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

References in corpus (6)

• An improved current potential method for fast computation of stellarator coil shapes
• New method to design stellarator coils without the winding surface
• Stellarators with permanent magnets
• Designing stellarators using perpendicular permanent magnets
• Geometric concepts for stellarator permanent magnet arrays
• A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation

Cited by in corpus (9)

• A quasi-isodynamic configuration with good confinement of fast ions at low plasma $\beta$
• Combined plasma-coil optimization algorithms
• Permanent magnet optimization for stellarators as sparse regression
• Greedy permanent magnet optimization
• Design of an arrangement of cubic magnets for a quasi-axisymmetric stellarator experiment
• Improved stellarator permanent magnet designs through combined discrete and continuous optimizations
• Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary
• A framework for discrete optimization of stellarator coils
• Permanent magnet optimization of stellarators with coupling from finite permeability and demagnetization effects