Gyrokinetic Simulation and Theory of Non-diffusive Transport and Chaotic Flows in Non-Equilibrium Magnetized Plasmas

热、粒子和动量的湍流输运影响着从聚变能应用的实验室磁约束和惯性约束系统到空间天气和等离子体天体物理学等广泛的等离子体现象。利用解析理论和数值模拟在理解等离子体湍流和输运方面取得了大量进展，如非线性模态相互作用、能量级联、二次不稳定性、湍流扩散和剪切流的作用。在这些由平衡驱动的系统中，输运的另一个特征是表现出复杂时空模式和连贯结构的大波动，从而导致较大的相对位移。正是这些位移，以及它们的时间依赖性，导致偏离了通常用局部菲克定律描述的经典的扩散通量。相反，非平衡系统根据空间非局部过程进化，可以表现出时间记忆和部分相干性。这类现象，即所谓的非扩散输运，在本提案中是在包含跨场压力和/或电流密度梯度的磁化等离子体的背景下解决的。最近的理论工作表明，非扩散输运性质与混沌动力学有关，分数扩散模型是一种适当的理论描述。在大型线性等离子体装置（大型等离子体装置（LAPD））的控制温度梯度实验中，记录了非扩散传输的实验证据，Gekelman等人，Rev. Sci。仪器。62,2875(1991))和潜在的微观结构被发现具有与确定性混沌相关的普遍特征。基于这些实验结果的新输运模型已经在分数阶Fokker-Planck方程和混沌平流的基础上建立。本研究的主要目的之一是应用完全非线性动力学模拟来解决主要问题，即潜在的微观动力学本质上是否确实是混沌的或随机的，并与基于分数扩散和混沌平流的预测进行比较。所采取的方法是基于圆柱形几何的三维陀螺动力学粒子模拟，包括应用于磁化温度丝实验中的热输运的电磁效应和相关的高电流密度通道，形成被称为通量绳的磁性结构。这些非平衡等离子体条件（温度丝或电流通道）也可以在天线发射时形成大振幅低频等离子体正常模式，称为剪切阿尔芬波。在所有情况下，将分析自洽电磁场的非线性演化以及带电粒子和热在lapd型等离子体中的扩散，并与实验和理论模型进行比较。全球陀螺仪动力学模拟使用了真实的等离子体参数，可以跟踪输运时间尺度上的演化。空间定位的合成探针将被开发出来，以产生可以与实验室测量相比较的时间序列，粒子的单个标记将使我们能够详细探索微观扩散率。诸如此类的数值模拟是开发各种等离子体环境中湍流输运预测能力的关键。学员的研究经验，在理论/建模和实验之间的前沿，将提供宝贵的技能和准备在学术和工业环境的工作。

The turbulent transport of heat, particles and momentum has an impact on a wide range of plasma phenomena ranging from laboratory magnetic and inertial confinement systems for fusion energy applications, to space weather and plasma astrophysics. A large number of advances in understanding plasma turbulence and transport have been made using analytic theory and numerical simulation, such as nonlinear mode interaction, energy cascades, secondary instabilities, turbulence spreading and the role of sheared flows. Another feature of transport in these systems that are driven from equilibrium, are large fluctuations that exhibit complex spatio-temporal patterns and coherent structures which induce large relative displacements. It is these displacements, and their temporal dependence, that cause departures from the classical, diffusive fluxes commonly described by a local Fick’s law. Instead the non-equilibrated systems evolve according to spatially non-local processes that can exhibit temporal memory and partial coherency. It is phenomena of this type, so-called non-diffusive transport, that is addressed in this proposal within the context of magnetized plasmas containing cross-field pressure and/or current density gradients. Recent theoretical work has suggested that non-diffusive transport properties are connected with chaotic dynamics and that fractional diffusion models are an appropriate theoretical description. Experimental evidence for non-diffusive transport has been documented in controlled temperature gradient experiments in a large linear plasma device (Large Plasma Device (LAPD), Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)) and underlying microscopic structures have been found to have universal features related to deterministic chaos. New transport models based on these experimental findings have been formulated based on the fractional Fokker-Planck equation and chaotic advection. One of the main purposes of this investigation is to apply fully nonlinear kinetic simulations to resolve the major question as to whether the underlying microscopic dynamics is indeed chaotic or stochastic in nature and to compare with predictions based on fractional diffusion and chaotic advection. The approach taken is based on 3D gyrokinetic particle simulation in cylindrical geometry including electromagnetic effects applied to thermal transport in magnetized temperature filament experiments and related high current density channels that form magnetic structures know as flux ropes. These non-equilibrium plasma conditions (temperature filaments or current channels) can also form during antenna-launch of large amplitude low frequency plasma normal modes called shear Alfven waves. In all cases the nonlinear evolution of the self-consistent electromagnetic fields as well as the diffusion of charged particles and heat in the LAPD-type plasmas will be analyzed and compared with experiment and theoretical models. The global gyrokinetic simulations use realistic plasma parameters and can follow the evolution on transport time scales. Spatially localized synthetic probes will be developed to generate time series that can be compared to laboratory measurements and individual tagging of particles will allow us to explore microscopic diffusivity in detail. Numerical simulations such as these are key to development of a predictive capability for turbulent transport in a variety of plasma environments. The research experience for trainees, at the leading edge between theory/modeling and experiment, will provide valuable skills and preparation for work in both academic and industrial settings.