Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design

TL;DR

This paper investigates the impact of manufacturing errors on stellarator coil performance and proposes an a-posteriori optimization method to significantly reduce these errors' effects, improving coil accuracy without altering shapes.

Contribution

It introduces a novel a-posteriori optimization approach for coil adjustments that effectively mitigates manufacturing errors in stellarator design.

Findings

Manufacturing errors cause noticeable performance degradation.

Stochastic optimization offers limited improvements.

A-posteriori adjustments reduce error impact by an order of magnitude.

Abstract

It was recently shown in [Wechsung et. al., Proc. Natl. Acad. Sci. USA, 2022] that there exist electromagnetic coils that generate magnetic fields which are excellent approximations to quasi-symmetric fields and have very good particle confinement properties. Using a Gaussian process based model for coil perturbations, we investigate the impact of manufacturing errors on the performance of these coils. We show that even fairly small errors result in noticeable performance degradation. While stochastic optimization yields minor improvements, it is not able to mitigate these errors significantly. As an alternative to stochastic optimization, we then formulate a new optimization problem for computing optimal adjustments of the coil positions and currents without changing the shapes of the coil. These a-posteriori adjustments are able to reduce the impact of coil errors by an order of magnitude, providing a new perspective for dealing with manufacturing tolerances in stellarator design.