Target-field design of surface permanent magnets

We present a target-field approach to analytically design magnetic fields using permanent magnets. We assume that their magnetization is bound to a two-dimensional surface and is composed of a complete basis of surface modes. By posing the Poisson’s equation relating the magnetic scalar potential to the magnetization using Green’s functions, we derive simple integrals that determine the magnetic field generated by each mode. This approach is demonstrated by deriving the governing integrals for optimizing axial magnetization on cylindrical and circular-planar surfaces. We approximate the governing integrals numerically and implement them into a regularized least-squares optimization routine to design permanent magnets that generate uniform axial and transverse target magnetic fields. The resulting uniform axial magnetic field profiles demonstrate more than a tenfold increase in uniformity across equivalent target regions compared to the field generated by an optimally separated axially magnetized pair of rings, as validated using finite element method simulations. We use a simple example to examine how two-dimensional surface magnetization profiles can be emulated using thin three-dimensional volumes and determine how many discrete intervals are required to accurately approximate a continuously varying surface pattern. Magnets designed using our approach may enable higher-quality bias fields for electric machines, nuclear fusion, fundamental physics, magnetic trapping, and beyond.