High-temperature superconducting (HTS) magnets and other advances have led to renewed interest in magnetic mirrors for fusion energy. The non-Maxwellian nature of mirror plasmas necessitates kinetic modeling to predict, optimize and design mirrors. Explicit gyrokinetic full-f codes can be used to study instabilities and turbulent transport in tokamaks and mirrors, but they have been prohibitively expensive to integrate directly over the very long time scales required to compute kinetic plasma equilibrium. We demonstrate that these studies are now feasible thanks to novel multiscale methods delivering a 30,000X speed-up. The resulting kinetic equilibrium, electrostatic potential, and ion confinement time are consistent with analytic theory. This transformative capability opens the door to a new way of obtaining equilibria for mirrors, and we discuss how this technique may also accelerate calculations for tokamaks and stellarators. The models presented in this article address critical multiscale problems in modeling magnetic mirrors, opening a new research avenue for equilibrium studies using an explicit continuum gyrokinetic code.
Two global invariants of two dimensional gyrokinetics are shown to be "rugged" (still conserved by the dynamics) concerning both Fourier and Hankel/Bessel Galerkin truncations. The truncations are made to keep only a finite range of wavenumber $\textbf{k}$ and the Hankel variable $b$ (or $z$ in the Bessel series). The absolute equilibria are used for the discussion of the spectral transfers in the configuration-velocity scale space of kinetic magnetized plasma turbulence. Some interesting aspects of recent numerical results, which were not well understood, are explained with more satisfaction.
A new constant of motion for helically symmetric equilibria in the vicinity of the magnetic axis is obtained in the framework of Vlasov theory. In view of this constant of motion the Vlasov theory is compared with drift kinetic and gyrokinetic theories near axis. It turns out that as in the case of axisymmetric equilibria [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 18, 064507 (2011)] the Vlasov current density thereon can differ appreciably from the drift kinetic and gyrokinetic current densities. This indicates some limitation on the implications of reduced kinetic theories, in partic…
We present a gyrokinetic theory for the electromagnetic waves and instabilities with frequencies much lower than the ion cyclotron frequency in finite-$β$ anisotropic uniform plasmas. Here, $β$ is the ratio between plasma and magnetic pressures. Kinetic effects due to both the finite Larmor radii and wave-particle resonances are fully kept in the analysis. Corresponding linear dispersion relation and wave polarizations, valid for general $β$ value and perpendicular wavelength, are then specifically derived for a bi-Maxwellian plasma. Analytic expressions for the criteria of kinetic firehose an…
A poloidal tilting symmetry of the local nonlinear $δf$ gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equ…
Nonlinear effects of the trapping of resonant particles by the combined action of the electric field and the magnetic mirror force is studied using a gyrokinetic description that includes the finite Larmor radius effects. A general nonlinear solution is found that is supported by the nonlinearity arising from the resonant particles, trapped by the combined action of the parallel electric field and the magnetic mirror force. Applying these results to the space plasma conditions, we demonstrate that in the magnetosheath plasma, coherent nonlinear magnetic depression may be created associated wit…
The gyrokinetic turbulence code GS2 was used to investigate the effects of plasma beta on linear, collisionless ion temperature gradient (ITG) modes and trapped electron modes (TEM) in National Compact Stellarator Experiment (NCSX) geometry. Plasma beta affects stability in two ways: through the equilibrium and through magnetic fluctuations. The first was studied here by comparing ITG and TEM stability in two NCSX equilibria of differing beta values, revealing that the high beta equilibrium was marginally more stable than the low beta equilibrium in the adiabatic-electron ITG mode case. Howeve…
Here we present details of a mixed implicit-explicit numerical scheme for the solution of the gyrokinetic-Poisson system of equations in the local limit. This scheme has been implemented in a new code called $\texttt{stella}$, which is capable of evolving electrostatic fluctuations with full kinetic electron effects and an arbitrary number of ion species in general magnetic geometry. We demonstrate the advantages of this mixed approach over a fully explicit treatment and provide linear and nonlinear benchmark comparisons for both axisymmetric and non-axisymmetric magnetic equilibria.
Validation of geometric proxies using negative and positive triangularity plasmas with varying elongation on TCV and multi-machine gyrokinetic simulations
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）；Istituto per la Scienza e la Tecnologia dei Plasmi, CNR（意大利国家研究委员会等离子体科学与技术研究所）；Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）
A general gyrokinetic dispersion relation is gotten and is applied to analysis linear kinetic coupling of anisotropic firehose (or, kinetic Alfven wave) and mirror mode. Nyquist stability analysis is also given.
High-power-density tokamaks offer a potential solution to design cost-effective fusion devices. One way to achieve high power density is to operate at a high $β$ value (the ratio of thermal to magnetic pressure), i.e., $β\sim 1$. However, a $β\sim 1$ state may be unstable to various pressure- and current-driven instabilities or have unfavorable microstability properties. To explore these possibilities, we generate $β\sim 1$ equilibria and investigate their stability. Initially, we study an analytical technique that was used in the past to generate $β\sim 1$ equilibria and outline its limitatio…
AI-Accelerated Gyrokinetic Predictions of Turbulent Transport for Stellarator Design Optimization and Experimental Planning
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；University of Maryland, College Park（马里兰大学帕克分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；Type One Energy；California Institute of Technology（加州理工学院）；Argonne National Laboratory（阿贡国家实验室）；Princeton University（普林斯顿大学）；University of Wisconsin, Madison（威斯康星大学麦迪逊分校）
Numerical and diagnostic extensions to the gyrokinetic $δf$ code stella
Institute of Physics, University of Greifswald（格赖夫斯瓦尔德大学物理研究所）；Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Rudolf Peierls Centre, University of Oxford（牛津大学鲁道夫·派尔斯中心）
In this work, we have formulated and implemented a mixed unstructured mesh-based finite element (FE)-Fourier decomposition scheme for gyrokinetic simulations in realistic tokamak geometry. An efficient particle positioning (particle-triangle mapping) scheme for the charge deposition and field scattering using an intermediate grid as the search index for triangles has been implemented and a significant speed-up by a factor of $\sim30$ is observed as compared with the brute force scheme for a medium-size simulation. The TRIMEG (TRIangular MEsh based Gyrokinetic) code has been developed. As an ap…
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization …
Plasma equilibria reconstructed from the Mega-Amp Spherical Tokamak (MAST) have sufficient resolution to capture plasma evolution during the short period between edge-localized modes (ELMs). Immediately after the ELM steep gradients in pressure, P, and density, ne, form pedestals close to the separatrix, and they then expand into the core. Local gyrokinetic analysis over the ELM cycle reveals the dominant microinstabilities at perpendicular wavelengths of the order of the ion Larmor radius. These are kinetic ballooning modes (KBMs) in the pedestal and microtearing modes (MTMs) in the core clos…
TRIMEG-GKX: an electromagnetic gyrokinetic particle code with a Piecewise Field-Aligned Finite Element Method for Micro- and Macro-Instability Studies in Tokamak Core Plasmas
Energetic particles, Shafranov shift and finite $β$ effects on TAE, KBM and ITG instabilities in global electromagnetic gyrokinetic simulations
Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）；Université de Lorraine（洛林大学）；De Vinci Higher Education（德文奇高等教育）；University of Warwick（华威大学）
Gyrokinetic simulations of ion temperature gradient mode and trapped electron mode driven impurity transport in a realistic tokamak geometry are presented and compared with results using simplified geometries. The gyrokinetic results, obtained with the GENE code in both linear and non-linear modes are compared with data and analysis for a dedicated impurity injection discharge at JET. The impact of several factors on heat and particle transport is discussed, lending special focus to tokamak geometry and rotational shear. To this end, results using s-alpha and concentric circular equilibria are…
A new linked mirror device for magnetic confinement experiment is proposed. The new linked mirror device consists of two straight magnetic mirrors connected by two half-torus. The structure of the configuration as a whole is three dimensional because the two linear mirror sections are not parallel. The angle between the two mirror sections generates rotational transform which results in good magnetic confinement of toroidally processing passing particles. In this way the usual loss cone of the traditional linear mirror machines is eliminated. The single particle confinement is similar to that …
The plasma equilibrium in a linear trap at $β\approx 1$ (or above the mirror-instability threshold) under the topology-conservation constraint evolves into a kind of diamagnetic "bubble". This can take two forms: either the plasma body greatly expands in radius while containing the same magnetic flux, or, if the plasma radius is limited, the plasma distribution across flux-tubes changes, so that the same cross-section contains a greatly reduced flux. If the magnetic field of the trap is quasi-uniform around its minimum, the bubble can be made roughly cylindrical, with radius much larger than t…
We have used the local-$δ{f}$ gyrokinetic code GS2 to perform studies of the effect of flux-surface shaping on two highly-shaped, low- and high-$β$ JT-60SA-relevant equilibria, including a successful benchmark with the GKV code. We find a novel destabilization of electrostatic fluctuations with increased elongation for plasma with a strongly peaked pressure profile. We explain the results as a competition between the local magnetic shear and finite-Larmor-radius (FLR) stabilization. Electromagnetic studies indicate that kinetic ballooning modes are stabilized by increased shaping due to an inc…
A largely unsolved theoretical issue in controlled fusion research is the consistent \textit{kinetic} treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchalleged to date. The goal…
Electrostatic gyrokinetic absolute equilibria with continuum velocity field are obtained through the partition function and through the Green function of the functional integral. The new results justify and explain the prescription for quantization/discretization or taking the continuum limit of velocity. The mistakes in the Appendix D of our earlier work [J.-Z. Zhu and G. W. Hammett, Phys. Plasmas {\bf 17}, 122307 (2010)] are explained and corrected. If the lattice spacing for discretizing velocity is big enough, all the invariants could concentrate at the lowest Fourier modes in a negative-t…
Reactor grade plasmas are likely to be fuelled by pellet injection. This technique transiently perturbs the profiles, driving the density profile hollow and flattening the edge temperature profile. After the pellet perturbation, the density and temperature profiles relax towards their quasi-steady-state shape. Microinstabilities influence plasma confinement and will play a role in determining the evolution of the profiles in pellet fuelled plasmas. In this paper we present the microstability analysis of pellet fuelled H-mode MAST plasmas. Taking advantage of the unique capabilities of the MAST…
A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al. 2009) for pressure-anisotropic plasmas, allowing for species drifts---a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas (e.g. intracluster medium). Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g., the Alfven ratio) are order-un…
How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning
1 Institute for Research in Electronics \& Applied Physics, University of Maryland, College Park, MD 20742, USA 2 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 3 Princeton Plasma Physics Laboratory, Princeton, NJ 08540, USA 4 Max Planck Institute for Plasma Physics, Wendelsteinstraße 1, 17491 Greifswald, Germany
