MHD equilibria with incompressible flows: symmetry approach

TL;DR

This paper explores a family of symmetric, incompressible MHD plasma equilibria with flows, derived using symmetry methods applied to the generalized Grad-Shafranov equation, revealing new solution structures.

Contribution

It introduces a novel approach to find plasma equilibrium solutions by exploiting Lie symmetries and incompressibility assumptions in the GGS equation.

Findings

Derivation of new equilibrium solutions with azimuthal symmetry.

Application of symmetry methods to simplify the GGS equation.

Identification of special 'weak' symmetries in plasma equilibria.

Abstract

We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and in particular a special type of "weak" symmetries.