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A problem arising in several engineering areas is to design magnets outside avolume that produce a desired magnetic field inside it. One instance of thisproblem is stellarator design, where it has recently been shown that permanentmagnets can provide the required shaping of the magnetic field. Here wedemonstrate a robust and efficient algorithm REGCOIL_PM to calculate thespatial distribution of these permanent magnets. The procedure involves a smallnumber of fixed-point iterations, with a linear least-squares problem solved ateach step. The method exploits the Biot-Savart Law's exact linearity inmagnetization density and approximate linearity in magnet size, for magnets farfrom the target region. No constraint is placed on the direction ofmagnetization, so Halbach solutions are found naturally, and the magnitude ofthe magnetization can be made uniformly equal to a target value.

Calculation of permanent magnet arrangements for stellarators: A linear least-squares method