Existence of weakly quasisymmetric magnetic fields in asymmetric toroidal domains with non-tangential quasisymmetry

TL;DR

This paper proves the existence of weakly quasisymmetric magnetic fields in asymmetric toroidal domains, providing explicit examples that could inform the design of advanced stellarator fusion reactors.

Contribution

It offers the first mathematical proof of weakly quasisymmetric magnetic fields by constructing explicit solutions tailored to fulfill quasisymmetry in complex geometries.

Findings

Constructed explicit weakly quasisymmetric magnetic field examples

Solutions are smooth with nested flux surfaces and non-vanishing current

Fields exhibit non-tangential quasisymmetry in asymmetric toroidal domains

Abstract

A quasisymmetry is a special symmetry that enhances the ability of a magnetic field to trap charged particles. Quasisymmetric magnetic fields may allow the realization of next generation fusion reactors (stellarators) with superior performance when compared with classical (tokamak) designs. Nevertheless, the existence of such magnetic configurations lacks mathematical proof due to the complexity of the governing equations. Here, we prove the existence of weakly quasisymmetric magnetic fields by constructing explicit examples. This result is achieved by a tailored parametrization of both magnetic field and hosting toroidal domain, which are optimized to fulfill quasisymmetry. The obtained solutions hold in a toroidal volume, are smooth, possess nested flux surfaces, are not invariant under continuous Euclidean isometries, have a non-vanishing current, exhibit a direction of quasisymmetry that is not tangential to the toroidal boundary, and fit within the framework of anisotropic magnetohydrodynamics.