Topology optimization for inverse magnetostatics as sparse regression: application to electromagnetic coils for stellarators

TL;DR

This paper introduces a novel topology optimization method for inverse magnetostatics, reformulating coil design as sparse regression to efficiently create electromagnetic coils for stellarator plasma experiments.

Contribution

It presents a convex, divergence-free current volume approach to magnetostatic topology optimization, enabling sparse regression formulation and coil design for stellarators.

Findings

Successfully designed topologically-exotic coils for stellarators

Demonstrated interpolation into filamentary coil representations

Optimized coils for multiple stellarator configurations

Abstract

Topology optimization, a technique to determine where material should be placed within a predefined volume in order to minimize a physical objective, is used across a wide range of scientific fields and applications. A general application for topology optimization is inverse magnetostatics; a desired magnetic field is prescribed, and a distribution of steady currents is computed to produce that target field. In the present work, electromagnetic coils are designed by magnetostatic topology optimization, using volume elements (voxels) of electric current, constrained so the current is divergence-free. Compared to standard electromagnet shape optimization, our method has the advantage that the nonlinearity in the Biot-Savart law with respect to position is avoided, enabling convex cost functions and a useful reformulation of topology optimization as sparse regression. To demonstrate, we consider the application of designing electromagnetic coils for a class of plasma experiments known as stellarators. We produce topologically-exotic coils for several new stellarator designs and show that these solutions can be interpolated into a filamentary representation and then further optimized.