Adjoint methods for quasisymmetry of vacuum fields on a surface

TL;DR

This paper introduces adjoint methods to efficiently optimize vacuum magnetic fields for stellarators, focusing on quasisymmetry and rotational transform, with a novel flux coordinate evaluation technique.

Contribution

It applies adjoint methods to vacuum fields for the first time, providing a new approach to measure quasisymmetry without assuming flux surface neighborhoods.

Findings

Shape gradients verified against finite differences

Efficient gradient computation demonstrated

Novel flux coordinate evaluation method proposed

Abstract

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared to finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasisymmetry and a rotational transform value on a surface. To measure quasisymmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.