Volume minimization for permanent-magnet structures

A method for designing permanent-magnet structures that minimizes the volume of magnetic material is described. The desired characteristics of the magnetic field are specified by a set of M linear constraints. This paper shows that minimum volume configurations can be determined by solving a system of M+1 nonlinear equations. A key feature of the method is that it always produces a global minimum. The methodʹs use is illustrated by the design of a helical undulator for a free-electron laser.