Some remarks on one-dimensional force-free Vlasov-Maxwell equilibria

TL;DR

This paper investigates the conditions under which one-dimensional force-free Vlasov-Maxwell equilibria can exist, revealing that known solutions correspond to attractive central pseudo-potentials and proposing a framework for further exploration.

Contribution

It derives a new theoretical framework for 1D VM equilibria, establishing necessary conditions for force-free solutions and linking known solutions to attractive central pseudo-potentials.

Findings

Linear force-free solutions correspond to attractive central pseudo-potentials.

A new necessary condition on the pseudo-potential for force-free equilibria is formulated.

Discussion of distribution functions leading to central pseudo-potentials.

Abstract

The conditions for the existence of force-free non-relativistic translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria are investigated using general properties of the 1D VM equilibrium problem. As has been shown before, the 1D VM equilibrium equations are equivalent to the motion of a pseudo-particle in a conservative pseudo-potential, with the pseudo-potential being proportional to one of the diagonal components of the plasma pressure tensor. The basic equations are here derived in a different way to previous work. Based on this theoretical framework, a necessary condition on the pseudo-potential (plasma pressure) to allow for force-free 1D VM equilibria is formulated. It is shown that linear force-free 1D VM solutions, which so far are the only force-free 1D VM solutions known, correspond to the case where the pseudo-potential is an attractive central potential. A general class of distribution functions leading to central pseudo-potentials is discussed.