Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field

TL;DR

This paper derives exact collisionless plasma equilibria for flux tubes combining the Gold-Hoyle model with a background field, revealing conditions for force-free states and potential applications in astrophysics and laboratory plasmas.

Contribution

It provides the first exact solutions for plasma equilibria with a combined flux tube and background magnetic field, including neutral and non-neutral configurations.

Findings

Exact solutions to Poisson's and Ampère's equations for these equilibria.

Conditions under which the magnetic field reverses at finite radius.

Equilibria applicable to solar, space, and laboratory plasmas.

Abstract

We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly force-free, but by reducing its magnitude the departure from force-free can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's Equation and Amp\`{e}re's Law are solved exactly, and the solution allows either electrically neutral or non-neutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space and astrophysical contexts, as well as in the laboratory.