Discretized Halbach spheres: Icosahedral symmetry for optimal field homogeneity

TL;DR

This paper explores discretized Halbach spheres with icosahedral symmetry, demonstrating they can produce highly homogeneous magnetic fields with larger usable volumes than traditional designs, suitable for portable applications.

Contribution

It introduces a practical method for assembling highly homogeneous magnetic fields using discrete icosahedral magnet arrays, advancing portable magnetic resonance and magnetophoretic technologies.

Findings

Icosahedral symmetry yields optimal field homogeneity and strength.

Homogeneous regions of several cubic centimeters with deviations below 1%.

Discretized magnet arrays outperform traditional Halbach configurations in accessible volume.

Abstract

Halbach spheres provide a theoretically elegant means of generating highly homogeneous magnetic fields, but practical implementation is hindered by challenging fabrication and restricted interior access. This study examines discrete spherical Halbach configurations assembled from permanent magnets placed at the vertices of Platonic and Archimedean solids. Analytical calculations, numerical field simulations, and experimental measurements indicate that polyhedra with icosahedral symmetry achieve the most favorable balance among field strength, homogeneity, and interior accessibility. They produce exceptionally flat fourth-order central saddle points, resulting in a usable homogeneous field volume up to a factor of 260 larger than that of traditional Halbach disk or cylindrical arrays. Several magnet assemblies composed of cubical NdFeB magnets are fabricated and their three dimensional field distributions characterized, demonstrating homogeneous regions of up to several cubic centimeters with deviations below 1%. The findings establish discrete icosahedrally symmetric magnet arrays as practical, scalable building blocks for compact, highly homogeneous magnetic field sources suited to mobile magnetic resonance, and magnetophoretic applications.