Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

Designing an array of permanent magnets for stellarator plasma confinement entails solving an optimization problem with tens of thousands of degrees of freedom whose solution, for practical reasons, should be constrained to a discrete space. 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. The approaches are both applied to design arrays of 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 fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable with the second approach (up to a 30% reduction from the first approach) while exceeding the field accuracy of what either approach can achieve on its own.