Magnetostatic reciprocity for MR magnet design

Electromagnetic reciprocity has long been a staple in magnetic resonance (MR) radio-frequency development, offering geometrical insights and a figure of merit for various resonator designs. In a similar manner, we use magnetostatic reciprocity to compute manufacturable solutions of complex magnet geometries, by establishing a quantitative metric for the placement and subsequent orientation of discrete pieces of permanent magnetic material. Based on magnetostatic theory and non-linear finite element modelling (FEM) simulations, it is shown how assembled permanent magnet setups perform in the embodiment of a variety of designs and how magnetostatic reciprocity is leveraged in the presence of difficulties associated with self-interactions, to fulfil various design objectives, including self-assembled micro-magnets, adjustable magnetic arrays, and an unbounded magnetic field intensity in a small volume, despite realistic saturation field strengths.