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

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.