Analytic approach to creating homogeneous fields with finite-size magnets

TL;DR

This paper develops analytic solutions for three-dimensional arrangements of finite-size magnets to generate more homogeneous magnetic fields, improving upon classical Halbach arrays with experimental validation.

Contribution

It introduces optimal 3D configurations for finite magnets, surpassing traditional Halbach designs in field strength and homogeneity, with explicit formulas and experimental tests.

Findings

Optimized arrangements outperform classical Halbach arrays.

Analytic formulas enable precise design of magnetic configurations.

Experimental results confirm theoretical improvements.

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.