Discrete approach for 3D magnetic field profiling

The aim of this work is to propose a methodology for computing the current distribution able to produce a known magnetic field in a specified domain in the 3D free space. By combination of the Biot-Savart law and the superposition theorem, an algebraic relationship between the predefined magnetic field and the searched current density has been established. So, this inverse problem formulation provides the magnet modeling through its equivalent current density. The discrete approach consists in modeling this current density by a list of values corresponding to a mesh of the magnet support surface. Furthermore, the use of the spherical harmonic expansion of the predefined magnetic field leads to a compact formulation of the inverse problem. The proposed matrix methodology has been developed on any magnet having a revolution axis (conical magnets). The matrix shape of this general methodology permits to formulate and to solve the inverse problem with optimal criteria. A computer code, which uses both approaches, has been developed and applied to Magnetic Resonance Imaging (MRI) magnet design. This code leads to good simulation results, showing great opportunities to new magnet design.