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弛豫到麦克斯韦平衡。然而，在许多天然等离子体中，这些时间尺度是很长的，并且似乎发生了到某种无碰撞平衡的松弛。是否存在与初始条件无关的(几类)无碰撞等离子体会收敛到的普适平衡？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以足够的分辨率进行动力学模拟，这些老问题一直悬而未决。随着计算机变得更加强大，后一种障碍正在被消除，而与无碰撞弛豫问题紧密交织在一起的相空间等离子体湍流的非线性理论最近朝着一个新的方向发展，即由于随机回波将自由能流抑制到短速度空间尺度而导致的等离子体湍流的流态化的概念。因此，现在是提出一种新的无碰撞弛豫理论的好时机。该项目的关键目标是推导出“无碰撞碰撞积分”，即无碰撞等离子体中平均分布函数向(类)宇宙平衡的松弛理论。为此，有必要求出细尺度粒子分布的二阶两点相空间关联函数。后一个目标本身是值得的，因为它是理解等离子体中相空间湍流的性质和结构的一条途径，而等离子体中的相空间湍流并不接近麦克斯韦平衡：一个看似简单但在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和湍流的非平衡统计力学)和数值探索(动力学模拟)的混合体。这两个项目的主要目标都是根本性的，所以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，对热量和动量的湍流传输等的计算正是依赖于这种理解，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到例如聚变装置中的等离子体约束的建模中。该项目正在牛津等离子体理论小组内进行，该小组正在进行从基础理论到数值模拟到实验驱动的验证和验证(后者与CCFE密切合作)的所有此类建模工作；这项研究还与由EPSRC计划赠款TDoTP资助的涉及约克、沃里克和斯特拉斯克莱德的多机构工作相结合。该项目是跨学科的，因此属于EPSRC的几个研究领域：等离子体和激光：主要主题领域；非线性系统和复杂性科学：研究对象是等离子体湍流，这是一种基本的非线性现象，涉及自由能的多尺度复杂分布和流动；虽然这一领域的大部分工作涉及流体系统，但该项目的主要新奇之处在于它关注6D(位置和速度)相空间的等离子体湍流；分析科学和数学物理：该项目涉及描述等离子体中相空间自由能级联和等离子体弛豫的新形式；英国磁聚变研究计划：聚变等离子体是弱碰撞的，是系统中最重要的例子，在该系统中，动能自由能级联出现并控制传输特性--从而控制聚变设备中的等离子体约束。

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.