Maximally efficient permanent magnet structures

A general theory is developed for determining the most efficient magnetic structure that generates a specified magnetic field. The structure is assumed to be composed of linear, isotropic magnetized material, occupying a given geometrical region. The efficiency is quantified by a figure of merit defined as the external field energy produced by the magnet divided by the maximum amount of energy that can be stored by the magnetized material. A set of equations is derived that determines the distribution of remanence needed to maximize this figure of merit, and several theorems concerning maximally efficient structures are given. Simple two-dimensional examples are used to illustrate the theory.