Analytical and discrete approaches for 3D magnetic field profiling

Abstract

Two methodologies are presented allowing to find the current density on a revolution surface to obtain a given 3D magnetic field distribution. The combination of the Biot-Savart law and the superposition theory is used to establish an algebraic relationship between the predefined magnetic field and the searched current density. Basically, two approaches are used: the continuous approach, in which the current density is modeled by an analytical function and the discrete method where the searched current density is given by a list of values that match a mesh of the magnet support. Furthermore, the use of the spherical harmonic development of the predefined magnetic field leads to a compact formulation of the inverse problem. The proposed matrix methodology has been developed for any magnet having a revolution axis (revolution magnets). A computer code which uses both approaches has been developed and gives good simulation results, which show an interesting prospects for new magnet design.