On quasisymmetric plasma equilibria sustained by small force

TL;DR

This paper constructs smooth, nearly quasisymmetric plasma equilibria with nested flux surfaces under small forces, advancing understanding of three-dimensional magnetohydrostatic configurations.

Contribution

It introduces a method to create non-symmetric plasma equilibria with quasisymmetry by modifying the space's metric, solving a generalized Grad-Shafranov equation.

Findings

Existence of smooth, non-symmetric equilibria with nested flux surfaces.

Solutions are nearly quasisymmetric and valid under small forces.

Method applies to configurations close to Euclidean symmetry.

Abstract

We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the magnetohydrostatic (steady three-dimensional incompressible Euler) equations with a small force. The solutions are also `nearly' quasisymmetric. The primary idea is, given a desired quasisymmetry direction $\xi$, to change the smooth structure on space so that the vector field $\xi$ is Killing for the new metric and construct $\xi$--symmetric solutions of the magnetohydrostatic equations on that background by solving a generalized Grad-Shafranov equation. If $\xi$ is close to a symmetry of Euclidean space, then these are solutions on flat space up to a small forcing.