Relaxation to universal non-Maxwellian equilibria in a collisionless plasma

TL;DR

This paper develops a theoretical framework for understanding how turbulent relaxation in collisionless plasmas leads to universal non-Maxwellian equilibria, confirmed by numerical simulations showing power-law tails in particle energy distributions.

Contribution

It introduces a new entropy-maximization approach that accounts for collisionless invariants and demonstrates the emergence of universal power-law equilibria in turbulent plasmas.

Findings

Universal power-law tail with exponent -2 in particle energy distribution.

Turbulence drives collisionless invariants to a universal form.

Numerical simulations confirm the theoretical predictions.

Abstract

Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows the system with a partial `memory' of its prior conditions, but is imperfect on long time scales due to the development of a turbulent cascade to small scales, which breaks the precise conservation of phase volume, making this memory imprecise. The equilibria are still determined by the short-time collisionless invariants, but the invariants themselves are driven to a universal form by the nature of the turbulence. This is numerically confirmed for the case of beam instabilities in one-dimensional electrostatic plasmas, where sufficiently strong turbulence appears to cause the distribution function of particle energies to develop a universal power-law tail, with exponent -2.