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A common optimization problem in the areas of magnetized plasmas and fusionenergy is the design of magnets to produce a given three-dimensional magneticfield distribution to high precision. When designing arrays of permanentmagnets for stellarator plasma confinement, such problems have tens ofthousands of degrees of freedom whose solutions, for practical reasons, shouldbe constrained to discrete spaces. We perform a direct comparison between twoalgorithms that have been developed previously for this purpose, anddemonstrate that composite procedures that apply both algorithms in sequencecan produce substantially improved results. One approach uses a continuous,quasi-Newton procedure to optimize the dipole moments of a set of magnets andthen projects the solution onto a discrete space. The second uses an inherentlydiscrete greedy optimization procedure that has been enhanced and generalizedfor this work. The approaches are both applied to design arrays cubicrare-Earth permanent magnets to confine a quasi-axisymmetric plasma with amagnetic field on axis of 0.5 T. The first approach tends to find solutionswith higher field accuracy, whereas the second can find solutions withsubstantially (up to 30%) fewer magnets. When the approaches are combined, theycan obtain solutions with magnet quantities comparable to the second approachwhile exceeding the field accuracy of what either approach can achieve on itsown.

Improved stellarator permanent magnet designs through combined discrete and continuous optimizations