Symmetries, weak symmetries and related solutions of the Grad-Shafranov equation

TL;DR

This paper explores new solutions to the Grad-Shafranov equation using Lie symmetry methods, including weak symmetries, to model D-shaped plasma equilibria with sharp edge gradients.

Contribution

It introduces a novel family of solutions derived from symmetry analysis, expanding the understanding of plasma equilibrium configurations.

Findings

New family of solutions for the Grad-Shafranov equation

Identification of weak symmetries in plasma equilibrium modeling

Comprehensive survey of symmetry-admitting flux functions

Abstract

We discuss a new family of solutions of the Grad--Shafranov (GS) equation that describe D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of "weak" symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.