Force-free collisionless current sheet models with non-uniform temperature and density profiles

TL;DR

This paper develops new force-free collisionless current sheet models with non-uniform temperature and density, extending previous models by incorporating Jacobian elliptic functions and analyzing their physical properties.

Contribution

It introduces a class of equilibrium distribution functions for force-free current sheets with non-uniform profiles, generalizing earlier models and providing conditions for positivity and detailed physical characteristics.

Findings

Models recover previous solutions in specific limits

Distribution functions are positive under certain conditions

Provides explicit expressions for physical parameters

Abstract

We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner (Phys. Plasmas 20, 102117, 2013) to allow for non-uniform density and temperature profiles. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al. (Phys. Plasmas 22, 112902, 2015). In one limit of the parameters, we recover the model of Kolotkov et al., while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk-flow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.