PPPL

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.)

Past

  • The shearing modes approach to the theory of plasma shear flow
    Vladimir Mikhailenko - Pusan National University, Busan, South Korea , abstract
    [#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
    Botsz Huang, The Graduate University for Advanced Studies, Japan, abstract
    [#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
    [#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 low $k$, 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)
    [4] R.B. White & M.S. Chance, Phys. Fluids 27, 2455 (1984)