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

TL;DR

This paper extends permanent magnet optimization for stellarators by incorporating finite permeability and demagnetization effects, improving design accuracy and providing a practical framework for advanced magnetic field shaping.

Contribution

Introduces GPMOmr, a magnet optimization method that accounts for finite permeability and demagnetization, enhancing the accuracy and applicability of stellarator magnetic field design.

Findings

Finite-permeability effects cause small tilts and magnitude changes in magnets.

GPMOmr achieves similar error levels as classical GPMO with more nonuniform magnetization.

The method is fast, practical, and extends to higher field strengths and materials.

Abstract

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 introducing a block-level macromagnetic model that accounts 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 and modify the surface-normal field $\mathbf B\cdot\mathbf n$ only at the percent level, yet for a fixed layout they increase the standard squared-flux objective by more than a factor of two. When the same model is embedded in the greedy loop, GPMOmr achieves $f_B$ histories and final errors within a few percent of classical GPMO while producing visibly more nonuniform magnetization patterns. Our formulation provides a fast and practical tool for quantifying and incorporating finite-permeability effects in permanent-magnet stellarator designs, and offers a framework for extending permanent-magnet optimization to higher field strengths and to materials with stronger macromagnetic coupling.