Minimax Current Density Coil Design

Introduction Gradient and shim coils are required to generate a magnetic field of particular spatial form when energised with electric current. The design of these coils is a well studied inverse problem [1] that is inherently ill-conditioned with an infinite number of solutions. In order to obtain a single solution, the system must be regularised, which is commonly achieved by minimising the stored energy or power dissipation of the coil [1]. In some cases, this results in a solution that possesses regions of high current density. This may cause problems with construction, localised heating and maximum field strength. In this work we design coils with minimum, maximum current density magnitude, or minimax|j|.