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

热、粒子和动量的湍流传输对广泛的等离子体现象产生影响，从用于聚变能源应用的实验室磁和惯性约束系统，到空间气象和等离子体天体物理。利用解析理论和数值模拟对等离子体湍流和输运的研究取得了许多进展，如非线性模式相互作用、能量级联、二次不稳定性、湍流扩散和剪切流的作用等。在这些系统中，由平衡驱动的输运的另一个特征是大涨落，表现出复杂的时空模式和相干结构，导致大的相对位移。正是这些位移及其时间依赖性，导致偏离了通常由局部费克定律描述的经典扩散通量。相反，非平衡系统根据可以表现出时间记忆和部分相干的空间非局部过程来进化。在包含交叉场压力和/或电流密度梯度的磁化等离子体的背景下，在本提案中讨论的正是这种类型的、所谓的非扩散传输现象。最近的理论工作表明，非扩散输运性质与混沌动力学有关，分数阶扩散模型是一个合适的理论描述。在大型线性等离子体设备中的受控温度梯度实验中已经记录了非扩散传输的实验证据(大型等离子体设备(LAPD)，Gekelman等人，Rev.Sci。Instrum。62,2875(1991))和潜在的微观结构已被发现具有与确定性混沌有关的普遍特征。基于这些实验结果，基于分数阶Fokker-Planck方程和混沌平流建立了新的输运模型。这项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潜在的微观动力学实际上是混沌还是随机的主要问题，并与基于分数阶扩散和混沌平流的预测进行比较。所采用的方法是基于圆柱几何中的三维回转运动粒子模拟，包括在磁化温度丝实验中应用于热传输的电磁效应以及形成称为磁通绳的磁性结构的相关高电流密度通道。这些非平衡等离子体条件(温度、细丝或电流通道)也可以在称为剪切阿尔芬波的大幅度低频等离子体正常模式的天线发射过程中形成。在所有情况下，我们都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。全球陀螺动力学模拟使用了真实的等离子体参数，并可以跟踪传输时间尺度上的演变。将开发空间局部化的合成探测器，以生成可与实验室测量进行比较的时间序列，并对颗粒进行单独标记，使我们能够详细探索微观扩散率。这样的数值模拟是发展各种等离子体环境中湍流传输预测能力的关键。学员的研究经验处于理论/建模和实验之间的前沿，将为学术和工业环境中的工作提供宝贵的技能和准备。

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.