New Exact Plasma Equilibria with Axial and Helical Symmetry

TL;DR

This paper derives exact static plasma equilibrium solutions with axial and helical symmetry, discusses their physical restrictions, and extends some solutions to include non-zero fluid velocities, relevant for confined and vacuum plasmas.

Contribution

It introduces new exact solutions to plasma equilibrium equations for both axial and helical symmetries, including physical restrictions and velocity extensions.

Findings

Two families of solutions for different pressure profiles

Periodic radial dependence in vacuum solutions

Boundary magnetic fields described by current sheets

Abstract

Exact solutions to the static equilibrium magnetohydrodynamic equations are presented and discussed for both axially and helically reduced systems. For both symmetries, physical restrictions on the solutions are discussed and it is seen that there arise two different families of physical solutions corresponding to two distinct pressure profiles. One is suitable for atmospherically confined plasma whereas the other is suitable for plasma residing in a vacuum. For solutions in vacuum, the radial dependence is found to behave periodically for both axial and helical symmetries. For these physical solutions, only a truncated solution inside of some chosen domain can be considered. The magnetic field boundary can than be described by a current sheet. In the last part of the paper, these static equilibrium solutions are transformed into solutions with non-zero fluid velocity.