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

聚变机中等离子体的核心和边缘之间的温差可以保持多大的问题，为我们打开了一扇窗户，让我们了解有关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。这些问题围绕着以电磁涨落的形式从系统的宏观不均匀(对于聚变等离子体的情况，从背景温度梯度)中提取的自由能如何在相空间(粒子的位置和动量)中分布，从而产生一种混乱的多尺度(=湍流)状态，其中容纳了从宏观尺度到微观尺度的稳定的能量流动，并以粒子热运动的形式返回其不可避免的静止之处。这种能量分布决定了湍急的等离子体如何传输热量和动量。这个项目的目的是跟进我们在理解这些现象方面的一些最新进展，并调查：进入相空间[1，2]的能量流的非线性抑制对传输模型的影响；等离子体激发的混乱场(“漂移波”)和自产生的规则的“带状”流之间的微妙平衡[3]，它将等离子体的非线性状态保持在分隔湍流和静止相的临界阈值附近；在所谓的“混沌边缘”出现持久的相干结构[4]--以及所有这些如何结合在一起并共同对背景梯度设置限制。该项目将包括分析、数值和可能的实验部分，这取决于进度和学生的兴趣。A.A.Schekochihin等人，J.血浆物理。82,905820212(2016年)2.T.Adkins和A.A.Schekochihin，J.血浆物理。84,905840107(2018年)3.G.J.Colyer等人，血浆物理。控制室。Fusion 59,055002(2017年)4.F.van Wyk等人，J.等离子体物理。82,905820609(2016年)5.M.F.J.福克斯等人，血浆物理。控制室。《融合59》，《034002》(2017年)

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)