A Family of One-Dimensional Vlasov-Maxwell Equilibria for the Force-Free Harris Sheet

TL;DR

This paper introduces a new family of collisionless distribution functions for the force-free Harris sheet, expanding previous models and demonstrating they produce identical magnetic field configurations under certain conditions.

Contribution

It presents a generalized family of distribution functions for the force-free Harris sheet, including known and new variants with different energy dependencies.

Findings

New distribution functions produce the same pressure and magnetic field as known models.

The family includes the Harrison and Neukirch distribution function as a special case.

Examples illustrate how to construct and apply these functions.

Abstract

A family of self-consistent collisionless distribution functions for the force-free Harris sheet is presented. This family includes the distribution function recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)] as well as distribution functions with a different dependence on the particle energy, but with the same dependence on the canonical momenta. It is shown generally that the other distribution functions in the family give rise to the same pressure function and thus to the same current density and magnetic field as the known distribution function, provided certain conditions on the parameters are satisfied. A number of examples of distribution functions from the new family are given, which illustrate the use of the general method.