Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

TL;DR

This paper compares and combines continuous and discrete optimization algorithms to design permanent magnet arrays for stellarator plasma confinement, achieving improved magnetic field accuracy and reduced magnet count.

Contribution

It introduces a combined optimization approach that leverages both continuous and discrete algorithms for better magnet array design in stellarators.

Findings

Combined methods yield solutions with fewer magnets and high field accuracy.

Sequential optimization improves magnetic field precision.

Hybrid approach balances magnet quantity and field fidelity.

Abstract

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. We perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. One approach uses a continuous, quasi-Newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. The second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. The approaches are both applied to design arrays cubic rare-Earth permanent magnets to confine a quasi-axisymmetric plasma with a magnetic field on axis of 0.5 T. The first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially (up to 30%) fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.