Point symmetries of 3D static plasma equilibrium systems: comparison and applications

TL;DR

This paper classifies point symmetries in static plasma equilibrium systems, revealing differences between isotropic and anisotropic cases, and introduces a Maple software tool for symmetry analysis to derive new solutions.

Contribution

It provides a complete classification of symmetries in static plasma equilibria and develops a Maple software package for symmetry and conservation law analysis.

Findings

No infinite point symmetries in static isotropic equilibria.

Static anisotropic equilibria have symmetries depending on one free function.

New exact solutions are obtained using symmetry analysis.

Abstract

Dynamic plasma equilibrium systems, both in isotropic and anisotropic framework, possess infinite-dimensional Lie groups of point symmetries, which depend on solution topology and lead to construction of infinite families of new physical solutions. By performing the complete classification, we show that in the static isotropic case no infinite point symmetries arise, whereas static anisotropic plasma equilibria still possess a Lie group of symmetries depending on one free function defined on the set of magnetic field lines. The finite form of the symmetries is found and used to obtain new exact solutions. We demonstrate how anisotropic axially- and helically-symmetric equilibria are obtained using conventional Grad-Shafranov and JFKO equations. A recently developed multifunctional automated Maple-based software package for symmetry and conservation law analysis is presented and used in this work.