磁化弱碰撞等离子体中的二维静电湍流在相空间中表现出熵的级联[Phys. Rev. Lett. 103，015003（2009）]。在尺度小于回转半径，该叶栅的特点是在热拉莫尔半径的尺度上测量的碰撞时间的涡流周转时间的无量纲比D。当D >> 1时，在位置和速度空间中都发现了亚拉莫尔尺度的宽谱涨落。分布函数将结构发展为v_{perp}的函数，v_{perp}是垂直于局部磁场的速度坐标。叶栅在位置空间和速度空间都表现出局部尺度的非线性相互作用，Kolmogorov的标度理论可以推广到相空间。
英文摘要：
Two-dimensional electrostatic turbulence in magnetized weakly-collisional plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103, 015003 (2009)]. At scales smaller than the gyroradius, this cascade is characterized by the dimensionless ratio D of the collision time to the eddy turnover time measured at the scale of the thermal Larmor radius. When D >> 1, a broad spectrum of fluctuations at sub-Larmor scales is found in both position and velocity space. The distribution function develops structure as a function of v_{perp}, the velocity coordinate perpendicular to the local magnetic field. The cascade shows a local-scale nonlinear interaction in both position and velocity spaces, and Kolmogorov's scaling theory can be extended into phase space.
The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, document…
Freely decaying turbulence in two-dimensional electrostatic gyrokinetics
在磁化等离子体中，在相空间中以小于热拉莫尔半径（“亚拉莫尔尺度”）的尺度发生湍流级联[Phys. Rev. Lett. 103，015003（2009）]。当湍流被限制在垂直于背景磁场的两个空间维度时，由于存在两个无碰撞不变量，两个独立的级联可能同时发生。本文采用唯象理论和直接数值模拟的方法研究了二维静电陀螺动力学的自由衰减湍流。一个双级联（正向和反向级联）观察到在速度空间，以及在位置空间，我们诊断的非线性传递函数的碰撞不变量。我们发现，湍流往往是一个时间渐近状态，占主导地位的一个单一的规模增长的时间。这种渐近状态的理论是以衰减定律的形式导出的。我们研究的每一种情况都属于三个区域之一（弱碰撞，边缘和强碰撞），由一个无量纲数D*，一个类似于雷诺数的量决定。边缘状态由在时间上保持的临界数D* = D 0来标记。初始化高于该值的湍流随时间变得越来越惯性，朝着越来越大的D* 发展;初始化低于D 0的湍流变得越来越碰撞，逐渐衰减到越来越小的D*。
This paper points out that the full-orbit density obtained in the standard electrostatic gyrokinetic model is not truly accurate at the order $\varepsilon^{σ-1}$ with respect to the equilibrium distribution $e^{-αμ}$ with $μ\in (0, μ_{\max})$, where $\varepsilon$ is the order of the normalized Larmor radius, $\varepsilon^σ$ the order of the amplitude of the normalized electrostatic potential, and $α$ a factor of $O(1)$. This error makes the exact order of the full-orbit density not consistent with that of the approximation of the full-orbit distribution function. By implementing a hybrid coord…
Axisymmetric ($m=0$) gyrokinetic and extended-MHD simulations of sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The electromagnetic MHD model includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. A prominent feature of this work is that the radial profiles for the plasma dens…
A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbule…
Gyrokinetic Theory of Linear Gravitational Flute Interchanges with Flow Shear Stabilization
University of Maryland, College Park（马里兰大学帕克分校）；Institute for Research in Electronics & Applied Physics, University of Maryland, College Park（马里兰大学电子与应用物理研究所）；Gridfire Inc（Gridfire公司）
We introduce and derive the Fourier-enhanced 3D electrostatic field solver of the gyrokinetic full-f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily parallelizable and thus save run time. The presented solver is then verified using two different approaches of manufactured solutions. The test setup used for this effort is a pinch geometry with ITG-like electric potential, containing one non-periodic and two periodic directions, one of which will be discrete Fourier transformed. The results of these…
Energetic particles produced by neutral beams are observed to excite energetic-particle-driven geodesic acoustic modes (EGAMs) in tokamaks. We study the effects of anisotropy of distribution function of the energetic particles on the excitation of such instabilities with ORB5, a gyrokinetic particle-in-cell code. Numerical results are shown for linear electrostatic simulations with ORB5. The growth rate is found to be sensitively dependent on the phase-space shape of the distribution function. The behavior of the instability is qualitatively compared to the theoretical analysis of dispersion r…
A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa- Mima equation, but does not conserve enstrophy, and, as a result, exhibits a forward cascade of energy, to small scales. The inertial-range energy spectrum is argued to be shallower than a -11/3 power law, as compared to the -5 law of the Hasegawa-Mima enstrophy cascade. This property, confirmed here by direct numerical simulations of the fluid system, may help explain the fluctuation spectrum observed in gyrokineti…
Gyrokinetic simulation of the effect of transient fueling on plasma turbulence in ADITYA-U tokamak
Indian Institute of Science Bangalore（印度科学研究所班加罗尔分院）；Institute for Plasma Research, Bhat（巴特等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Centre for Development of Advanced Computing（高级计算发展中心）；Department of Physics and Astronomy, University of California Irvine（加州大学尔湾分校物理与天文学系）
A novel type of internal transport barrier (ITB) called F-ATB (fast ion-induced anomalous transport barrier) has been recently observed in state-of-the-art global gyrokinetic simulations on a properly optimized ASDEX Upgrade experiment [A. Di Siena et al. Phys. Rev. Lett. {\bf 127} 025002 (2021)]. Unlike the transport barriers previously reported in literature, the trigger mechanism for the F-ATB is a basically electrostatic wave-particle resonant interaction between supra-thermal particles - generated via ion cyclotron resonance heating (ICRH) - and ion scale plasma turbulence. This resonant …
We present a stellarator configuration optimized for a large threshold (``critical gradient'') for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with exce…
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）
Detecting Shearless Phase-Space Transport Barriers in Global Gyrokinetic Turbulence Simulations with Test Particle Map Models
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Zhejiang University（浙江大学）；Princeton University（普林斯顿大学）；University of São Paulo（圣保罗大学）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）
Sub-Second Collisionless Gyrokinetic Eigenvalue Solutions via Orbit-Invariant Decomposition
Beijing VeloAlpha Technology Co., Ltd.（北京维洛阿尔法科技有限公司）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院）；School of Physics, Peking University（北京大学物理学院）
GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulations
ELLIS Unit, Institute for Machine Learning, JKU Linz（JKU林茨机器学习研究所ELLIS单元）；United Kingdom Atomic Energy Authority, Culham campus（英国原子能局库勒姆校区）；EMMI AI, Linz（林茨EMMI人工智能）
