An adjoint method for gradient-based optimization of stellarator coil shapes

TL;DR

This paper introduces an adjoint method for efficient gradient-based optimization of stellarator coil shapes, improving coil properties and providing insights into engineering tolerances.

Contribution

It applies the adjoint method to the REGCOIL approach for stellarator coil design, enabling efficient computation of gradients and enhanced coil optimization.

Findings

Optimized coil shapes reduce normal magnetic field on plasma surface.

Winding surfaces show decreased curvature and increased coil-to-plasma distance.

Method improves engineering properties and offers sensitivity visualization techniques.

Abstract

We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for visualization of the sensitivity of figures of merit to normal surface displacement of the winding surface is presented, with potential applications for understanding engineering tolerances.