An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

TL;DR

This paper introduces a new exact collisionless equilibrium model for the Force-Free Harris Sheet that accommodates plasma beta values below unity, expanding the range of physically realistic force-free magnetic field solutions.

Contribution

It provides the first exact collisionless equilibrium for the Force-Free Harris Sheet that allows plasma beta below one, with a distribution function expressed as an infinite Hermite polynomial series.

Findings

Distribution function converges and remains non-negative.

Model applies to plasma beta below unity.

Comparison shows deviations from Maxwellian distribution.

Abstract

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely the Force-Free Harris Sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite Polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.