Analytic approach to creating homogeneous fields with finite-size magnets
Phys. Rev. Applied 23, 064029 – Published 11 June, 2025
DOI: https://doi.org/10.1103/9nnk-jytn
Abstract
Homogeneous magnetic fields can be generated through the strategic arrangement of permanent magnets. The Halbach array serves as a prominent example of an effective design following this principle. However, it is a two-dimensional approach because it is optimal when placing infinitely long magnets—line dipoles—on a circle. If shorter, more realistic magnets are to be used, the optimal arrangement of magnetic moments diverges from the classical Halbach geometry. This paper presents optimal solutions for three-dimensional arrangements calculated for point dipoles, including optimized orientations for single rings and stacks of two rings. They are superior to the original Halbach arrangement and a modification described in the literature, both in terms of the strength and the homogeneity of the magnetic field. Analytic formulae are provided for both cases and tested by experimental realizations.
