A detailed investigation of the properties of a Vlasov-Maxwell equilibrium for the force-free Harris sheet

TL;DR

This paper thoroughly analyzes the Vlasov-Maxwell equilibrium of the force-free Harris sheet, focusing on the distribution function's properties, parameter dependence, and potential stability implications.

Contribution

It provides a detailed derivation and analysis of the distribution function for the force-free Harris sheet, highlighting its parameter dependence and stability considerations.

Findings

Distribution function can be single-peaked or multi-peaked.

Shape of the distribution function depends on parameters.

Implications for stability and current sheet thickness.

Abstract

A detailed discussion is presented of the Vlasov-Maxwell equilibrium for the force-free Harris sheet recently found by Harrison and Neukirch (Phys. Rev. Lett. 102, 135003, 2009). The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be single-peaked or multi-peaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.