Universal equilibria, phase-space structure of collisionless plasma systems, and turbulence in non-Maxwellian plasmas

我们从统计物理和动力学理论中知道，等离子体在粒子碰撞时间尺度上松弛到麦克斯韦平衡。然而，在许多天然等离子体中，这些时间尺度很长，并且似乎会发生松弛到某些无碰撞平衡。是否存在独立于初始条件的通用平衡（类），使无碰撞等离子体收敛于此？这样的等离子体是否具有由集体场-粒子相互作用引起的有效对撞性？由于非线性理论的困难和不可能在足够的分辨率下进行动力学模拟，这些老问题一直没有解决。随着计算机的日益强大，后一个障碍正在被消除，而相空间等离子体湍流的非线性理论（与无碰撞松弛问题密切相关）最近在一个新的方向上取得了进展，即等离子体湍流的流化概念，这是由于随机回波抑制自由能流进入短速度空间尺度。因此，现在是研究无碰撞弛豫新理论的好时机。该项目的主要目标是推导出一个“无碰撞碰撞积分”，即无碰撞等离子体中平均分布函数向（类）普遍平衡的松弛理论。为此，需要求解细尺度粒子分布的二阶两点相空间相关函数。后一个目标本身是有价值的，作为理解不接近麦克斯韦平衡的等离子体中相空间湍流的性质和结构的途径：一个看似简单但概念上令人着迷的问题是，在这样的系统中，湍流能量级联的对应物是什么（特别是，级联不变量是什么）。该项目将是分析理论（无碰撞等离子体的动力学理论与湍流的非平衡统计力学相结合）和数值探索（动力学模拟）的混合。这两个项目的主要目标都是基础性质的，因此主要的影响将是对无碰撞、湍流等离子体作为非平衡统计力学系统的基本理解。在应用方面，诸如热和动量的紊流输运的计算依赖于这样的理解和发展一种数学语言来表达这种理解；这些计算的结果直接用于，例如，模拟聚变装置中的等离子体约束。该项目由牛津等离子体理论小组（Oxford Plasma Theory Group）负责，该小组正在开展此类建模的所有工作，从基础理论到数值模拟，再到实验驱动的验证和验证（后者与CCFE密切合作）；这项研究还结合了一个多机构的努力，包括约克，沃里克和斯特拉斯克莱德，由EPSRC项目资助TDoTP。该项目是跨学科的，因此属于几个EPSRC研究领域的范围：等离子体和激光：主要主题领域；非线性系统与复杂性科学：研究对象是等离子体湍流，这是一种涉及多尺度复杂分布和自由能流动的基本非线性现象；虽然该领域的大部分工作都与流体系统有关，但该项目的关键新颖之处在于它专注于6D（位置和速度）相空间中的等离子体湍流；分析科学与数学物理：该项目涉及描述等离子体相空间自由能级联的新形式主义和等离子体向普遍平衡的弛豫；英国磁聚变研究计划：弱碰撞的聚变等离子体是一个系统中最重要的例子，在这个系统中，动态自由能级联出现并控制传输特性——从而在聚变装置中限制等离子体。

We know from statistical physics & kinetic theory that a plasma relaxes to a Maxwellian equilibrium on particle-collision timescales. However, in many natural plasmas, these timescales are long and relaxation to some collisionless equilibrium appears to occur. Are there (classes of) universal equilibria, independent of initial conditions, that a collisionless plasma will converge to? Do such plasmas have an effective collisionality, caused by collective field-particle interactions? These old questions have stayed open because of the difficulty of nonlinear theory and impossibility of kinetic simulations at sufficient resolution. The latter obstacle is being lifted as computers get more powerful, while the nonlinear theory of phase-space plasma turbulence, with which the problem of collisionless relaxation is intimately intertwined, has recently advanced in a new direction, viz., the concept of fluidisation of plasma turbulence due to stochastic echoes suppressing free-energy flow into short velocity-space scales. It is, therefore, a good time to undertake a new theory of collisionless relaxation. The project's key objective is to derive a "collisionless collision integral", i.e., a theory of relaxation of mean distribution functions in collisionless plasmas towards (classes of) universal equilibria. For that, it is necessary to work out the second-order, two-point phase-space correlation function of the fine-scale particle distribution. The latter objective is worthwhile in its own right, as a route to understanding the nature and structure of phase-space turbulence in plasmas that are not close to Maxwellian equilibrium: a seemingly simple but conceptually fascinating question is what is the counterpart to the turbulent energy cascade in such systems (in particular, what is the cascaded invariant). The project will be a mixture of analytical theory (kinetic theory of collisionless plasmas coupled with non-equilibrium statistical mechanics of turbulence) and numerical exploration (kinetic simulations). Both of the project's main objectives are of a fundamental nature, so the primary impact will be a fundamental understanding of collisionless, turbulent plasma as a non-equilibrium statistical-mechanical system. In applied terms, calculations of such things as turbulent transport of heat and momentum rely on just such an understanding and on developing a mathematical language in which this understanding is expressed; the outcomes of such calculations feed directly into, e.g., modelling plasma confinement in fusion devices. The project is being pursued within Oxford Plasma Theory Group, which is working across the full spectrum of such modelling, from fundamental theory to numerical simulation to experimentally driven validation & verification (the latter in close collaboration with CCFE); this research is also coupled to a multi-institutional effort involving York, Warwick and Strathclyde, funded by EPSRC Programme Grant TDoTP. The project is interdisciplinary and so falls within the ambit of several EPSRC research areas: Plasma and lasers: primary topical area; Nonlinear systems & Complexity science: the object of study is plasma turbulence, a fundamentally nonlinear phenomenon involving emergence of multi-scale complex distribution and flows of free energy; while the majority of work in this area has concerned fluid systems, the key novelty of this project is its focus on plasma turbulence in 6D (positions & velocities) phase space; Analytical science & Mathematical physics: the project involves development of new formalism for describing phase-space free-energy cascades in plasmas and plasma relaxation towards universal equilibria; UK Magnetic Fusion Research Programme: fusion plasmas, which are weakly collisional, are the most consequential example of a system where kinetic free-energy cascades emerge and control transport properties - and thus plasma confinement in fusion devices.