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

Abstract A problem arising in several engineering areas is to design magnets outside a volume that produce desired magnetic field inside it. One instance of this stellarator design, where it has recently been shown permanent can provide the required shaping field. Here we demonstrate robust and efficient algorithm REGCOIL_PM calculate spatial distribution these magnets. The procedure involves small number fixed-point iterations, with linear least-squares solved at each step. method exploits Biot–Savart Law’s exact linearity magnetization density approximate magnet size, for far from target region. No constraint placed on direction magnetization, so Halbach solutions are found naturally, magnitude be made uniformly equal value.