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

我们从统计物理学和动力学理论中知道，等离子体在粒子碰撞时间尺度上弛豫到麦克斯韦平衡。然而，在许多自然等离子体中，这些时间尺度很长，并且似乎会发生弛豫到某种无碰撞平衡。是否存在独立于初始条件的普适平衡点（类），使无碰撞等离子体收敛到？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碰撞性？这些老问题一直悬而未决，因为非线性理论的困难和不可能的动力学模拟在足够的分辨率。后一个障碍随着计算机变得更强大而被解除，而与无碰撞弛豫问题密切相关的相空间等离子体湍流的非线性理论最近在一个新的方向上取得了进展，即，由于随机回波抑制自由能流进入短速度空间尺度的等离子体湍流的fludenation的概念。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“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，有必要计算出细尺度粒子分布的二阶两点相空间关联函数。后一个目标本身就有价值，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一种途径：一个看似简单但概念上有趣的问题是什么是湍流的对应物在此类系统中的能量级联（特别是，什么是级联不变量）。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）的混合物。该项目的两个主要目标都是基础性的，因此主要影响将是对作为非平衡物理力学系统的无碰撞湍流等离子体的基本理解。在应用方面，对热量和动量的湍流传输等事情的计算依赖于这样一种理解，并依赖于开发一种表达这种理解的数学语言;这种计算的结果直接输入，例如，模拟聚变装置中的等离子体约束。该项目正在牛津等离子体理论小组内进行，该小组正在研究这种建模的全方位，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）;这项研究还与涉及约克，沃里克和斯特拉斯克莱德的多机构努力相结合，由EPSRC计划资助TDoTP资助。该项目是跨学科的，因此福尔斯属于几个EPSRC研究领域的范围：等离子体和激光：主要专题领域;非线性系统和复杂性科学：研究对象是等离子体湍流，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;虽然在这个领域里的大部分工作都是关于流体系统的，但是这个项目的主要新奇在于它把重点放在了6D空间中的等离子体湍流上（位置和速度）相空间;分析科学和数学物理学：该项目涉及开发新的形式主义，用于描述等离子体中的相空间自由能级联和等离子体弛豫到普遍平衡;英国磁聚变研究计划：弱碰撞的聚变等离子体是动力学自由能级联出现并控制输运性质从而控制聚变装置中的等离子体约束的系统的最重要的例子。

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.