Non-equilibrium plasma physics near criticality: phase-space cascades, wave-flow interactions, edge-of-chaos structures and turbulent transport

在核聚变机中，等离子体的核心和边缘之间能保持多大的温差，这一问题为研究磁化等离子体中非线性、非平衡态结构的一些最基本的理论问题打开了一扇窗。这些问题围绕着从系统的宏观不均匀性（在聚变等离子体的情况下，从背景温度梯度）中以电磁波动的形式提取的自由能如何分布在相空间（粒子的位置和动量）中，从而产生混沌，多尺度（=湍流）状态，它容纳能量从宏观尺度到微观尺度的稳定流动，并以粒子热运动的形式返回其必然的静止位置。能量的这种分布决定了湍流等离子体如何传递热量和动量。这个项目的目的是跟进我们对这些现象的理解的一些最新发展，并研究：非线性抑制能量流进入相空间[1,2]对输运模型的影响；等离子体激发的混沌场（“漂移波”）和自生的规则“带状”流动[3]之间的微妙平衡，使等离子体的非线性状态保持在分离湍流和静止阶段的临界阈值附近；在这个所谓的“混沌边缘”[4]出现了持续连贯的结构，以及所有这些结构是如何组合在一起并密谋限制背景梯度的。该项目将有分析，数值和可能的实验[5]组件，取决于进展速度和学生的倾向。李建军，刘建军，李建军，等。等离子体物理学报，2016,32(2):557 - 557。[3]陈建军，陈建军，陈建军，等。等离子体物理学报，2016,37(5):557 - 557。G. J. Colyer等，等离子体物理。控制。核聚变59,055002 （2017）李建军，张建军，李建军，等。等离子体物理学报，2016,32(4):557 - 557。M. F. J. Fox等，等离子体物理学。控制。Fusion 59, 034002 （2017）

The question of how large a temperature difference can be maintained between the core and the edge of the plasma in a fusion machine opens a window onto some of the most fundamental theoretical questions about the structure of nonlinear, non-equilibrium states in magnetised plasma. These questions revolve around the ways in which free energy extracted from macroscopic inhomogeneities of the system (in the case of a fusion plasma, from the background temperature gradient) in the form of electromagnetic fluctuations is distributed in phase space (particles' positions and momenta) so as to give rise to a chaotic, multiscale (=turbulent) state that accommodates a steady flow of energy from macro to micro scales and its return to its inevitable resting place in the form of the thermal motion of the particles. This distribution of energy is then what determines how the turbulent plasma transports heat and momentum. This project's aim is to follow up on a number of recent developments in our understanding of these phenomena and investigate: the implications of the nonlinear suppression of energy flows into phase space [1,2] for transport models; the delicate balance between a chaotic field of plasma excitations ("drift waves") and self-generated regular "zonal" flows [3] that maintains the nonlinear state of a plasma near the critical threshold separating the turbulent and quiescent phases; the emergence of persistent coherent structures at this so-called "edge of chaos" [4] --- and how all this fits together and conspires to set limits on the background gradients. The project will have analytical, numerical and possibly experimental [5] components, depending on rate of progress and student's inclinations.1. A. A. Schekochihin et al., J. Plasma Phys. 82, 905820212 (2016)2. T. Adkins & A. A. Schekochihin, J. Plasma Phys. 84, 905840107 (2018)3. G. J. Colyer et al., Plasma Phys. Control. Fusion 59, 055002 (2017)4. F. van Wyk et al., J. Plasma Phys. 82, 905820609 (2016)5. M. F. J. Fox et al., Plasma Phys. Control. Fusion 59, 034002 (2017)