A family of Vlasov-Maxwell equilibrium distribution functions describing a transition from the Harris sheet to the force-free Harris sheet

TL;DR

This paper introduces a family of Vlasov-Maxwell equilibrium distribution functions that smoothly transition between Harris and force-free Harris sheets, addressing previous limitations and potential applications in space and astrophysical plasmas.

Contribution

It presents a new approach to model current sheet equilibria that overcomes earlier issues in the zero guide field limit, enabling a continuous transition between different magnetic configurations.

Findings

Successfully derived a family of distribution functions for intermediate current sheets.

Identified and resolved problems in previous models when guide field approaches zero.

Demonstrated potential applications to space and astrophysical plasma studies.

Abstract

We discuss a family of Vlasov-Maxwell equilibrium distribution functions for current sheet equilibria that are intermediate cases between the Harris sheet and the force-free (or modified) Harris sheet. These equilibrium distribution functions have potential applications to space and astrophysical plasmas. The existence of these distribution function had been briefly discussed in by Harrison and Neukirch 2009, but here it is shown that their approach runs into problems in the limit where the guide field goes to zero. The nature of this problem will be discussed and an alternative approach will be suggested that avoids the problem. This is achieved by considering a slight variation of the magnetic field profile, which allows a smooth transition between the Harris and force-free Harris sheet cases.