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

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.