Permanent magnet optimization of stellarators with coupling from finite permeability and demagnetization effects

Permanent magnets provide an attractive path for shaping university-scale stellarator magnetic fields. Previous work has shown that greedy permanent magnet optimization (GPMO) can produce sparse, grid-aligned arrays that match target surfaces with high accuracy under an ideal rigid-remanence model. Here, we extend this approach to a greedy permanent magnet optimization with macromagnetic refinement (GPMOmr) by accounting for magnet–magnet and magnet–coil coupling from finite permeability and demagnetizing interactions, and apply it to the published magnet grid from the MUSE stellarator design. Finite-permeability effects produce degree-scale tilts and few-percent magnitude changes in individual magnets. When the same model is embedded in the greedy loop, GPMOmr achieves final errors within a few percent of the uncoupled GPMO code, while producing more nonuniform magnetization patterns. Our formulation provides a fast and practical tool for quantifying and incorporating finite-permeability and other coupling effects in permanent-magnet stellarator designs, and offers a framework for extending permanent-magnet optimization to higher field strengths and to materials with stronger coupling.