A one-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet

TL;DR

This paper introduces the first non-linear force-free Vlasov-Maxwell equilibrium, where magnetic shear maintains force balance with constant plasma pressure and density, expanding understanding of plasma equilibria.

Contribution

It presents a novel force-free equilibrium solution for the Vlasov-Maxwell system, using a pseudo-particle analogy and Fourier transform methods, generalizing the Harris sheet model.

Findings

First non-linear force-free Vlasov-Maxwell equilibrium

Equilibrium maintains force balance via magnetic shear

Generalizes Harris sheet to a family of equilibria

Abstract

In this paper the first non-linear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudo-particle in a two-dimensional conservative potential. This potential is equivalent to one of the diagonal components of the plasma pressure tensor. After finding the appropriate functional form for this pressure tensor component, the corresponding distribution functions can be found using a Fourier transform method. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet.