kHz), and the TAE band (~50-200 kHz). An overall framework is presented to utilise this tool for generic tokamaks, for possible future use on MAST-U and DIII-D.
[1] E. D. Fredrickson, N.N. Gorelenkov et al., Nucl. Fusion 54, 093007 (2014)
• Conservative Discontinuous Galerkin Discretization for the Landau Collision Operator
Alexander Frank, Technical University of Munich, abstract, slides
[#s773, 21 Jun 2018]
This talk presents a mass-, momentum- and energy conserving discretization of the nonlinear Landau collision integral. The semi-discrete form is achieved using a modal discontinuous Galerkin method on a tensor product mesh and a recovery method to define second derivatives at the element boundaries. Combined with an explicit time stepping scheme this gives a fully discrete conservative form. The conservation properties are proven algebraically and shown numerically for a two dimensional relaxation test problem.
• Computing local sensitivity and tolerances for stellarators using shape gradients
Matt Landreman, University of Maryland, abstract, slides
[#s741, 14 Jun 2018]
• Energy-, momentum-, density-, and positivity-preserving spatio-temporal discretizations for the nonlinear Landau collision operator with exact H-theorems
Eero Hirvijoki, PPPL, abstract, slides
[#s737, 31 May 2018]
This talk explores energy-, momentum-, density-, and positivity-preserving spatio-temporal discretizations for the nonlinear Landau collision operator. We discuss two approaches, namely direct Galerkin formulations and discretizations of the underlying infinite-dimensional metriplectic structure of the collision integral. The spatial discretizations are chosen to reproduce the time-continuous conservation laws that correspond to Casimir invariants and to guarantee the positivity of the distribution function. Both the direct and the metriplectic discretization are demonstrated to have exact H-theorems and unique, physically exact equilibrium states. Most importantly, the two approaches are shown to coincide, given the chosen Galerkin method. A temporal discretization, preserving all of the mentioned properties, is achieved with so-called discrete gradients. The proposed algorithm successfully translates all properties of the infinite-dimensional time-continuous Landau collision operator to time- and space-discrete sparse-matrix equations suitable for numerical simulation.
• Spontaneous reconnection in thin current sheet: the “ideal” tearing mode
Anna Tenerani, Department of Earth, Planetary and Space Sciences, UCLA, abstract, slides
[#s734, 24 May 2018]
Magnetic field reconnection is considered one of the most important mechanisms of magnetic energy conversion and reorganization acting in astrophysical and laboratory plasmas. Although our knowledge has been greatly advanced in the last few decades, the problem of how magnetic reconnection can be triggered explosively in weakly collisional (quasi-ideal) plasmas (as observed e.g in solar flares, geomagnetic substorms and sawtooth crashes in tokamaks) still remains an open field of research. Here we discuss a possible scenario for the triggering of explosive reconnection via the onset of an ‘ideal’ tearing instability within forming current sheets and we show results from MHD numerical simulations that support our scenario. We demonstrate that the same reasoning, if applied recursively, can describe the complete nonlinear disruption of the original current sheet until microscopic marginally-stable current sheets are formed. We show that the ‘ideal’ tearing mode provides a general frame of work that can be extended to include other effects such as kinetic effects and different current profiles.
• Design of a new quasi-axisymmetric stellarator equilibrium
Sophia Henneberg, IPP Greifswald, abstract, slides
[#s730, 17 May 2018]
A new quasi-axisymmetric, two-field-period stellarator configuration has been designed following a broad study using the optimization code ROSE (Rose Optimizes Stellarator Equilibria). Because of the toroidal symmetry of the magnetic field strength, quasi-axisymmetric stellarators share many neoclassical properties of tokamaks, such as a comparable bootstrap current which can be employed to simplify the coil structure, which is favorable for finding compact equilibria. The ROSE code optimizes the plasma boundary calculated with VMEC based on a set of physical and engineering criteria. Various aspect ratios, number of field periods and iota profiles are investigated. As an evaluation of the design, the bootstrap current, the ideal MHD stability, the fast-particle losses, and the existence of islands are examined. The main result of this extensive study – a compact, MHD-stable, two-field-period stellarator with small fast-particle loss fraction – will be presented.
• Bringing the GBS plasma turbulent simulation code from limited to diverted configurations
Paola Paruta, École Polytechnique Fédérale de Lausanne, abstract
[#s729, 17 May 2018]
The GBS code has been developed to describe the plasma turbulent behaviour in the SOL,[1] [2], by solving the two-fluids Drift Reduced Braginskii equations.[3] We report on the implementation of diverted magnetic equilibria in GBS: by abandoning flux coordinates systems, which are not defined at the X-point, the model equations are written in toroidal coordinates, and a 4th order finite difference scheme is used for the implementation of the spatial operators on staggered poloidal and toroidal grids. The GBS numerical implementation is verified through the Method of Manufactured Solutions.[4] Its convergence properties are tested. First results of TCV-like simulations are presented.
[1] F. D. Halpern, P. Ricci et al., J. Comput. Phys. 315, 388 (2016)
[2] P. Ricci, F. D. Halpern et al., Plasma Phys. Control. Fusion 54, 124047 (2012)
[3] A. Zeiler, J. F. Drake & B. Rogers, Phys. Plasmas 4, 2134 (1997)
[4] Patrick J. Roache, J. Fluids Eng. 124, 4 (2002)
• Modeling Resonant Field Penetration and Its Effects on Transport in the DIII-D Tokamak
Qiming Hu, PPPL, abstract, slides
[#s665, 05 Apr 2018]
We use the nonlinear cylindrical two fluid MHD code (TM1) [1-4] to model the effects of multiple magnetic islands in the DIII-D tokamak. The TM1 code has been previously used to study classical and neoclassical tearing mode (TM) stability, TM stabilization by ECCD, and plasma response (transport and stability) to resonant magnetic perturbations (RMPs). Recently, TM1 has been used to understand the effects of multiple locked magnetic islands on heat transport in DIII-D Ohmic plasmas. It is found that co-existence of 2/1, 3/1 and 4/1 locked islands can produce a large (~50%) reduction in the central electron temperature, even without island overlap. However, the observed reduction in the edge temperature requires island overlap and stochasticity within the TM1. X-ray imaging reveals the appearance of multiple locked islands in the plasma edge at the time of the thermal collapse [5], consistent with TM1 modeling. For ELM suppression studies, we analyze the nonlinear evolution of edge magnetic islands in response to resonant magnetic perturbations [6]. The observed increase in pedestal toroidal rotation with the decrease in the core toroidal rotation is shown to be quantitatively consistent with TM1 modeling of multiple locked non-overlapping magnetic islands in the plasma edge. The TM1 results reveal interesting physics effects of locked modes that motivate further study using more comprehensive physics models.
[1] Qingquan Yu, Phys. Plasmas 4, 1047 (1997)
[2] Q. Yu, S. Günter & B. D. Scott, Phys. Plasmas 10, 797 (2003)
[3] Q. Yu, Nucl. Fusion 50, 025014 (2010)
[4] S. Günter, Q. Yu et al., J. Comput. Phys. 209, 354 (2005)
[5] X. D. Du et al., Phys. Rev . Lett. (submitted)
[6] R. Nazikian, C. Paz-Soldan et al., Phys. Rev. Lett. 114, 105002 (2015)
• Two etudes on unexpected behaviour of drift-wave turbulence near stability threshold
Alex Schekochihin, University of Oxford, abstract, slides
[#s664, 04 Apr 2018]
I will discuss some recent results — numerical and experimental — on the nature of drift-wave turbulence in MAST, obtained in the doctoral theses of my students Ferdinand van Wyk [1,4], Michael J. Fox [2] and Greg Colyer [3]. At ion scales, in the presence of flow shear, we find numerically [1,4] a type of transition to turbulence that is new (as far as we know) in the tokamaks, but reminiscent of some fluid dynamical phenomena (e.g., pipe flows or accretion discs in astrophysics): close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Such a transition has its roots in the subcritical nature of the turbulence in the presence of flow shear. It can be diagnosed in terms of the breaking of the statistical up-down symmetry of turbulence: this manifests itself in the form of tilted two-point correlation functions and skewed distributions of the fluctuating density field, found both in simulations and in BES-measured density fields in MAST [2]. The governing (order) parameter in the system is the distance from the threshold, rather than individual values of equilibrium gradients; the symmetries — and drift-wave/zonal-flow turbulence of conventional type — are restored away from the threshold. The experiment appears to lie just at the edge of this latter transition rather than at the exact stability threshold. At electron scales in MAST, the conventional streamer-dominated state of ETG turbulence turns out to be a long-time transient, during which an initially unimportant zonal component continues to grow slowly, eventually leading to a new saturated state dominated by zonal modes, rather similar to ITG turbulence [3]. In this regime, the heat flux turns out to be proportional to the collision rate, in approximate agreement with the experimentally observed collisionality scaling of the energy confinement in MAST. Our explanation of this effect is based on a model of ETG turbulence dominated by zonal–nonzonal interactions and on an analytically derived scaling of the zonal-mode damping rate with the electron–ion collisionality. These developments open some intriguing possibilities both for enterprising theoreticians tired of the V&V routine and for ingenious experimentalists interested in making use of tokamaks to probe transitions to turbulence in nonlinear plasma systems.
[1] F. van Wyk, E. G. Hichcock et al., J. Plasma Phys. 82, 905820609 (2016)
[2] M. F. J. Fox, F. van Wyk et al., Plasma Phys. Control. Fusion 59, 034002 (2017)
[3] G. J. Colyer, A. A. Schekochihin et al., Plasma Phys. Control. Fusion 59, 055002 (2017)
[4] F. van Wyk, E. G. Highcock et al., Plasma Phys. Control. Fusion 59, 114003 (2017)
Elizabeth Joy Paul, University of Maryland, abstract, slides
[#s659, 15 Mar 2018]
We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL [Landreman, Nucl. Fusion 57, 046003 (2017)] approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for computing the local sensitivity of figures of merit to normal displacement of the winding surface is presented, with potential applications for understanding engineering tolerances.
• Reduced MHD and gyrokinetic studies on auroral plasmas
Tomo-Hiko Watanabe, Nagoya University, abstract, slides
[#s658, 14 Mar 2018]
The reduced MHD and gyrokinetics developed from fusion theory have been applied to a variety of topics in space and astrophysical plasmas. Our theoretical and numerical methods developed from fusion studies at NU have also facilitated to understand key issues in auroral physics. Here, I would like to discuss some of the topics, such as structural formation of auroras and their dynamics, where competitive process of the ballooning, Kelvin-Helmholtz, and feedback instabilities in the magnetosphere-ionosphere (M-I) coupling are investigated [1, 2]. Furthermore, in the nonlinear stage of auroral growth, the M-I coupling system transits into the Alfvénic turbulence state [2]. The auroral turbulence is resulted from interactions of the shear Alfvén waves propagating in the opposite directions, and is an interesting application of the Goldreich-Sridhar theory. I would also like to discuss the gyrokinetic extension of the auroral theory including auroral electron acceleration [3].
[1] T.-H. Watanabe, Phys. Plasmas 17, 022904 (2010)
[2] Tomo-Hiko Watanabe, Hiroaki Kurata & Shinya Maeyama, New J. Phys. 18, 125010 (2016)
[3] T.-H. Watanabe, Geophys. Res. Lett. 41, 6071 (2014)
• Parametric Instability, Inverse Cascade, and the $1/f$ Range of Solar-Wind Turbulence
Ben Chandran, University of New Hampshire, abstract, slides
[#s626, 22 Feb 2018]
Turbulence likely plays an important role in generating the solar wind, and spacecraft measurements indicate that solar-wind turbulence is largely non-compressive and Alfvén-wave-like. Although compressive fluctuations are sub-dominant, Alfvén waves in the solar wind couple to compressive slow magnetosonic waves (“slow waves”) via the parametric-decay instability. In this instability, an outward-propagating Alfvén wave decays into an outward-propagating slow wave and an inward-propagating Alfvén wave. In this talk, I will describe a weak-turbulence calculation of the nonlinear evolution of the parametric instability in the solar wind at wavelengths much greater than the ion inertial length under the assumption that slow waves, once generated, are rapidly damped. I'll show that the parametric instability leads to an inverse cascade of Alfvén-wave quanta and present several exact solutions to the wave kinetic equations. I will also present a numerical solution to the wave kinetic equations for the solar-wind-relevant case in which most of the Alfvén waves initially propagate away from the Sun in the plasma rest frame. In this case, the outward-propagating Alfvén waves evolve toward a $1/f$ frequency spectrum that shows promising agreement with spacecraft measurements of interplanetary turbulence in the fast solar wind. I will also present predictions that will be tested by NASA's upcoming Solar Probe Plus mission, which will travel much closer to the Sun than any previous spacecraft.
• On the Global Attractor of 2D Incompressible Turbulence with Random Forcing
John Bowman, U. Alberta, abstract, slides
[#s630, 19 Feb 2018]
We revisit bounds on the projection of the global attractor in the energy-enstrophy plane obtained by Dascaliuc, Foias, and Jolly [1,2]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of random forcing. Numerical simulations in particular often use a stochastic white-noise forcing to achieve a prescribed mean energy injection rate. The analytical bounds are illustrated numerically for the case of white-noise forcing.
[1] R. Dascaliuc, C. Foias & M.S. Jolly, J. Dynam. Differential Equations 17, 643 (2005)
[2] R. Dascaliuc, C. Foias & M.S. Jolly, J. Differential Equations 248, 792 (2010)
• Magnetic Reconnection in Three Dimensional Space
Prof. Allen Boozer, Columbia University, abstract, slides
[#s623, 02 Feb 2018]
The breaking of magnetic field line connections is of fundamental importance in essentially all applications of plasma physics: laboratory to astrophysics. For sixty years the theory of magnetic reconnection has been focused on two-coordinate models. When dissipative time scales far exceed natural evolution times, such models are not realistic for ordinary three dimensional space. The ideal (dissipationless) evolution of a magnetic field is shown to in general lead to a state in which the magnetic field lines change their connections on an Alfvénic (inertial), not resistive, time scale. Only a finite mass of the lightest current carrier, the electron, is required. During the reconnection, the gradient in $j_\parallel/B$ relaxes while conserving magnetic helicity in the reconnecting region. This implies a definite amount of energy is released from the magnetic field and transferred to shear Alfvén waves, which in turn transfer their energy to the plasma. When there is a strong non-reconnecting component of the magnetic field, called a guide field, $j_\parallel/B$ obeys the same evolution equation as that of an impurity being mixed into a fluid by stirring. Although the enhancement of mixing by stirring has been recognized by every cook for many millennia, the analogous effect in magnetic reconnection is not generally recognized. An interesting mathematical difference is a three-coordinate model is required for the enhancement of magnetic reconnection while only two coordinates are required in fluid mixing. The issue is the number of spatial coordinates required to obtain an exponential spatial separation of magnetic field lines versus streamlines of a fluid flow.
• A moment approach to plasma fluid/kinetic theory and closures
Jeong-Young Ji, Utah State University, abstract, slides
[#s611, 11 Jan 2018]
A system of exact fluid equations always involves more unknowns than equations. This is called the closure problem. An important aspect of obtaining quantitative closures is an accurate account of collisional effects. Recently, analytical calculations of the Landau (Fokker-Planck) collision operator as well the derivation of an infinite hierarchy of moment equations have been carried out using expansions for the distribution function in terms of irreducible Hermite polynomials. In this talk, I will present solutions to the moment hierarchy that provide closure for the set of five-moment fluid equations. In the collisional limit, improved Braginskii closures are obtained by increasing the number of moments and considering the ion-electron collision effects. For magnetized plasmas, I highlight the effect of long mean free path and derive parallel integral closures for arbitrary collisionality. Finally, I will show how the integral closures can be used to study radial transport due to magnetic field fluctuations and electron parallel transport for arbitrary collisionality.
• Overview of ENN and Fusion Technology
Dr. Minsheng Liu, ENN Sci. & Tech. Co. Ltd., China, abstract
[#s602, 19 Dec 2017]
The talk includes 3 parts: 1.overview of ENN; 2.ENN research areas and achievements; and 3.ENN fusion technology roadmap.
• The Development and Applications of CLT
Wei Zhang, Zhejiang University, abstract
[#s599, 19 Dec 2017]
CLT is an explicit, three-dimensional, fully toroidal, non-reduced, Hall-MHD code, which is developed in Zhejiang University. Through CLT, I find that electron diamagnetic rotation, which is well described by the CLT code, can significantly modify the dynamics of the tearing mode. It can also affect the characteristics of the sawtooth oscillations. Besides, I have also studied the influence of driven current on tearing mode instabilities, which can explain some experimental data of EAST. Now CLT is updating to study the influence of RMPs (Resonant Magnetic Perturbations) on tearing mode instabilities. Preliminary results show that the threshold for ‘mode locking’ increases with the frequency of RMPs, which is consistent with theory prediction.
• The JET 2020 Program: D-T and Alpha physics with the ITER Like Wall
M. Romanelli, JET, Culham Science Centre, abstract, slides
[#s560, 18 Dec 2017]
The 2018-2019 JET program in preparation for DTE2 has been launched in November 2017 and will start in March 2018 with the first of the 2018 analysis and modeling campaigns followed by the first experimental campaign in D lasting until October 2018. The program will feature also an H campaign followed by a full T campaign in 2019 and aims at studying differences in plasma dynamics related to operation with pure and mixed hydrogen isotopes along with the impact of fast particles on heating, transport and confinement followed by a H campaign with NBI in H, and a D campaign for finalising the plasma preparation for DTE2. Extensive modeling and analysis has been devoted to the preparation of successful scenarios that will allow to achieving during D-T operations a fusion power of 15MW continuously for at least 5s and observing clear alpha-particle effects. In this seminar I’ll present the striking results on the isotope (H/D) effect on transport and global confinement from the latest experimental campaigns along with the plans for experiments on transport and confinement in the 2018-2020 campaigns.
e-mail contact of the main author: michele.romanelli@ukaea.uk
• Understanding mechanisms underlying ohmic breakdown in a tokamak by considering multi-dimensional plasma responses
Min-Gu Yoo, Seoul National University, abstract, slides
[#s598, 18 Dec 2017]
The ohmic breakdown is generally used to produce initial plasmas in tokamaks. However, the complex electromagnetic structure of tokamaks has obscured the physical mechanism of ohmic breakdown for several decades. Previous studies ignored plasma responses to external electromagnetic fields and adopted only the simplest Townsend avalanche theory. However, we found clear evidence that experimental results cannot be explained by the Townsend theory. Here, we propose a completely new type of breakdown mechanism that systematically considers multi-dimensional plasma responses in the complex electromagnetic topology. As the plasma response, self-electric fields produced by space-charge were found to be crucial for significantly reducing plasma density growth rate and enhancing perpendicular transport via $\small {\bf E}\times{\bf B}$ drifts. A particle simulation code, BREAK, clearly captured these effects and provided a remarkable reproduction of the mysterious experimental results in KSTAR. These new physical insights into complex electromagnetic topology provide general design guideline for a robust breakdown scenario in a tokamak fusion reactor.
• Investigation of whistler-electron interaction in Earth’s radiation belt
Lei Zhao, New Mexico Consortium, abstract, slides
[#s570, 15 Dec 2017]
In this talk, I will focus on how to describe the energetic electron dynamics through quasilinear whislter-electron interactions in Earth’s magnetosphere. First of all, we explore gyro-resonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the March 17 2013 storm. We consider the Earth’s magnetic dipole field as a reference, and compare the results against non-dipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with RAM-SCB, a code that models the Earth’s ring current and provides a realistic model of the Earth’s magnetic field. By applying quasi-linear theory, the bounce- and magnetic local time (MLT) averaged electron pitch angle, mixed term and energy diffusion coefficients are calculated for each magnetic field configuration. The results show that the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons (∼ 1MeV ), while a realistic model of the magnetic field configuration is necessary to adequately describe the diffusion rates of lower energy electrons (∼ 100keV )
In the second part of the talk, a Test Particle Model (TPM) is used to explore the limitations of quasilinear theory when applied to whistler wave-electron resonance. We consider the influence of wave amplitude and wave bandwidth on the wave-particle interaction within the quasilinear theory limit. The result implies that quasilinear theory tends to breakdown more easily for energetic particles even at small wave amplitude. While for broad wave bandwidths, it allows for more stochasticity for particles in phase space. On the contrary, electron phase trapping and bunching (nonlinear wave-particle interaction phenomenon) will dominate a narrow bandwidth spectrum that resembles a monochromatic wave.
• Nonlinear ECDI and anomalous transport in $\small {\bf E} \times {\bf B}$ discharges
S. Janhunen, U. Saskatchewan, abstract, slides
[#s559, 14 Dec 2017]
Cross-field anomalous transport is an important feature affecting the operation and performance of $\small {\bf E} \times {\bf B}$ discharges. Instabilities excited by the $\small {\bf E} \times {\bf B}$ flow cause anomalous current to develop, elicited in the nonlinear regime as a large amplitude coherent wave driven by the energy input from the unstable cyclotron resonances. A persistent train of soliton-like waves characterized by the fundamental harmonic of the electron cyclotron oscillations appears in the ion density. Simultaneously, there is an observable energy cascade toward long wavelength (inverse cascade) which is manifested by the formation of the long wavelength envelope of the wave train in 1D simulations. It is shown that the long wavelength part of the turbulent spectrum provides a dominant contribution to anomalous electron mobility.[1]
We present results from high fidelity 1D3V and 2D3V particle-in-cell simulations for a simplified Hall-effect thruster like plasma. We describe the non-linear evolution of the system and speculate on mechanisms behind the coherent structures and their interactions. The 2D the picture is complicated by the existence of a simultaneous long-wavelength mode (modified two-stream instability), in addition to the non-linear cascades observable in 1D.
[1] S. Janhunen, A. Smolyakov et al., Phys. Plasmas 25, 011608 (2018)
[2] Movie 1) 1D case with $T_e = 10 eV$
[2] Movie 2) 1D with $T_e = 0 eV$
[2] Movie 3) Ion density fluctuations in 2D simulation
[2] Movie 4) Electron temperature in 2D simulation
• A fast integral equation based solver for the computation of Taylor states in toroidal geometries
Antoine Cerfon, Courant Institute, New York University , abstract, slides
[#s531, 08 Nov 2017]
The stellarator equilibrium code SPEC [S.R. Hudson et al.,, Phys. Plasmas 19, 112502 (2012)] computes 3D equilibria by subdividing the plasma into separate regions assumed to have undergone Taylor relaxation to a minimum energy state subject to conserved fluxes and magnetic helicity, and separated by ideal MHD barriers. In this talk, we present a numerical scheme for the fast and high order computation of Taylor states in toroidal regions based on an integral formulation of the problem. Our formulation offers the advantage that the unknowns are only defined on the boundary of the toroidal regions. As a result, high accuracy is reached with a small number of unknowns, leading to a code which is fast and has low memory requirements. In the context of SPEC, in which the locations of the ideal MHD interfaces are iteratively updated until force balance is satisfied at each interface, our formulation gives the possibility to apply the entire iterative procedure without ever discretizing the plasma volume, only discretizing the ideal interfaces.

This is joint work with M. O'Neil, L. Greengard, and L.-M. Imbert-Gerard

• The shearing modes approach to the theory of plasma shear flow
Vladimir Mikhailenko, Pusan National University, South Korea , abstract, slides
[#s502, 18 Oct 2017]
The basic point in the understanding the processes of the evolution of the instabilities and turbulence in the plasma shear flows across the magnetic field is the proper treatment the effects of the persistent distortion of the perturbations by the shearing flow, particularly in the applications of the spectral transforms to the governing equations. The problem of extracting the separate spatial Fourier mode in the stability theory of the plasma shearing flows, and joined with it the problem of the limits of the applicability to such a plasma the spectral methods of the investigation of the stability properties on the base of the dispersion equations, may be resolved by employing the non-modal fluid and kinetic theory, which grounds on the methodology of the shearing modes and completely involves the effect of the persistent deformation of the perturbations by the sheared flows. That theory displays, that the application of the methodology of the shearing modes and convective-shearing coordinates and solution of the initial value problem in the wave vector and time variables, instead of the application of the static spatial Fourier modes and spectral transform in time, has the decisive impact on the understanding the wave-particle interaction in the shearing flow. That theory recovers main linear and non-linear processes and corresponding numerous characteristic time scales, which may be observable in the experiments and numerical simulations, but can’t be distinguished, when the spectral transform in time is applied. A most famous is the ”quench rule”, which was detected in first in the numerical simulations, but was not confirmed analytically in the calculations of the shearing flows stability, grounded on the spectral transformations in time. The primary intent of this report is to show that a non-modal approach is a decisive in the reconciling observational evidence with stability theory of plasma shearing flows and to suggest a more frequent use of that approach.
• Gyrokinetic simulation of boundary plasma in contact with material wall
Seung-Hoe Ku, PPPL, abstract, slides
[#s449, 11 Sep 2017]
Boundary plasma is in a non-equilibrium statistical state governed by self-organization among multiscale physics, and needs to be modeled with total-f gyrokinetic equations. A unique pariticle-in-cell technique will be introduced that has enabled XGC to be the world’s first, and only, gyrokinetic code that simulates the boundary plasma across the magnetic separatrix into the scrape-off layer in contact with a material wall. Examples of successful boundary physics discoveries enabled by the technique will also be presented.
• Role of electron physics in 3D two-fluid 10-moment simulations of the Ganymede’s magnetosphere
Liang Wang, U. New Hampshire, abstract, slides
[#s445, 31 Aug 2017]
We studied the role of electron physics in 3D two-fluid 10-moment simulations of the Ganymede’s magnetosphere. The model captures non-ideal physics like the Hall effect, the electron inertia, and anisotropic, non-gyrotropic 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 non-gyrotropy 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 (HST). The correlation between the observed emission morphology and spatial variability in electron/ion pressure was demonstrated. We also briefly discussed the relevance of this work to the future JUICE mission.
• A new coil design code FOCUS for designing stellarator coils without the winding surface
Caoxiang Zhu, U. Sci. & Tech. China, Hefei, China , abstract, slides
[#s444, 30 Aug 2017]
Finding an easy-to-build coils set has been a critical issue for stellarator design for decades. Conventional approaches assume a toroidal “winding” surface and suffer the difficulties of nonlinear optimization. A new coil design method, the FOCUS code, is introduced by representing each discrete coil as an arbitrary, closed space curve. The first and second derivatives of the target function that covers both physical requirements and engineering constraints are calculated analytically. We have employed several advanced nonlinear optimization algorithms, like the nonlinear conjugate gradient and the modified Newton method, for minimizing the target function. Numerical illustrations show that the new method can be applied to different types of coils for various configurations with great flexibilities and robustness. An extended application for analyzing the error field sensitivity is also presented.
• Stochastic modelling of fluctuations in scrape-off layer plasmas
Ralph Kube, UIT, Tromso, Norway, abstract, slides
[#s412, 24 Aug 2017]
Scrape-off layer plasmas feature intermittent, large-amplitude fluctuations which are attributed to the radial outwards propagation of plasma blobs through this volume. We introduce a stochastic model which describes scrape-off layer time series by superposing uncorrelated pulses with variable amplitude. The resulting time series is Gamma distributed where the lowest order statistical moments are given by the pulse parameters. The power spectral density is governed by the pulse shape - for a double exponential pulse shape presents the power spectral density a flat region for low frequencies and a steep power law scaling for high frequencies. Predictions from this model are compared to fluctuation measurements of electron density, temperature and plasma potential by mirror Langmuir probes in the SOL during an ohmic L-mode discharge in Alcator C-Mod.
• Simulation of resonant wave-particle interaction in tokamaks
Meng Li, IFS, The University of Texas, Austin, abstract, slides
[#s415, 17 Aug 2017]
We present a numerical procedure for modeling resonant response of energetic particles to waves in tokamaks. With Littlejohn Lagrangian for guiding center motion, we use the action-angle variables to simplify simulations of the fast ion dynamics to one dimensional. The transformation also involves construction of canonical straight field line coordinates, which render a Hamiltonian description of the guiding center motion. This module can be integrated with the modified MHD code AEGIS to simulate wave-particle interactions.
• Tearing mode dynamics and sawtooth oscillation in Hall-MHD
Zhiwei Ma, Zhejiang University, Hangzhou, China, abstract, slides
[#s414, 09 Aug 2017]
Tearing mode instability is one of the most important dynamic processes in space and laboratory plasmas. Hall effects, resulted from the decoupling of electron and ion motions, could cause the fast development and perturbation structure rotation of the tearing mode and become non-negligible. A high accuracy nonlinear MHD code (CLT) is developed to study Hall effects on the dynamic evolution of tearing modes with Tokamak geometries. It is found that the rotation speed of the mode structure from the simulation is in a good agreement with that from the analytical theory in a single tearing mode. The linear growth rate increases with increase of the ion skin depth. The self-consistent generated rotation largely alters the dynamic behaviors of the double tearing mode and the sawtooth oscillation.
• Continuum kinetic schemes for Vlasov-Maxwell equations, with applications to laboratory and space plasmas
Ammar Hakim, PPPL, abstract, slides
[#s179, 22 Jun 2017]
Increasingly accurate laboratory experiments and satellite observations have led to a "golden age" in plasma physics. Detailed kinetic features, including distribution functions, can now be measured in-situ, putting severe strain on theory and modeling to explain the experiments/observations. The Particle-In-Cell (PIC) method remains a powerful and widely used tool to study such kinetic physics numerically. Recently, complimenting the PIC approach, significant progress has been made in discretizing the Vlasov equation directly, treating it as a partial differential equation (PDE) in 6D phase-space. In this talk, I present a high-order discontinuous Galerkin (DG) algorithm to solve the Vlasov equation. This continuum scheme leads to noise-free solutions and, with the use of specially optimized computational kernels, can be very efficient, in particular, for problems in which the structure of distribution functions and its higher-moments are required. In addition, with a proper choice of basis functions and numerical fluxes, the scheme conserves energy exactly, while conserving momentum to a high degree of accuracy. Applications of the scheme to (a) kinetic saturation mechanism of Wiebel-like instability and (b) turbulence in the solar wind are presented. We demonstrate a new and novel mechanism for the nonlinear saturation of the Wiebel instability that comes about from a balance between filamentation and a secondary electrostatic two-stream instability. We use 5D simulations of turbulent plasmas to study detailed kinetic physics of magnetized turbulence, showing that the solution contains remarkable amount of detail in the distribution function, leading to new and novel insights the nature of kinetic wave-particle exchange in turbulent plasmas.
• Nonthermal particle acceleration in magnetic reconnection and turbulence in collisionless relativistic plasmas
Dmitri Uzdensky, IAS & U. Colorado Boulder, abstract, slides
[#s177, 12 Jun 2017]
One of the key recurrent themes in high-energy plasma astrophysics is relativistic nonthermal particle acceleration (NTPA) necessary to explain the bright X-ray and gamma-ray flaring emission with ubiquitous power-law spectra in astrophysical objects such as pulsar wind nebulae, hot accretion flows and coronae of accreting black holes, and black-hole powered relativistic jets in active galactic nuclei and gamma-ray bursts. Two leading physical processes often invoked as possible NTPA mechanisms are collisionless magnetic reconnection and turbulence. In order to understand these processes, as well as their resulting observable radiation signatures, I have recently initiated a broad theoretical and computational research program in kinetic radiative plasma astrophysics. This program employs large-scale first-principles particle-in-cell kinetic simulations (including those that self-consistently incorporate radiation-reaction effects) coupled with analytical theory. In this talk I will review the resulting progress that we have achieved in recent years towards understanding and quantitative characterization of NTPA in reconnection and turbulence over a broad range of physical regimes. I will present 2D and 3D simulation results that demonstrate that both reconnection and turbulence in relativistic collisionless astrophysical plasmas can robustly produce non-thermal energy spectra with power-law indices that show an intriguingly similar characteristic dependence on the plasma magnetization. I will also describe the effects of strong radiative cooling on reconnection and turbulence.
• Hot Particle Equilibrium code (HPE) with plasma anisotropy and toroidal rotation
Leonid Zakharov, LiWFusion, abstract, slides
[#s162, 26 May 2017]
The HPE code represents the extension of ESC (Equilibrium and Stability Code) to tokamak equilibria with plasma anisotropy and toroidal rotation. In addition to conventional 1-D input profiles of plasma pressure $p(a)$ and safety factor $q(a)$ HPE accepts the poloidal Mach number ${\cal M}(a)$ of plasma rotation and 2-D parallel pressure profile of hot particles $p_\parallel(a,B)$ as the input. Here, $a$ is the normalized radial flux coordinate of magnetic configuration and $B$ is the strength of magnetic field. The HPE code includes the effect of finite width of hot particle orbits and for the case of powerful NBI injection the code can generate the plasma equilibria for theory needs as well as use the experimental (or kinetic simulations) data for interpretation of experiments.
• Anomalous Diffusion across a Tera Gauss Field in accreting Neutron Stars
Russell Kulsrud, PPPL, abstract, slides
[#s161, 25 May 2017]
A large amount of mass falls on the polar region of neutron star in Xray binaries and the question is, is the mass completely frozen on the field lines or can it diffuse through them? In this talk we present a mechanism for the latter possibility. A strong MHD instability occurs in the top layers of the neutron star driven by the incoming mass. This instability has the same properties as the Schwarzschild instability in the solar convection zone. It gives rise to a turbulent cascade which mixes up the field lines so that lines originally far apart can come with a resistivity diffusion distance and transfer the masses between them. However, the lines of force themselves are not disrupted. This leads to an equilibrium which is marginal with respect to the instability just as happens in the Schwarzschild case.
• Modeling substrom dipolarizations and particle injections in the terrestrial magnetosphere
Konstantin Kabin, Royal Military College of Canada, abstract, slides
[#s156, 11 May 2017]
Increased fluxes of energetic electrons and ions in the inner magnetosphere of the Earth are often associated with sudden reconfigurations of the magnetotail, often referred to as substorm dipolarizations. We describe a novel model of the magnetotail which is easily controlled by several adjustable parameters, such as the thickness of the tail and the location of transition from dipole-like to tail-like magnetic field lines. This model is fully three-dimensional and includes the day-night asymmetry of the terrestrial magnetosphere, however, the field lines are confined to the meridional planes. Our model is well suited to studies of the magnetotail dipolarizations which we consider to be the tailward movements of the transition between dipole-like and tail-like field lines. We also study the effects of a dipolarizing electromagnetic pulse propagating towards the Earth. The calculated electric and magnetic fields are used to describe the motion of electrons and ions and changes in their energies. In some cases, particle energies increase by a factor of 25 or more. The energized particles are transported earthward where they are often observed by geostationary satellites as substorm injections. The energization level obtained in our model is reasonably consistent with satellite and ground-based observation (e.g. carried out by riometers), and therefore we consider our scenario of the dipolarization process to be feasible.
• DCON for Stellarators
Alan Glasser, Fusion Theory & Computation, Inc., abstract, slides
[#s158, 10 May 2017]
We report the development of a new version of DCON for nonaxisymmetric toroidal plasmas, e.g. stellarators. The DCON code is widely used for fast and accurate determination of ideal MHD stability of axisymmetric toroidal plasmas. Minimization of the ideal MHD energy principle $\delta W$ is reduced to adaptive numerical integration of a coupled set of ordinary differential equations for the complex poloidal Fourier harmonics of the perturbed normal displacement. For a periodic cylindrical plasma, both the poloidal and toroidal coordinates are ignorable, allowing for treatment of single harmonics $m$ and $n$. For an axisymmetric toroidal plasma, poloidal symmetry is broken, causing different $m$’s to couple and requiring simultaneous treatment of $M$ harmonics. For a nonaxisymmetric plasma, toroidal symmetry is also broken, causing different $n$’s to couple and requiring treatment of $N$ harmonics. For a stellarator with field period $l$, e.g. $l = 5$ for W7X, each toroidal harmonic $n$ is coupled to toroidal harmonics $n+k \, l$, for all integers $k$. Both $M$ and $N$ are truncated on the basis of convergence. Singular surfaces occur at all values of safety factor $q = m/n$ in the plasma. The DCON equations have been generalized to allow for multiple $n$’s with coupling matrices $F$, $K$, and $G$. An interface has been developed for the nonaxisymmetric equilibrium code VMEC, which provides values for these matrices. Their Fourier harmonics are fit to cubic splines as a function of the radial coordinate $s$, allowing for adaptive integration of the ODEs. The status of the code development will be presented.
• Disintegration threshold of Langmuir solitons in inhomogeneous plasmas
Yasutaro Nishimura, National Cheng Kung University, Taiwan, abstract, slides
[#s140, 04 May 2017]
Dynamics of Langmuir solitons in inhomogeneous plasmas is investigated numerically employing Zakharov equations. The solitons are accelerated toward a lower background density side. With the steep density gradients, balance between the electric field part of the soliton and the density cavity breaks and the solitons disintegrate. The disintegration threshold is given by regarding the electric field part of the soliton as a point mass moving along the self-generated potential well produced by the density cavity. On the other hand, when the density gradient is below the threshold, Langmuir solitons adjust themselves by expelling the imbalanced portion as density cavities at the sound velocity. When the gradient is below the threshold, the electric field part of the soliton bounces back and forth within the potential well. The study is extended to kinetic simulation. Generation mechanism of high energy electron tails in the presence of solitons is discussed. The electron distribution function resembles that of the Lorentzian type. The particle acceleration is explained as a transport process toward high energy side due to overlapping of multiple resonant islands in the phase space.
• Gyrokinetic simulation of a fast L-H bifurcation dynamics in a realistic diverted tokamak edge geometry
Seung-Hoe Ku, PPPL, abstract, slides
[#s141, 27 Apr 2017]
Despite its critical importance in the fusion program and over 30 years of H-mode operation, there has been no fundamental understanding at the kinetic level on how the H-mode bifurcation occurs. We report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a realistic C-Mod like diverted tokamak edge geometry under strong forcing by a high rate of heat deposition. The results show that the synergistic action between two multiscale dynamics, the turbulent Reynolds-stress driven [1] and the neoclassical X-point orbit loss drive [2] sheared ${\bf E}\times{\bf B}$ flows, works together to quench turbulent transport and form a transport barrier just inside the last closed magnetic flux surface. The synergism helps reconcile experimental reports of the key role of turbulent stress in the bifurcation [3, and references therein] with some other experimental observations that ascribe the bifurcation to X-point orbit loss/neoclassical effects [4,5]. The synergism could also explain other experimental observations that identified a strong correlation between the L-H transition and the orbit loss driven ${\bf E}\times{\bf B}$ shearing rate [6,7]. The synergism is consistent with the general experimental observation that the L-H bifurcation is more difficult with the $\nabla B$-drift away from the single-null X-point, in which the X-point orbit-loss effect is weaker [2].
[1] P.H. Diamond, S-I Itoh et al., Plasma Phys. Controlled Fusion 47, R35 (2005)
[2] C.S. Chang, Seunghoe Kue & H. Weitzner, Phys. Plasmas 9, 3884 (2002)
[3] G.R. Tynan, M. Xu et al., Nucl. Fusion 53, 073053 (2013)
[4] T. Kobayashi, K. Itoh et al., Phys. Rev. Lett. 111, 035002 (2013)
[5] M. Cavedon, T. Pütterich et al., Nucl. Fusion 57, 014002 (2017)
[6] D.J. Battaglia, C.S. Chang et al., Nucl. Fusion 53, 113032 (2017)
[7] S.M. Kaye, R. Maingi et al., Nucl. Fusion 51, 113109 (2011)
• Parasitic momentum flux in the tokamak core
Timothy Stoltzfus-Dueck, PPPL, abstract
[#s138, 20 Apr 2017]
Tokamak plasmas rotate spontaneously in the absence of applied torque. This so-called “intrinsic rotation” may be very important for future low-torque devices such as ITER, since rotation can stabilize certain instabilities. In the mid-radius “gradient region”, which reaches from the sawtooth inversion radius out to the pedestal top, intrinsic rotation profiles are sometimes flat and sometimes hollow. Profiles may even transition suddenly between these two states, an unexplained phenomenon referred to as rotation reversal. Theoretical efforts to identify the origin of the mid-radius rotation shear have focused primarily on quasilinear models, in which the phase relationships of some selected instability result in a nondiffusive momentum flux (“residual stress”). In contrast to these efforts, the present work demonstrates the existence of a robust, fully nonlinear symmetry-breaking momentum flux that follows from the free-energy flow in phase space and does not depend on any assumed linear eigenmode structure. The physical origin is an often-neglected portion of the radial ${\bf E}\times {\bf B}$ drift, which is shown to drive a symmetry-breaking outward flux of co-current momentum whenever free energy is transferred from the electrostatic potential to ion parallel flows [1]. The resulting rotation peaking is counter-current and scales as temperature over plasma current. As originally demonstrated by Landau [2], this free-energy transfer (thus also the corresponding residual stress) becomes inactive when frequencies are much higher than the ion transit frequency, which may explain the observed relation of density and counter-current rotation peaking in the core. Simple estimates suggest that this mechanism may be consistent with experimental observations, in both hollow and flat rotation regimes.
[1] T. Stoltzfus-Dueck, Phys. Plasmas 24, 030702 (2017)
[2] L. Landau, J. Exp. Theor. Phys. 16, 574 (1946); English translation in J. Phys. (USSR) 10, 25 (1946)
• Transport in the Coupled Pedestal and Scrape-off layer region of H-mode plasmas
Michael Churchill, PPPL, abstract, slides
[#s139, 18 Apr 2017]
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. I will present research exploring characteristics of this transport using the family of X-point Gyrokinetic Codes (XGC). First, the variation of pressure in the scrape-off layer (important to understand in order to avoid divertor wall degradation) is widely believed to follow simple fluid prescriptions, due to high collisionality. However, simulation results in the near-SOL indicate a significant departure from the simple fluid models, even after including additional terms from neutral drag and the Chew-Goldberger-Low form of parallel ion viscosity to the parallel momentum balance. Second, turbulence characteristics in the edge region show nonlocal behavior, including convective transport of turbulent eddies (“blobs”) born just inside the closed field line region out into the SOL. These large intermittent structures can be created even in the absence of collisions in the simulation. Tracking these structures show that on average their radial velocity is very small, even in the near-SOL, while their poloidal velocity is significant. The potential structure within these blobs is monopolar with a peak shifted from the density structure, contrary to the dipolar structure expected by analytical models for blob generation and transport based on interchange turbulence. Finally, coherent phase space structures in blobs are searched for, however only broad regions of velocity space are found to show significant structure.
• Improved Neoclassical Transport Simulation for Helical Plasmas
[#s135, 30 Mar 2017]
This work contains the following studies: (1) benchmark of the neoclassical transport models and clarify the impact of their approximations among drift-kinetic equations in helical plasmas; and (2) apply the local models for a quantitative evaluation of bootstrap current in FFHR-d1 DEMO. In part 1, this work reports that the benchmarks of the neoclassical transport codes based on the several local drift-kinetic models. The drift-kinetic models are zero-orbit-width (ZOW), zero-magnetic-drift (ZMD), DKES-like, and global, as classified in [1]. The magnetic geometries of HSX, LHD, and W7-X are employed. It is found that the assumption of ${\bf E} \times {\bf B}$ incompressibility causes discrepancy of neoclassical radial flux and parallel flow among the models when ${\bf E} \times {\bf B}$ is sufficiently large compared to the magnetic drift velocities. For example, ${\cal M}_p ≤ 0.4$ where ${\cal M}_p$ is the poloidal Mach number. On the other hand, when ${\bf E} \times {\bf B}$ and the magnetic drift velocities are comparable, the tangential magnetic drift plays a role in suppressing the unphysical peaking of neoclassical radial-fluxes in the other local models at $E_r ≃ 0$. In low collisional frequency plasmas, the tangential drift suppress such unphysical behavior in the radial transport well. This work demonstrates that the ZOW model not only mitigates the unphysical behavior but also implements evaluation of bootstrap current in LHD with the low computation cost compared to the global model. In part 2, the impact of the parallel momentum conservation on the boot-strap current among the ZOW, DKES, and PENTA models are demonstrated. The ZOW model is extended to include the ion parallel mean flow effect on the electron-ion parallel friction. The DKES model employs the pitch-angle-scattering as the collision operator. The PENTA code employs the Sugama-Nishimura method to correct the momentum balance of DKES results. Therefore, the ZOW model and PENTA codes both conserve the parallel momentum in like-species collisions and include the electron-ion parallel frictions. The work shows that the ZOW and the PENTA code agree with each other well on the calculations of the bootstrap current. Then, this verifies the reliability of the bootstrap current calculation with the ZOW model and the PENTA code for FFHR-d1 DEMO.
[1] Seikichi Matsuoka, Shinsuke Satake et al., Phys. Plasmas 22, 072511 (2015)
• Recent progress of understanding 3D magnetic topology in stellarators and tokamaks
Yasuhiro Suzuki, National Institute for Fusion Science, Japan, abstract, slides
[#s134, 23 Mar 2017]
Recent progress of 3D equilibrium calculation will be reported. The 3D equilibrium calculation is a fundamental consideration to understand the magnetic topology. In particular, for stellarators, the topological change due to the beta-sequences has been found and it is an important issue how to make good flux surfaces in general 3D configuration in the presence of the plasma beta. On the other hand, the 3D equilibrium calculation is also an important issue for tokamaks, because the RMP is widely used to control the stability and transport. In this talk, recent results of 3D equilibrium calculations based on the HINT code, which is a 3D equilibrium calculation code without an assumption of perfectly nested flux surfaces. Impacts of the beta-sequences and the plasma rotation will be discussed.
• Self-organizing knots
Christopher Smiet, Leiden University, The Netherlands, abstract, slides
[#s133, 16 Mar 2017]
Magnetic helicity, a measure for the linking and knotting of magnetic field lines, is a conserved quantity in Ideal MHD. In the presence of resistivity, helicity constrains the rate at which magnetic energy can be dissipated. When a localized, helical magnetic field is set to relax in a low-resistance high-beta plasma, the magnetic pressure drives the plasma to expand whilst the helicity is still approximately conserved. Using numerical simulations I show how this interplay gives rise to a novel MHD equilibrium: the initially linked field lines self-organize to form a structure where field lines lie on nested toroidal surfaces of constant pressure. The Lorentz forces are balanced by the gradient in pressure, with a minimum in pressure on the magnetic axis. Interestingly, the rotational transform is nearly constant on all magnetic surfaces, making the structure topologically nearly identical to a famous knotted structure in Topology: the Hopf fibration. I will explore the nature of this equilibrium, and how it relates geometrically to the structure of the Hopf map. Additional dynamics give rise phenomena that are well known from magnetic confinement devices; magnetic islands can occur at rational surfaces, and in certain regimes the equilibrium becomes nonaxisymmetric, triggering a marginal core-interchange mechanism.
• Development and application of BOUT++ for large scale turbulence simulation
Jarrod Leddy - The University of York, UK, abstract, slides
[#s132, 28 Feb 2017]
The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the self-consistent evolution of plasma fluctuations, global profiles, and flows, but the numerical tools capable of doing this in realistic (diverted) geometry are only now being developed. BOUT++ is one such tool that has had many recent develops towards this goal. A novel coordinate system has been developed to improve the resolution around the X-point and strike points in the divertor region. A 5-field reduced 2-fluid plasma model for the study of instabilities and turbulence in magnetised plasmas has been built on the BOUT++ framework that allows the evolution of global profiles, electric fields and flows on transport timescales, with flux-driven cross-field transport determined self-consistently by electromagnetic turbulence. Models for neutral evolution have also been included, and the interaction of these neutrals with the plasma is characterised through charge exchange, recombination, ionisation, and radiation. Simulation results for linear devices, MAST-U, and DIII-D are presented that shed light on the nature of plasma-neutral interaction, detachment in the super-X divertor, and turbulence in diverted geometry.
• Studies on proton effective heating in magnetic reconnection by means of particle simulations
Shunsuke Usami, National Institute for Fusion Science, Japan, abstract
[#s130, 23 Feb 2017]
By means of two-dimensional electromagnetic particle simulations, ion heating mechanism is investigated in magnetic reconnection with a guide magnetic field. These simulations mimic dynamics of two torus plasmas merging through magnetic reconnection in a spherical tokamak (ST) device. It is found that protons are effectively heated in the downstream by the pickup mechanism, since a ring-like structure of proton velocity distribution, which is theoretically predicted to be formed by picked-up ions, is observed at a local region of the downstream. Furthermore, based on the theory by J. F. Drake et al., only heavy ions were believed to be heated by suffering the pickup mechanism, however it is pointed out that the pickup of protons is consistent with the theory in the cases that the plasma beta is much less than 1 in the upstream, which can be satisfied in STs.
• Low-Frequency $\delta f$ PIC Models with Fully Kinetic Ions
Benjamin J. Sturdevant, University of Colorado at Boulder, USA, abstract, slides
[#s131, 22 Feb 2017]
A fully kinetic ion model is useful for the verification of gyrokinetic turbulence simulations in certain regimes where the gyrokinetic model may break down due to the lack of small ordering parameters. For a fully kinetic ion model to be of value, however, it must first be able to accurately simulate low-frequency drift-type instabilities typically well within the domain of gyrokinetics. In this talk, we present a fully kinetic ion model formulated with weak gradient drive terms and applied to the ion-temperature-gradient (ITG) instability. A $\delta f$ implementation in toroidal geometry is discussed, where orthogonal coordinates are used for the particle dynamics, but field-line-following coordinates are used for the field equation, allowing for high resolution of the field-aligned mode structure. Variational methods are formulated for integrating the particle equations of motion, allowing for accuracy on a long time scale with modest timestep sizes. Finally, an implicit orbit averaging and sub-cycling scheme for the fully kinetic ion model is considered.
• Exact collisional plasma fluid theories
Eero Hirvijoki/David Pfefferlé, PPPL, abstract, slides
[#s129, 10 Feb 2017]
Following Grad’s procedure, an expansion of the velocity space distribution functions in terms of multi-index Hermite polynomials is carried out to derive a consistent set of collisional fluid equations for plasmas. The velocity-space moments of the often troublesome nonlinear Landau collision operator are evaluated exactly, and to all orders with respect to the expansion. The collisional moments are shown to be generated by applying gradients on two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The expansion can be truncated at arbitrary order with quantifiable error, providing a consistent and systematic alternative to the Chapman-Enskog procedure which, in plasma physics, amounts to the famous Braginskii equations. To illustrate our approach, we provide the collisional ten-moment equations and prove explicitly that the exact, nonlinear expressions for the momentum- and energy-transfer rate satisfy the correct conservation properties.
• Recent advances in the variational formulation for reduced Vlasov-Maxwell equations
Alain Brizard, Saint Michael’s College, Colchester, USA, abstract, slides
[#s126, 02 Feb 2017]
The talk presents recent advances in the variational formulation of reduced Vlasov-Maxwell equations. First, the variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric. Next, the Eulerian variational principle for the nonlinear electromagnetic gyrokinetic Vlasov-Maxwell equations is presented in the parallel-symplectic representation, where the gyrocenter Poisson bracket contains contributions from the perturbed magnetic field.
• Discrete Exterior Calculus Discretization of the Navier-Stokes Equations
Ravindra Samtaney, King Abdullah University Sci. & Technology, abstract, slides
[#s127, 10 Jan 2017]
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). The DEC discretization is carried out for the exterior calculus form of Navier-Stokes equations, where the velocity field is represented by a 1-form. A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme for structured-triangular meshes, and first order accuracy for general unstructured meshes. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of various discrete Hodge star definitions based on both circumcentric and barycentric dual meshes is also demonstrated. The barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes instead of being limited only to Delaunay meshes, as in previous DEC-based discretizations. The convergence order attained through the circumcentric Hodge operator is retained when using the barycentric Hodge. The discretization scheme is presented in detail along with numerical test cases demonstrating its numerical convergence and conservation properties. Preliminary results regarding the implementation of hybrid (circumcentric/barycentric) Hodge star operator are also presented. We conclude with some ideas for employing a similar method for magnetohydrodynamics.
• Global electromagnetic gyrokinetic and hybrid simulations of Alfvén eigenmodes
Michael Cole, Max Planck Institute for Plasma Physics, Greifswald , abstract, slides
[#s125, 09 Dec 2016]
The pursuit of commercial fusion power has driven the development of increasingly complex and complete numerical simulation tools in plasma physics. Recent work with the EUTERPE particle-in-cell code has made possible global, electromagnetic, fully gyrokinetic and fluid-gyrokinetic hybrid simulations in a broad parameter space, where previously global gyrokinetic simulations had been hampered by the so-called ‘cancellation problem’. This has been applied to the simulation of the interaction between Alfvén eigenmodes and energetic particles. In this talk, the range of numerical methods used will be detailed, and it will be shown with practical examples that self-consistent global simulations may be necessary for even a qualitatively accurate prediction of the perturbation of the magnetic field and fast particle transport due to wave-particle interaction. A brief outline will be given of the future direction of this work, such as the possibility of gyrokinetic simulation of the interaction between fine-scale turbulence and MHD modes.
• Sparse grid techniques for particle-in-cell schemes
Lee Ricketson, Courant Institute, New York University , abstract, slides
[#s124, 21 Nov 2016]
The particle-in-cell (PIC) method has long been the standard technique for kinetic plasma simulation across many applications. The downside, though, is that quantitatively accurate, 3-D simulations require vast computing resources. A prominent reason for this complexity is that the statistical figure of merit is the number of particles per cell. In 3-D, the number of cells grows rapidly with grid resolution, necessitating an astronomical number of particles. To address this challenge, we propose the use of sparse grids: by a clever combination of the results from a variety of grids, each of which is well resolved in at most one coordinate direction, we achieve similar accuracy to that of a full grid, but with far fewer grid cells, thereby dramatically reducing the statistical error. We present results from test cases that demonstrate the new scheme's accuracy and efficiency. We also discuss the limitations of the approach and, in particular, its need for an intelligent choice of coordinate system.
• Optical collapse and nonlinear laser beam combining
Pavel Lushnikov, U. New Mexico , abstract, slides
[#s121, 18 Nov 2016]
Many nonlinear systems of partial differential equations admit spontaneous formation of singularities in a finite time (blow up). Blow up is often accompanied by a dramatic contraction of the spatial extent of solution, which is called by collapse. A collapse in a nonlinear Schrodinger equation (NLSE) describes the self-focusing of the intense laser beam in the nonlinear Kerr medium (like usual glass) with the propagation distance $z$ playing the role of time. NLSE in the dimension two (two transverse coordinates) corresponds the stationary self-focusing of the laser beam eventually causing optical damage as was routinely observed in experiment since 1960s. NLSE in the dimension three (two transverse coordinates and time) is responsible for the formation of the optical bullet making pulse much shorter in time in addition to the spatial self-focusing. We address the universal self-similar scaling near collapse. In the critical 2D case the collapsing solutions have a form of rescaled soliton such that the $z$-dependence of that scale determines the $z$-dependent collapse width $L(z)$ and amplitude $\sim 1/L(z)$. At the leading order $L(z) \sim (z_c-z)^{1/2}$, where $z_c$ is the collapse time with the required log-log modification of that scaling. Log-log scaling for NLSE was first obtained asymptotically in 1980s and later proven in 2006. However, it remained a puzzle that this scaling was never clearly observed in simulations or experiment. We found that the classical log-log modification NLSE requires double-exponentially large amplitudes of the solution $\sim 10^{10^{100}}$, which is unrealistic to achieve in either physical experiments or numerical simulations. In contrast, we developed a new asymptotic theory which is valid starting from quite moderate (about 3 fold) increase of the solution amplitude compare with the initial conditions. We use that new theory to propose a nonlinear combining of multiple laser beams into a diffraction-limited beam by beam self-focusing in Kerr medium. Multiple beams with total power above critical are combined in near field and propagated through multimode optical fiber. Random fluctuations during propagation first trigger the formation of the strong optical turbulence. During subsequent propagation, the inverse cascade of optical turbulence tends to increase the transverse spatial scale of fluctuation until it efficiently triggers a strong optical collapse event producing diffraction-limited beam with the critical power.
• On Degenerate Lagrangians, Noncanonical Hamiltonians, Dirac Constraints and their Discretization
Michael Kraus, Max Planck Institute for Plasma Physics, Garching , abstract, slides
[#s123, 17 Nov 2016]
Most systems encountered in plasma physics are Hamiltonian and therefore have a rich geometric structure, most importantly symplecticity and conservation of momentum maps. As most of these systems are formulated in noncanonical coordinates, they are not amenable to standard symplectic discretisation methods, which are popular for the integration of canonical Hamiltonian systems.
Variational integrators, which can be seen as the Lagrangian equivalent to symplectic methods, seem to provide an alternative route towards the systematic derivation of structure-preserving numerical methods for such systems. However, for noncanonical Hamiltonian systems the corresponding Lagrangian is often found to be degenerate. This degeneracy gives rise to instabilities of the variational integrators which need to be overcome in order to make long-time simulations possible.
In this talk, recent attempts to devise long-time stable structure-preserving integrators for noncanonical Hamiltonian and degenerate Lagrangian systems will be reviewed. The guiding-centre system will be used to exemplify the problems which arise for such systems and to demonstrate the good long-time fidelity of the newly developed integrators.
• Development and applications of Verification and Validation procedures
Fabio Riva, EPFL, Switzerland , abstract
[#s110, 14 Nov 2016]
The methodology used to assess the reliability of numerical simulation codes constitutes the Verification and Validation (V&V) procedure. V&V is composed by three separate tasks: the code verification, which is a mathematical issue targeted to assess that the physical model is correctly implemented in a simulation code; the solution verification, which evaluates the numerical errors affecting a simulation; and the validation, which determines the consistency of the code results, and therefore of the physical model, with experimental data.
To perform a code verification, we propose to use the method of manufactured solutions, a methodology that we have generalized to PIC codes, overcoming the difficulty of dealing with a numerical method intrinsically affected by statistical noise. The solution verification procedure we put forward is based on the Richardson extrapolation, used as higher order estimate of the exact solution. These verification procedures were applied to GBS, a three-dimensional fluid code for SOL plasma turbulence simulation based on a finite difference scheme, and to a unidimensional, electrostatic, collisionless PIC code. To perform a detailed validation of GBS against experimental measurements, we generalized the magnetic geometry of the simulation code to include elongation and non-zero triangularity, and we investigated theoretically the impact of plasma shaping effects on SOL turbulence. An experimental campaign is now planned on TCV, to validate our findings against experimental measurements in tokamak limited configurations.
• Modeling efforts in hybrid kinetic-MHD and fully kinetic theories
Cesare Tronci, University of Surrey, UK , abstract, slides
[#s111, 28 Oct 2016]
Over the decades, multiscale modeling efforts have resorted to powerful methods, such as asymptotic/perturbative expansions and/or averaging techniques. As a result of these procedures, finer scale terms are typically discarded in the fundamental equations of motion. Although this process has led to well consolidated plasma models, consistency issues may emerge in certain cases especially concerning the energy balance. This may lead to the presence of spurious instabilities that are produced by nonphysical energy sources. The talk proposes alternative techniques based on classical mechanics and its underlying geometric principles. Inspired by Littlejohn's guiding-center theory, the main idea is to apply physical approximations to the action principle (or the Hamiltonian structure) underlying the fundamental system, rather than operating directly on its equations of motion. Here, I will show how this method provides new energy-conserving variants of hybrid kinetic-MHD models, which suppress the spurious instabilities emerging in previous non-conservative schemes. Also, this method allows for quasi-neutral approximations of fully kinetic Vlasov theories, thereby neglecting both radiation and Langmuir oscillations.
• Extending geometrical optics: A Lagrangian theory for vector waves
Daniel Ruiz, Princeton University , abstract
[#s114, 27 Oct 2016]
Even diffraction aside, the commonly known equations of geometrical optics (GO) are not entirely accurate. GO considers wave rays as classical particles, which are completely described by their coordinates and momenta, but rays have another degree of freedom, namely, polarization. As a result, wave rays can behave as particles with spin. A well-known example of polarization dynamics is wave-mode conversion, which can be interpreted as rotation of the (classical) wave spin.'' However, there are other less-known manifestations of the wave spin, such as polarization precession and polarization-driven bending of ray trajectories. This talk presents recent advances in extending and reformulating GO as a first-principle Lagrangian theory, whose effective-gauge Hamiltonian governs both mentioned polarization phenomena simultaneously. Examples and numerical results are presented. When applied to classical waves, the theory correctly predicts the polarization-driven divergence of left- and right- polarized electromagnetic waves in isotropic media, such as dielectrics and nonmagnetized plasmas. In the case of particles with spin, the formalism also yields a point-particle Lagrangian model for the Dirac electron, i.e. the relativistic spin-1/2 electron, which includes both the Stern-Gerlach spin potential and the Bargmann-Michel-Telegdi spin precession. Additionally, the same theory contributes, perhaps unexpectedly, to the understanding of ponderomotive effects in both wave and particle dynamics; e.g., the formalism allows to obtain the ponderomotive Hamiltonian for a Dirac electron interacting with an arbitrarily large electromagnetic laser field with spin effects included.
• Understanding and Predicting Profile Structure and Parametric Scaling of Intrinsic Rotation
Weixing Wang, PPPL , abstract
[#s120, 27 Oct 2016]
This talk reports on a recent advancement in developing physical understanding and a first-principles-based model for predicting intrinsic rotation profiles in magnetic fusion experiments, including ITER. It is shown for the first time that turbulent fluctuation-driven residual stress (a non-diffusive component of momentum flux) can account for both the shape and magnitude of the observed intrinsic toroidal rotation profile. The model predictions of core rotation based on global gyrokinetic simulations agree well with the experimental measurements for a set of DIII-D ECH discharges. The characteristic dependence of residual stress and intrinsic rotation profile structure on the multi-dimensional parametric space covering turbulence type, q-profile structure, collisionality and up-down asymmetry in magnetic geometry has been studied with the goal of developing physics understanding needed for rotation profile control and optimization. Finally, the first-principles-based model is applied to elucidating the ρ∗-scaling and predicting rotations in ITER regime.
• Laser-Driven Magnetized Collisionless Shocks
Derek Schaeffer, Princeton University , abstract
[#s113, 14 Oct 2016]
Collisionless shocks -- supersonic plasma flows in which the interaction length scale is much shorter than the collisional mean free path -- are common phenomena in space and astrophysical systems, including the solar wind, coronal mass ejections, supernovae remnants, and the jets of active galactic nuclei. These systems have been studied for decades, and in many the shocks are believed to efficiently accelerate particles to some of the highest observed energies. Only recently, however, have laser and diagnostic capabilities evolved sufficiently to allow the detailed study in the laboratory of the microphysics of collisionless shocks over a large parameter regime. We present experiments that demonstrate the formation of collisionless shocks utilizing the Phoenix laser laboratory and the LArge Plasma Device (LAPD) at UCLA. We also show recent observations of magnetized collisionless shocks on the Omega EP laser facility that extend the LAPD results to higher laser energy, background magnetic field, and ambient plasma density, and that may be relevant to recent experiments on strongly driven magnetic reconnection. Lastly, we discuss a new experimental regime for shocks with results from high-repetition (1 Hz), volumetric laser-driven measurements on the LAPD. These large parameter scales allow us to probe the formation physics of collisionless shocks over several Alfvenic Mach numbers ($M_A$), from shock precursors (magnetosonic solitons with $M_A<1$) to subcritical ($M_A<3$) and supercritical ($M_A>3$) shocks. The results show that collisionless shocks can be generated using a laser-driven magnetic piston, and agree well with both 2D and 3D hybrid and PIC simulations. Additionally, using radiation-hydrodynamic modeling and measurements from multiple diagnostics, the different shock regimes are characterized with dimensionless formation parameters, allowing us to place disparate experiments in a common and predictive framework.
• Radiation effects on the runaway electron avalanche
Chang Liu, Princeton University , abstract, slides
[#s118, 14 Oct 2016]
Runaway electrons are a critical area of research into tokamak disruptions. A thermal quench on ITER can result in avalanche production of a large amount of runaway electrons and a transfer of the plasma current to be carried by runaway electrons. The potential damage caused by the highly energetic electron beam poses a significant challenge for ITER to achieve its mission. It is therefore extremely important to have a quantitative understanding of the runaway electron avalanche process. It is found that the radiative energy loss and the pitch angle scattering from radiative E&M fields plays an important role in determining the runaway electron distribution in momentum space. In this talk we discuss three kinds of radiation from runaway electrons, synchrotron radiation, Cerenkov radiation, and electron cyclotron emission (ECE) radiation. Synchrotron radiation, which mainly comes from the cyclotron motion of highly relativistic runaway electrons, dominates the energy loss of runaway electrons in the high-energy regime. The Cerenkov radiation from runaway electrons gives an additional correction to the Coulomb logarithm in the collision operator, which changes the avalanche growth rate. The ECE emission mainly comes from electrons in the energy range 1.2<γ<3, and gives an important approach to diagnose the runaway electron distribution in momentum and pitch angle. We developed a novel tool to self-consistently calculate normal mode scattering of runaway electrons using the quasi-linear method, and implement that in the a well-developed runaway electron kinetic simulation code CODE. Using this we successfully reproduce the experimental result of ECE signal qualitatively.
• Plasmoids formation in a laboratory and large-volume flux closure during simulations of Coaxial Helicity Injection in NSTX-U
Fatima Ebrahimi, PPPL and Princeton University , abstract
[#s117, 14 Oct 2016]
In NSTX-U, transient Coaxial Helicity Injection (CHI) is the primary method for current generation without reliance on the solenoid. A CHI discharge is generated by driving current along open field lines (the injector flux) that connect the inner and outer divertor plates on NSTX/NSTX-U, and has generated over 200 kA of toroidal current on closed flux surfaces in NSTX. Extrapolation of the concept to larger devices requires an improved understanding of the physics of flux closure and the governing parameters that maximizes the fraction of injected flux that is converted to useful closed flux. Here, through comprehensive resistive MHD NIMROD simulations conducted for the NSTX and NSTX-U geometries, two new major findings will be reported. First, formation of an elongated Sweet-Parker current sheet and a transition to plasmoid instability has for the first time been demonstrated by realistic global simulations [1]. This is the first observation of plasmoid instability in a laboratory device configuration predicted by realistic MHD simulations and then supported by experimental camera images from NSTX. Second, simulations have now, for the first time, been able to show large fraction conversion of injected open flux to closed flux in the NSTX-U geometry [2]. Consistent with the experiment, simulations also show that reconnection could occur at every stage of the helicity injection phase. The influence of 3D effects, and the parameter range that supports these important new findings is now being studied to understand the impact of toroidal magnetic field and the electron temperature, both of which are projected to increase in larger ST devices.
[1] F. Ebrahimi & R. Raman, Phys. Rev. Lett. 114, 205003 (2015)
[2] F. Ebrahimi & R. Raman, Nucl. Fusion 56, 044002 (2016)
• Generation of helium and oxygen EMIC waves by the bunch distribution of oxygen ions associated with weak fast magnetosonic shocks in the magnetosphere
Lou-Chuang Lee, Academia Sinica, Taiwan , abstract, slides
[#s119, 11 Oct 2016]
Electromagnetic ion cyclotron (EMIC) waves are often observed in the magnetosphere with frequency usually in the proton and helium cyclotron bands and sometimes in the oxygen band. The temperature anisotropy, caused by injection of energetic ions or by compression of magnetosphere, can efficiently generate proton EMIC waves, but not as efficient for helium or oxygen EMIC waves. Here we propose a new generation mechanism for helium and oxygen EMIC waves associated with weak fast magnetosonic shocks, which are observed in the magnetosphere. These shocks can be associated with either dynamic pressure enhancement or shocks in the solar wind and can lead to the formation of a “bunch” distribution in the perpendicular velocity plane of oxygen ions. The oxygen bunch distribution can excite strong helium EMIC waves and weak oxygen and proton waves. The dominant helium EMIC waves are strong in quasi-perpendicular propagation and show harmonics in frequency spectrum of Fourier analysis. The proposed mechanism can explain the generation and some observed properties of helium and oxygen EMIC waves in the magnetosphere.
• Penetration and amplification of resonant perturbations in 3D ideal-MHD equilibria
Stuart Hudson, PPPL , abstract
[#s112, 10 Oct 2016]
The nature of ideal-MHD equilibria in three-dimensional geometry is profoundly affected by resonant surfaces, which beget a non-analytic dependence of the equilibrium on the boundary. Furthermore, non-physical currents arise in equilibria with continuously-nested magnetic surfaces and smooth pressure and rotational-transform profiles. We demonstrate that three-dimensional, ideal-MHD equilibria with nested surfaces and δ-function current densities that produce a discontinuous rotational-transform are well defined and can be computed both perturbatively and using fully-nonlinear equilibrium calculations. The results are of direct practical importance: we predict that resonant magnetic perturbations penetrate past the rational surface (i.e. “shielding” is incomplete, even in purely ideal-MHD) and that the perturbation is amplified by plasma pressure, increasingly so as stability limits are approached.
• Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER
C.S. Chang, PPPL , abstract
[#s115, 10 Oct 2016]
The total-f edge gyrokinetic code XGC1 shows that the divertor heat-flux width $λ_q$ in three US tokamaks (DIII-D for conventional aspect ratio, NSTX for tight aspect ratio, and C-Mod for high BP) obeys the experimentally observed $λ_q\propto 1/B_P^\gamma$ scaling in the so called “sheath-dominant regime.” The low-beta edge plasma is non-thermal and approaches the quasi-steady state in a kinetic non-diffusive time scale. Nonlinear Fokker-Planck-Landau collision operator is used. Monte-Carlo neutral atoms are recycled near the material wall. Successful validation of the XGC1 simulation results on three US tokamak devices will be presented in the so called "sheath-limited" regime. It is found that $λ_q$ on DIII-D, NSTX, and lower-$B_P$ C-Mod is dominated by the neoclassical orbit dynamics of the supra-thermal ions. However, C-Mod at higher $B_P$ shows blob-dominance, while still fitting into the $λ_q\propto 1/B_P^\gamma$ graph. Predictive simulation on ITER shows that $λ_q$ is over 5 times greater than that predicted by the empirical $λ_q\propto 1/B_P^\gamma$ scaling.
• Relativistic Electrons and Magnetic Reconnection in ITER
Allen Boozer, Columbia University , abstract, slides
[#s109, 22 Sep 2016]
ITER, the largest scientific project ever undertaken, “has been designed to prove the feasibility of fusion” energy. That mission could be compromised if the net current in the plasma were transferred to relativistic-electron carriers, which can result in great damage to the device. More than a hundred-fifty papers on the topic have appeared in the twenty years since it was realized that a sudden drop in the plasma temperature could cause such a transfer. The theoretical papers have focused on electron runaway when magnetic field lines remain confined to the plasma volume. Experiments and their simulation imply most magnetic field lines intercept the walls when a sudden drop in the temperature occurs. In simulations not all of the magnetic field lines intercept the walls. If these non-intercepting flux tubes survive until outer magnetic surfaces reform, an especially dangerous situation arises in which the relativistic electrons can be lost in a short pulse along a narrow flux tube.
Maxwell’s equations imply the conservation of magnetic helicity during fast magnetic reconnections. Helicity conservation clarifies features, such as the spike in the plasma current during a thermal quench, and shows that a rapid, ~1ms, acceleration of electrons can occur. Magnetic reconnection can occur on a time scale of tens of Alfvén transit times either due to the formation of multiple plasmoids or as a result of the exponential sensitivity to non-ideal effects when an ideal evolution causes neighboring magnetic field lines to increase their separation exponentially with distance along the lines. In either case, magnetic flux tubes that had different force-free parallel currents $j_{\parallel}/B$ and different poloidal magnetic fluxes external to their surfaces can be joined in a fast reconnection. The differing parallel currents relax by Alfvén waves, and the change in the poloidal flux associated with a given enclosed toroidal magnetic flux is given by helicity conservation. Based on the observed time scale of current spikes, a few hundred toroidal transits are required to relax the $j_{\parallel}/B$ profile, which is consistent with distance along magnetic field lines implied by the speed of the electron temperature drop. Helicity conservation implies that although changes in the poloidal flux can occur on a time scale determined by the Alfvén transit time, the magnetic helicity and most of the poloidal flux can change only on a long resistive, $L/\mathcal{R}$, time scale. Rapid plasma terminations require plasma cooling.
The potential for damage, the magnitude of the extrapolation from existing devices, and the importance of the atypical—incidents that occur once in a thousand shots—make theory and simulation essential for ensuring that relativistic runaway electrons will not prevent ITER from achieving its mission. The U.S. DoE Office of Science has established a Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM) with a two-year funding of 3.9M$\$$. The danger of runaway of electrons to relativistic energies can be avoided in magnetically confined fusion systems by making the net current the$j_{\parallel}/B$sufficiently small. This is possible in the non-axisymmetric stellarator geometry though not in axisymmetric tokamaks, such as ITER. • Variational current-coupling gyrokinetic-MHD Josh Burby, Courant Institute, New York University , abstract, slides [#s105, 07 Sep 2016] In this talk I will describe the details and derivation of a new current-coupling gyrokinetic-MHD model. In particular, I will show that the model can be derived from a variational principle. Energy, and hot charge are conserved exactly regardless of the form of the background magnetic field. Likewise, when the background field admits a continuous rotation or translation symmetry, the corresponding component of the total momentum is conserved. The theory relies on a new gauge-invariant formulation of the motion of gyrocenters in prescribed electromagnetic fields, and this will be described in detail. • Implicit Multiscale Full Kinetics as an Alternative to Gyrokinetics Scott E. Parker, University of Colorado , abstract [#s103, 30 Aug 2016] Recent progress has been made developing full kinetic Lorentz force ion dynamics using implicit multiscale techniques [1]. It is now possible to capture low-frequency physics along with finite Larmor radius (FLR) effects with a fully kinetic multiscale$\delta f$particle simulation. The utility of such a model is to be able to verify gyrokinetics in situations where the smallness of the ordering parameters is questionable. Additionally, such a model can help identify what higher order terms in gyrokinetics might be important. Orbit averaging and sub-cycling are utilized with an implicit particle time advance based on variational principles. This produces stable and accurate ion trajectories on long time scales. Excellent agreement with the gyrokinetic dispersion relation is obtained including full FLR effects. Ion Bernstein waves and the compressional Alfvén wave are easily suppressed with the implicit time advance. We have developed a global toroidal electrostatic adiabatic electron Lorentz ion code. We will report preliminary linear results benchmarking Lorentz ions with gyrokinetics for the Cyclone base case. We will begin by reviewing recent results from the GEM code simulating electromagnetic gyrokinetic turbulence in the edge pedestal where the timestep required is comparable to the ion cyclotron period. [1] Benjamin J. Sturdevant, Scott E. Parker et al., J. Comput. Phys. 316, 519 (2016) • Current status of the LHD and the prospect for Deuterium experiment Dr. Masaki Osakabe, National Institute for Fusion Science, Japan [#s106, 26 Aug 2016] • Dissipation and Intermittency in Gyrokinetic Turbulence and Beyond Jason TenBarge, University of Maryland , abstract, slides [#s102, 25 Aug 2016] Turbulence is a ubiquitous process in space and astrophysical plasmas that serves to mediate the transfer of large-scale motions to small scales at which the turbulence can be dissipated and the plasma heated. In situ solar wind observations and direct numerical simulations demonstrate that sub-proton scale turbulence is dominated by highly anisotropic and intermittent, low frequency, kinetic Alfvénic fluctuations. I will review recent work on the dissipation of Alfvénic turbulence observed in gyrokinetic simulations and discuss the coherent structures and intermittency associated with the turbulence, which suggest a non-local and non-self-similar energy cascade. Moving beyond the confines of gyrokinetics, I will also briefly discuss work on a full Eulerian Vlasov-Maxwell code, Gkeyll, being developed at Princeton and the University of Maryland. • Effective resistivity in collisionless magnetic reconnection Zhi-Wei Ma, Zhejiang University, China , abstract [#s80, 18 Aug 2016] The well-known, physical mechanism for fast, magnetic reconnection in collisionless plasmas is that the off-diagonal terms of the electron-pressure tensor give rise to a larger electric-fields in the reconnection region. The electron-pressure tensor fully associated with electron kinetic effects is difficultly implemented into the MHD model. In this talk, we try to use a simple equation$E = \eta J$(where$\eta$is an effective resistivity) to illustrate the fast reconnection in collisionless, magnetic reconnection. The physical mechanism and formulation of the effective resistivity are addressed. • Turbulence in shear MHD flows: Implications for accretion disks Farrukh Nauman, Niels Bohr International Academy, Copenhagen , abstract, slides [#s63, 04 Aug 2016] Accretion flows are found in a large variety of astrophysical systems, from protoplanetary disks to active galactic nuclei. Our present understanding of such flows is severely limited by both observational and numerical resolution. I will discuss some new numerical results on zero magnetic flux shear MHD turbulence and its relation to the magnetic Prandtl number. I will then briefly discuss the effects of rotation on large scale magnetic fields. My talk will end with some speculations about how one might construct a self-consistent model for accretion flows based on our current understanding. • Dynamics of the ELMs in pre-crash and crash suppressed period in KSTAR Hyeon Park, NFRI/UNIST, Korea , abstract, slides [#s77, 28 Jul 2016] Following the first operation of H-mode in KSTAR in 2009, study of the edge localized modes (ELM) has been actively conducted. A unique in-vessel control coil (IVCC) set (top, middle and bottom) capable of generating resonant (and non-resonant) magnetic perturbation (RMP) at low n(=1,2) number was successfully utilized to suppress and/or mitigate the ELM-crash in KSTAR. Extensive study of dynamics of the ELMs in both pre-crash and crash suppressed phase under magnetic perturbation with the 2D/3D Electron Cyclotron Emission Imaging (ECEI) system revealed new phenomenology of the ELMs and ELM-crash dynamics that were not available from conventional diagnostics. Since the first 2D images of the ELM time evolution from growth to crash through saturation, the detailed images of the ELMs leading to the crash together with the fast RF emission (<200MHz) signal demonstrated that the pre-crash events are complex. The measured 2D image of the ELM was validated by direct comparison with the synthetic 2D image by the BOUT++ code and non-linear modelling study is in progress. Recently, the observed dynamics of the ELMs at both high and low field sides such as asymmetries in intensity, mode number and rotation direction casted a doubt in peeling-ballooning mode. Response of high field side ELM to the RMP was more pronounced compared to that of the low field side. Other study includes observation of multi-modes and sudden mode number transition. During the ELM-crash suppression experiment, various types of ELM-crash patterns were observed and often the suppression was marginal. The observed semi-coherent turbulence spectra under the RMP provided an evidence of non-linear interaction between the ELMs and turbulence. • Statistical origin and properties of kappa distributions George Livadiotis, Southwest Research Institute , abstract, slides [#s62, 07 Jul 2016] Classical particle systems reside at thermal equilibrium with their velocity distribution function stabilized into a Maxwell distribution. On the contrary, collisionless and correlated particle systems, such as space and astrophysical plasmas, are characterized by a non-Maxwellian behavior, typically described by so-called$\kappa$distributions, or combinations thereof. Empirical$\kappa$distributions have become increasingly widespread across space and plasma physics. A breakthrough in the field came with the connection of$\kappa$distributions to non-extensive statistical mechanics. Understanding the statistical origin of$\kappa$distributions was the cornerstone of further theoretical developments and applications, some of which will be presented in this talk: (i) The physical meaning of thermal parameters, e.g., temperature and kappa index; (ii) the multi-particle description of$\kappa$distributions; (iii) the generalization to phase-space$\kappa$distribution of a Hamiltonian with non-zero potential; (iv) the Sackur-Tetrode entropy for$\kappa$distributions, and (v) the existence of a large-scale phase-space cell, characteristic of collisionless space plasmas, indicating a new quantization constant,$\hbar ^* \sim 10^{-22} Js$. • Explosive Solution of a Time Delayed Nonlinear Cubic Equation Derived for Fluids (Hickernell) and Plasmas (Berk-Breizman) Herb Berk, Institute for Fusion Studies, U. Texas at Austin, abstract, slides [#s61, 27 Jun 2016] This presentation will describe new explosive attractor solutions to the universal cubic delay equation found in both the fluid [1] and (for a kinetic system) in the plasma literature [2]. The cubic delay equation describes a system governed by a control parameter$\phi$(in plasmas its value is determined by the linear properties of the kinetic response). The simulation of the temporal evolution reveals the development of an explosive mode, i.e. a mode growing without bound in a finite time. The two main features of the response are: (1) a well-known explosive envelope$(t_0-t)^{-5/2}$, with$t_0$the blow-up time of the amplitude; (2) a spectrum with ever-increasing oscillation frequencies whose values depend on the parameter$\phi$. Analytic modeling explains the results and quantitatively nearly replicates the attractor solutions found in the simulations. These analytic attractor solutions are linearly stable except in some cases where the nonlinear solution needs to be corrected to include higher harmonics. Our analysis explains almost all of the rather complicated numerical attractor solutions for the cubic delay equation. [1] F.J. Hickernell, J. Fluid Mech. 142, 431 (1984) [2] B.N. Breizman, H.L. Berk et al., Phys. Plasmas 4, 1559 (1997) • Physics of tokamak flow relaxation to equilibrium Bruce Scott, Max-Planck-IPP, EURATOM Association, abstract [#s59, 23 Jun 2016] The theorem for toroidal angular momentum conservation within gyrokinetic field theory is used as a starting point for consideration of flow equilibration at low frequencies (less than fast-Alfvén or gyrofrequencies). Quasineutrality and perpendicular MHD force balance are inputs to the theory and therefore never violated. However, the gyrocenter densities are not ambipolar in equilibrium, since the flow vorticity is given by their difference. From an arbitrary initial state, flows evolve acoustically and via Landau damping into divergence balance, in which radial force balance of the electric field is a part. On collisional time scales, which in the tokamak core are longer, the neoclassical electric field is brought into balance by collisions, and it is only on these slow time scales that the collisional transport is ambipolar (ie, the time derivative of the vorticity is small). Computations from 2014 showing the relaxation on tokamak core spatial scales are displayed. I will also give relevant cases of edge-layer relaxation and discuss the dependence on the finite poloidal gyroradius. Total-$f$two-species gyrokinetic relaxation cases from 2009/10 are available to show that the basic processes in fluid and gyrokinetic models are the same for these purposes. • Equilibrium Potential Well due to Finite Larmor Radius Effects at the Tokamak Edge W. W. Lee, PPPL , abstract, slides [#s49, 16 Jun 2016] We present a novel mechanism for producing the 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,$E_r$, as observed at the edge of many tokamak experiments. We will show that this theoretically predicted$E_r$field, which can be regarded as producing a long radial wave length zonal flow, agrees well with recent experimental measurements. The work is in collaboration with R. B. White [1]. [1] W.W. Lee & R.B. White, PPPL Report 5254 (2016) • Predicting solar magnetic activity and its implications for global dynamo models Nishant Kumar Singh, KTH Royal Institute of Technology, abstract, slides [#s51, 09 Jun 2016] Using the solar surface mode, i.e. the$f$-mode, we attempt to predict the emergence of active regions (ARs) in the days before they can be seen in magnetograms. Our study is motivated by earlier numerical findings of Singh et al. [1], who showed that, in the presence of a nonuniform magnetic field which is concentrated a few scale heights below the surface, the$f$-mode fans out in the diagnostic$k$-$\omega$diagram at high wavenumbers. Here we exploit this property using data from the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory, and show for about six ARs that at large latitudinal wavenumbers (corresponding to horizontal scales of around 3000 km), the$f$-mode displays strengthening about two days prior to AR formation and thus provides a new precursor for AR formation. I will also discuss ways to isolate signals from newly forming ARs in a crowded environment where existing ones are expected to pollute the neighbouring patches. The idea that the$f$-mode is perturbed days before any visible magnetic activity occurs on the surface can be important in constraining dynamo models aiming at understanding the global magnetic activity of the Sun. [1] Nishant K. Singh, Harsha Raichur & Axel Brandenburg, arxiv.org/abs/1601.00629 (2014) • Statistical analysis of turbulent transport for flux driven toroidal plasmas Johan Anderson, Chalmers University of Technology, abstract, slides [#s26, 07 Jun 2016] During recent years an overwhelming body of evidence shows that the overall transport of heat and particles is, to a large part, caused by intermittency (or bursty events) related to coherent structures. A crucial question in plasma confinement is thus the prediction of the probability distribution functions (PDFs) of the transport due to these structures and of their formation. This work provides a theoretical interpretation of numerically generated PDFs of intermittent plasma transport events, as well as offering an explanation for elevated PDF tails of heat flux. Specifically, we analyse time traces of heat flux generated by global nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence by the GKNET software [1]. The simulation framework is global, flux-driven and considers adiabatic electrons. In the simulations, SOC type intermittent bursts are frequently observed and transport is often regulated by non-diffusive processes, thus the PDFs of e.g. heat flux are in general non-Gaussian with enhanced tails. A key finding of this study is that the intermittent process in the context of drift-wave turbulence appears to be independent of the specific modelling framework, opening the way to the prediction of its salient features. Although the same PDFs were previously found in local gyrokinetic simulations [2], there are some unique features present inherently coming from the global nature of the physics. The main part of this work consists in providing a theoretical interpretation of the PDFs of radial heat flux. The numerically generated time traces are processed with Box–Jenkins modelling in order to remove deterministic autocorrelations, thus retaining their stochastic parts only. These PDFs have been shown to agree very well with analytical predictions based on a fluid model, on applying the instanton method. In this talk, the theory and comparisons to the numerical work will be presented. The result points to a universality in the modelling of the intermittently stochastic process while the analytical theory offers predictive capability, extending the previous result to be globally applicable. [1] K. Imadera et al., 25th FEC, TH/P5-8 (2014) [2] Johan Anderson & Pavlos Xanthopoulos, Phys. Plasmas 17, 110702 (2010) • Parasitic Momentum Flux in the Tokamak Core Tim Stoltzfus-Dueck, PPPL, abstract, slides [#s50, 06 Jun 2016] A higher-order portion of the${\bf E}\times {\bf B}drift causes an outward flux of co-current momentum when electrostatic potential energy is transferred to ion-parallel flows. The robust 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 there are adequate fluctuations at low enough frequencies to excite ion parallel flows, which may explain some experimental observations related to rotation reversals • Experimental study of the role of electron pressure in fast magnetic reconnection with a guide field Will Fox, PPPL , abstract [#s25, 03 Jun 2016] Magnetic reconnection, the change of magnetic topology in the presence of plasma, is observed in space, laboratory, and enables the explosive energy release by plasma instabilities, as in solar flares or magnetospheric substorms, and the change in topology allows the rapid heat transport associated with sawtooth relaxation and self-organization in RFPs. In numerous environments, especially in toroidal confinement devices, reconnection proceeds in the presence of a net guide field. We report detailed laboratory observations in MRX of the structure of reconnection current sheets with a guide field regime in a two-fluid plasma regime (ion gyro-radius comparable to the current sheet width) . We observe experimentally for the first time the quadrupolar electron pressure variation in the ion-diffusion region, an analogue of the quadrupolar "Hall" magnetic fields in anti-parallel reconnection. The quadrupolar pressure perturbation was originally predicted by extended MHD simulation as essential to balancing the large parallel reconnection electric fields over the ion-scale current-sheet We observe that electron density variations dominate temperature variations and may provide a new diagnostic of reconnection with finite guide field for fusion experiments and spacecraft missions. We discuss consequences for force balance in the reconnection layer and implications for fast reconnection in fusion devices. • 2D Full-wave simulations of plasma waves in space and tokamak plasmas Eun-Hwa Kim, PPPL, abstract, slides [#s12, 28 Apr 2016] A 2D full-wave simulation code (so-called FW2D) has been recently developed. This code currently solves the cold plasma wave equations using the finite element method. One advantage of using the finite element method is that the local basis functions can be readily adapted to boundary shapes and can be packed in such a way as to provide higher resolution in regions where needed. We have constructed a 2D triangular mesh given a specified boundary and a target mesh density function. Moreover, the density of the mesh can be specified based on the expected wavelength obtained from solution of the local dispersion (except close to resonances) so that the most efficient resolution is used. Another advantage of this wave code is short running time. For instance, by using node number of 24,395, the computing time is approximately 300 seconds CPU time to obtain a solution. The wave code has been successfully applied to describe low frequency waves in Earth and Mercury's multi-ion magnetospheres. The results include (a) mode conversion from the incoming fast to the transverse wave modes at the ion-ion hybrid resonance, (b) mode coupling and polarization reversal between left-handed (i.e., electromagnetic ion cyclotron waves: EMIC waves) and right-handed polarized waves (i.e., fast mode), and (c) refraction and reflection of field-aligned propagating EMIC waves near the heavier ion cyclotron frequency. Very recently FW2D code has been improved to adopt tokamak geometry and examine radio frequency (RF) waves in the scape-off layer (SOL) of tokamaks, which is the region of the plasma between last closed flux surface and tokamak vessel. The SOL region is important for RF wave heating of tokamaks because significant wave power loss can occur in this region. This code is ideal for waves in SOL plasma, because realistic boundary shapes and arbitrary density structures can be easily adopted in the code and the SOL plasma can be approximated as cold plasma. • Parallel electron force balance and the L-H transition Tim Stoltzfus-Dueck, Princeton University, abstract, slides [#s13, 14 Apr 2016] In a popular description of the L-H transition, energy transfer to the mean flows directly depletes kinetic energy from turbulent fluctuations, resulting in suppression of the turbulence and a corresponding transport bifurcation. However, electron parallel force balance couples non-zonal velocity fluctuations with electron pressure fluctuations on rapid timescales, comparable with the electron transit time. For this reason, energy in the non-zonal velocity stays in a fairly fixed ratio to electron thermal free energy, at least for frequency scales much slower than electron transit. In order for direct depletion of the energy in turbulent fluctuations to cause the L-H transition, energy transfer via Reynolds stress must therefore drain enough energy to significantly reduce the sum of the free energy in non-zonal velocities and electron pressure fluctuations. At lowk, the electron thermal free energy is much larger than the energy in non-zonal velocities, posing a stark challenge for this model of the L-H transition. • Realistic characterizations of chirping instabilities in tokamaks Vinícius Duarte, PPPL, abstract, slides [#s14, 31 Mar 2016] In tokamak plasmas, the dynamics of phase-space structures with their associated frequency chirping is a topic of major interest in connection with mechanisms for fast ion losses. The onset of phase-space holes and clumps which produce chirping phenomena has been theoretically shown to be related to the emergence of an explosive solution of an integro-differential, nonlocal cubic equation [1,2] that governs the early mode amplitude evolution in the nonlinear regime near marginal stability. We have extended the analysis of the model to quantitatively account for multiple resonance surfaces of a given mode in the presence of drag and diffusion (due to collisions and micro-turbulence) operators. Then a more realistic criterion is found that takes into account the details of the mode structure and the variation of transport coefficients in phase space, to determine whether steady-state solutions can or cannot exist. Stable, steady-state solutions indicate that chirping oscillations do not arise, while the lack of steady solutions due to the predominance of drag is indicative that a frequency chirping response is likely in a plasma. Waves measured in experiments have been analyzed using the NOVA and NOVA-K codes, with which we can realistically account for the mode structure and varying resonance responses spread over phase space. In the experiments presently analyzed, compatibility has been found between the theoretical predictions for whether chirping should or should not arise and the experimental observation or lack of observation of toroidicity-induced Alfvén eigenmodes in NSTX, DIII-D and TFTR. We have found that stochastic diffusion due to wave micro-turbulence is the dominant energetic particle transport mechanism in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise. [1] H.L. Berk, B.N. Breizman & M. Pekker, Phys. Rev. Lett. 76, 1256 (1996) [2] M.K. Lilley, B.N. Breizman & S.E. Sharapov, Phys. Rev. Lett. 102, 195003 (2009) • Speed-Limited Particle-in-Cell (SLPIC) Method John R. Cary, U. Colorado, Boulder, abstract, slides [#s15, 25 Mar 2016] The Speed-Limited Particle-In-Cell (SLPIC) Method reduces computational requirements for simulations that evolve on ion time scales while keeping appropriate kinetic electron effects. This method works by introducing an ansatz for the distribution function that allows the new unknown phase-space function to be solved by the method of characteristics, where those characteristics move slowly through phase space. Therefore, the solution can be obtained by particle-in-cell (PIC) methods, where the electrons have speeds much smaller than their actual speeds, ultimately leading to a much relaxed numerical (CFL) stability condition on the time step. Ultimately, the time step can be increased by the square root of the ion-electron mass ratio. SLPIC can be easily implemented in existing PIC codes as it requires no changes to deposition and field solution. Its explicit nature makes it ideal for modern computing architectures with vector instruction sets. • Free-Boundary Axisymmetric Plasma Equilibria: Computational Methods and Applications Holger Heumann, INRIA, France, abstract, slides [#s16, 03 Mar 2016] We present a comprehensive survey of the various computational methods for finding axisymmetric plasma equilibria. Our focus is on free-boundary plasma equilibria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a Newton-type method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we discuss as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate performance and application areas. • Mixed finite-element/finite difference method for toroidal field-aligned elliptic electromagnetic equations Salomon Janhunen, PPPL, abstract [#s17, 29 Feb 2016] Gyrokinetic simulations -- such as those performed by the XGC code -- provide a self-consistent framework to investigate a wide range of physics in strongly magnetized high temperature laboratory plasmas, global modes usually considered to be in the realm of MHD simulations. However, the present simulation models generally concentrate on short wavelength electro-magnetic modes mostly to convenience the field solver performance. To incorporate more global fluid-like modes, also non-zonal long wavelength physics needs to be retained. In this work we present development of a fully 3D mixed FEM/FDM electro-magnetic field solver for use in the gyrokinetic code XGC1. We present optimization for use on massively parallel computational platforms, investigation of numerical accuracy characteristics using the method of manufactured solutions, and evaluate importance of field line length calculations on the stability of the discretization. We also invite discussion on the importance of the perpendicular vector potential for pressure driven modes. • Gyrokinetic Particle Simulation of Fast Electron Driven Beta-induced Alfvén Eigenmodes Wenlu Zhang, Chinese Academy of Science & U.C. Irvine, abstract [#s18, 25 Feb 2016] The fast electron driven beta induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electrons are described by the drift kinetic model. The phase space structure shows that only the processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels such as transit, drift-bounce, and processional resonance. Frequency chirping is observed in nonlinear simulations with both weak and strong drives in the absence of sources and sinks, which provide a complement to the standard bump-on-tail paradigm for the frequency chirping of Alfvén eigenmodes. For weakly nonlinear driven case, frequency is observed to be in phase with the particle energy flux, and mode structure is almost the same as linear stage. While in the strongly driven nonlinear case, BAAE is excited along with BAE after the BAE mode saturated. Analysis of nonlinear wave-particle interactions show that the frequency chirping is induced by the nonlinear evolution of the coherent structures in the energetic-particle phase space, where the dynamics of the coherent structure is controlled by the formation and destruction of phrase space islands of energetic particles in the canonical variables. Zonal flow and zonal field are found to affect wave-particle resonance in the nonlinear e-BAE simulations. • Theory for Transport Properties of Warm Dense Matter Scott Baalrud, University of Iowa, abstract, slides [#s5, 18 Feb 2016] Progress in a number of research frontiers relies upon an accurate description of the transport coefficients of warm and hot dense matter, characterized by densities near those of solids and temperatures ranging from several to hundreds of eV. Examples include inertial confinement fusion, evolution of giant planets, exoplanets, and other compact astrophysical objects such as white dwarf stars, as well as numerous high energy density laboratory experiments. These conditions are too dense for standard plasma theories to apply and too hot for condensed matter theories to apply. The challenge is to account for the combined effects of strong Coulomb coupling of ions and quantum degeneracy of electrons. This seminar will discuss the first theory to provide fast and accurate predictions of ionic transport coefficients in this regime. The approach combines two recent developments. One is the effective potential theory (EPT), which is a physically motivated approach to extend plasma kinetic theory into the strong coupling regime. The second is a new average atom model, which provides accurate radial density distributions at high-density conditions, accounting for effects such as pressure ionization. Results are compared with state-of-the-art orbital-free density functional theory computations, revealing that the theory is accurate from high temperature through the warm dense matter regime, breaking down when the system exhibits liquid-like behaviors. A number of properties are considered, including diffusion, viscosity and thermal conductivity. • Nonlinear Fishbone Dynamics in Spherical Tokamaks with Toroidal Rotation Feng Wang, PPPL, abstract, slides [#s19, 11 Feb 2016] Fishbone is one of the most important energetic particles driven modes in tokamaks. A numerical study of the nonlinear dynamics of fishbone has been carried out in this work. Realistic parameters with finite toroidal plasma rotation are used to understand nonlinear frequency chirping in NSTX. We have carried out a systematic study of nonlinear frequency chirping and energetic particle dynamics. It is found that, linearly, the mode is driven by both trapped particles and passing particles, with resonance condition\omega_{d} \simeq \omega$for trapped particles and$\omega_{\phi}+\omega_{\theta}\simeq\omega$for passing particles, where$\omega_{d}$is trapped particle toroidal precession frequency, and$\omega_{\phi}$,$\omega_{\theta}$are passing particle transit frequency in toroidal and poloidal direction. As the mode growing, trapped resonant particles oscillate and move outward radially, which reduces particle precessional frequency. We believe this is the main reason for the mode frequency chirping down. Finally, as the mode frequency chirping down, initially non-resonant particles with lower precessional frequencies become resonant particles in the nonlinear regime. This effect can sustain a quasi-steady state mode amplitude observed in the simulation. • Generation of anomalously energetic suprathermal electrons due to collisionless interaction of an electron beam with a nonuniform plasma Igor Kaganovich, PPPL, abstract, slides [#s4, 04 Feb 2016] Electrons emitted by electrodes surrounding or immersed in the plasma are accelerated by the sheath electric field and become the electron beams penetrating the plasma. Recently, it was reported that an electron energy distribution measured in a dc-rf discharge with 800V dc voltage has not only a peak at 800eV corresponding to the electrons emitted from the dc-biased electrode, but also a significant fraction of accelerated electrons with energy up to several hundred eV. The particle-in-cell simulation results show that the acceleration may be caused by the effects related to the plasma nonuniformity. The electron beam excites plasma waves whose wavelength and phase speed gradually decrease towards anode. The short waves near the anode accelerate plasma bulk electrons to suprathermal energies because of multiple interactions of electron with wave region [1]. The two-stream instability of an electron beam propagating in finite-size plasma placed between two electrodes was also studied analytically. It is shown that the growth rate in such a system is much smaller than that of infinite plasma or finite size plasma with periodic boundary conditions. We show that even if width of the plasma matches the resonance condition for standing waves; standing waves do not develop and transform into spatially growing wave, whose growth rate is small compared to that of the standing wave in a system with periodic boundary conditions. The frequency and growth rate as a function of plasma width form a bandwidth structure [2]. [1] D. Sydorenko, I.D. Kaganovich et al., "Generation of anomalously energetic suprathermal electrons by an electron beam interacting with a nonuniform plasma", arXiv:1503.05048 (2015) [2] I.D. Kaganovich & D.Sydorenko, "Band Structure of the Growth Rate of the Two-Stream Instability of an Electron Beam Propagating in a Bounded Plasma" arXiv:1503.04695 (2015). • Nonlinear Alfvén waves in generalized magnetohydrodynamics - a creation on Casimir leaves Hamdi M. Abdelhamid, University of Tokyo, abstract [#s3, 03 Feb 2016] Alfvén waves are the most typical electromagnetic phenomena in magnetized plasma. In particular, nonlinear Alfvén waves deeply affect various plasma regimes in laboratory as well as in space, which have a crucial role in plasma heating, turbulence, etc. Large-amplitude Alfvén waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfvén wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. Here we investigate the underlying mechanism invoking a more accurate framework, generalized MHD. When we take into account dispersion effects (we consider both ion and electron inertial effects), the wave forms are no longer arbitrary. Interestingly, these "small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat different from that of solitons. The Casimir invariants of the system is the root cause of this interesting property. • Runaway Mitigation Issues on ITER Allen Boozer, Columbia University, abstract, slides [#s2, 25 Jan 2016] The plasma current in ITER can be transferred from near thermal to relativistic electrons by the runaway phenomenon. If such a current of relativistic electrons were to strike the chamber walls in ITER, the machine could be out of commission for many months. For ITER to be operable as a research device, the shortest credible time between such events must be years. The physics of the runaway process is remarkably simple and clear. The major uncertainty is what range of plasma conditions may arise in post thermal quench ITER plasmas. Consequently, a focused effort that includes theory, experiments, and engineering could relatively quickly clarify whether ITER will be operable with the envisioned mitigation strategy and what mitigation strategies could enhance the credibility that ITER will be operable. • Non-twist map bifurcation of drift-lines and drift-island formation in saturated 3D MHD equilibria David Pfefferlé, PPPL, abstract [#s1, 21 Jan 2016] Based on non-canonical perturbation theory of the field-line action [1], guiding-centre drift equations are identified as perturbed magnetic field-line equations. In this context, passing-particle orbits are called drift-lines, and their topology is completely determined by the magnetic configuration. In axisymmetric tokamak fields, drift-lines lie on shifted flux-surfaces, i.e. drift-surfaces, the shift being proportional at lowest order to the parallel gyro-radius and the q-profile [2]. Field-lines as well as drift-lines produce island structures at rational surfaces [3] only when a non-axisymmetric magnetic component is added. The picture is different in the case of 3D saturated MHD equilibrium like the helical core associated with a non-resonant internal kink mode. In assuming nested flux-surfaces, such bifurcated states, expected for a reversed q-profile with qmin close yet above unity [4] and conveniently obtained in VMEC [5], feature integrable field-lines. The helical drift-lines however become resonant with the axisymmetric component in the region of qmin and spontaneously generate drift-islands. Due to the locally reversed sheared q-profile, the drift-island structure follows the bifurcation/reconnection mechanism found in non-twist maps [6, 7]. This result provides a theoretical interpretation of NBI fast ion helical hot-spots in Long-Lived Modes [8] as well as snake-like impurity density accumulation in internal MHD activity [9]. [1] John R. Cary & Robert G. Littlejohn, Ann. Physics 151, 1 (1983) [2] Machiel de Rover, Niek J. Lopes Cardozo & Attila Montvai, Phys. Plasmas 3, 4478 (1996) [3] M. Brambilla & A.J. Lichtenberg, Nucl. Fusion 13, 517 (1973) [4] F.L. Waelbroeck, Phys. Fluids B 1, 499 (1989) [5] W.A. Cooper, J.P. Graves et al., Phys. Rev. Lett. 105, 035003 (2010) [6] P.J. Morrison, Phys. Plasmas 7, 2279 (2000) [7] R. Balescu, Phys. Rev. E 58, 3781 (1998) [8] D. Pfefferlé, J.P. Graves et al., Nucl. Fusion 54, 064020 (2014) [9] L. Delgado-Aparicio, L. Sugiyama et al., Phys. Rev. Lett. 110, 065006 (2013) • Nonlinear quantum electrodynamics in strong laser fields: From basic concepts to electron-positron photoproduction Sebastian Meuren, Max-Planck-Institut für Kernphysik, Germany, abstract, slides [#s20, 14 Jan 2016] Since the work of Sauter in 1931 it is known that quantum electrodynamics (QED) exhibits a so-called "critical" electromagnetic field scale, at which the quantum interaction between photons and macroscopic electromagnetic fields becomes nonlinear. One prominent example is the importance of light-light interactions in vacuum at this scale, which violates the superposition principle of classical electrodynamics. Furthermore, an electromagnetic field becomes unstable in this regime, as electron-positron pairs can be spontaneously created from the vacuum at the expenses of electromagnetic-field energy (Schwinger mechanism). Unfortunately, the QED critical field scale is so high that experimental investigations are challenging. One promising pathway to explore QED in the nonlinear domain with existing technology consists in the combination of modern (multi) petawatt optical laser systems with highly energetic particles. The suitability of this approach was first demonstrated in the mid-1990s at the seminal SLAC E-144 experiment. Since then, laser technology continuously developed, implying the dawn of a new era of strong-field QED experiments. For instance, the basic processes nonlinear Compton scattering and Breit-Wheeler pair production are expected to influence laser-matter interactions and in particular plasma physics at soon available laser intensities. Therefore, a considerable effort is being undertaken to include these processes into particle-in-cell (PIC) codes used for numerical simulations. In the first part of the talk the most prominent nonlinear QED phenomena are presented and discussed on a qualitative level. Afterwards, the mathematical formalism needed for calculations with strong plane-wave background fields is introduced with an emphasize on fundamental concepts. Finally, the nonlinear Breit-Wheeler process is considered more in depth. In particular, the semiclassical approximation is elaborated, which serves as a starting point for the implementation of quantum processes into PIC codes. • Attempting a Theoretical Framework for High Energy Density Matter Swadesh Mahajan, U. Texas, Austin, abstract, slides [#s21, 08 Jan 2016] Two distinct approaches to construct a theoretical framework for fully relativistic high energy density (HED) systems- in particular, an assembly of particles in the field of an electromagnetic (EM) wave of arbitrary magnitude- are explored: 1) The Statistical-Mechanical model for the HED matter is built through the following steps: First, the eigenvalue problem for a quantum relativistic particle immersed in an arbitrary strength EM field is solved; the resulting energy eigenvalue (dependent on$A$,$\omega$and$k$) is invoked to define the appropriate Boltzmann factor for constructing expressions for physical variables for a weakly interacting system of these field-dressed particles. The fluid equations are the conservation laws, 2) In the second approach, an equivalent nonlinear quantum mechanics is constructed to represent a hot fluid with and without internal degrees of freedom (like spin). Representative initial results are displayed and discussed. Some notable results are: 1) fundamental changes in the particle energy momentum relationship, 2) The EM wave induces anisotropy in the energy momentum tensor, 3) the EM wave splits the spin-degenerate states, 4) the propagation characteristics of the EM wave are modified by thermal and field effects causing differential self-induced transparency, 5) Particle trapping and pushing'' by the high amplitude EM wave. Attempts will be made to highlight testable predictions. • The electrostatic response to edge islands induced by Resonant Magnetic Perturbations Gianluca Spizzo, Consorzio RFX, Italy, abstract, slides [#s22, 03 Dec 2015] Measurements of plasma potential have been experimentally determined in great detail in the edge of the RFX reversed-field pinch (RFP) [1], and of the TEXTOR tokamak, with applied magnetic perturbations (MP's) [2]. Generally speaking, the potential has the form$\Phi(r,t,z) = \Phi_0 \sin u$, with$u\$ the helical angle: this fact implies a strong correlation between the magnetic field topology and the poloidal/toroidal modulation of the measured plasma potential. In a chaotic tokamak edge, the ion and electron drifts yield a predominantly electron driven radial diffusion when approaching the island X-point, while ion diffusivities are generally an order of magnitude smaller. In the RFP the picture is more complicated, since X-points can act both as drivers of electron diffusion, or dynamical traps (reduced electron diffusion), depending on the helicity of the dominant island [3]. In both devices, this differential electron-to-ion diffusion, causes a strong radial electric field structure pointing outward (inward) from the island O-point. An analytical model for the plasma potential is implemented in the code Orbit [4], and analyses of the ambipolar flow shows that both ion- and electron-dominated transport regimes can exist, which are known as ion and electron roots in stellarators. Moreover, the good agreement found between measured and modeled plasma potential supports that a magnetic island in the plasma edge can act as convective cell. These findings and comparison with stellarator literature, suggests that the role of magnetic islands as convective cells and hence as major radial particle transport drivers could be a generic mechanism in 3D plasma boundary layers.
[1] P. Scarin, N. Vianello et al., Nucl. Fusion 51, 073002 (2011)
[1] N. Vianello, C. Rea et al., Plasma Phys. Control. F. 57, 014027 (2015)
[2] G. Ciaccio, O. Schmitz et al., Phys. Plasmas 22, 102516 (2015)
[3] G. Spizzo, N. Vianello et al., Phys. Plasmas 21, 056102 (2014)
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