Theory of spatially non-symmetric kinetic equilibria for collisionless plasmas

TL;DR

This paper develops a non-perturbative gyrokinetic framework to construct and analyze spatially non-symmetric kinetic equilibria in collisionless plasmas, revealing conditions for their existence and the possibility of self-generated magnetic fields.

Contribution

It introduces a novel gyrokinetic-based approach to establish the existence of non-symmetric kinetic equilibria in collisionless plasmas, including conditions for magnetic field self-generation.

Findings

Existence of generalized bi-Maxwellian equilibria in non-symmetric plasmas.

Analytical treatment of fluid moments from kinetic equilibria.

Identification of conditions for kinetic dynamo in astrophysical and laboratory plasmas.

Abstract

The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas this involves the construction of stationary solutions of the Vlasov-Maxwell equations. In this paper the issue is addressed for non-relativistic plasmas both in astrophysical and laboratory contexts. The treatment is based on a Lagrangian variational description of single-particle dynamics. Starting point is a non-perturbative formulation of gyrokinetic theory, which allows one to construct "a posteriori" with prescribed order of accuracy an asymptotic representation for the magnetic moment. In terms of the relevant particle adiabatic invariants generalized bi-Maxwellian equilibria are proved to exist. These are shown to recover, under suitable assumptions, a Chapman-Enskog form which permits an analytical treatment of the corresponding fluid moments. In particular, the constrained posed by the Poisson and the Ampere equations are analyzed, both for quasi-neutral and non-neutral plasmas. The conditions of existence of the corresponding non-symmetric kinetic equilibria are investigated. As a notable feature, both astrophysical and laboratory plasmas are shown to exhibit, under suitable conditions, a kinetic dynamo, whereby the equilibrium magnetic field can be self-generated by the equilibrium plasma currents.