Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry

TL;DR

This paper introduces a robust bilevel optimization algorithm for designing electromagnetic coils that produce magnetic fields with nested flux surfaces and precise quasi-symmetry, effectively healing islands and chaos.

Contribution

The novel method combines outer coil optimization with inner magnetic surface identification, enabling the design of coils with improved nested flux surfaces and quasi-symmetry, even from cold-start initial conditions.

Findings

Successfully heals magnetic islands and chaos.

Optimizes quasi-symmetry up to aspect ratio 6.

Reduces flux surface aspect ratio from 6 to 4.

Abstract

We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least-squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two stage coil design process, as well as coils from a near axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. The last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization.