Optimization of the Magnetic Field Produced by Frustum Permanent Magnets for Single Magnet and Planar Halbach Array Configurations

Abstract

The potential benefits of frustum-shaped magnets over cuboidal magnets have been seldom studied. This article compares these magnet shapes by optimizing frustum geometry for both a single magnet and a multi-magnet planar Halbach array to produce a desirable field. This field is compared to the equivalent field for optimized cuboidal magnets and differences quantified. A single magnet is considered, where the field strength above the center of a magnet is maximized. If the field is measured close to the magnet surface, an optimized frustum magnet can produce a field stronger than an optimized cuboidal magnet. If the field is measured further from the magnet, there is little benefit in using a frustum magnet over a cuboid. In addition, a planar magnet array is considered, in which the field strength and how closely the field resembled a sinusoidal profile are maximized. In this case, no significant benefit is observed using frustum magnets over cuboidal magnets.