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 i n the 3D free space. By combination of the Biot-Savart law and the superpos ition theorem, an algebraic relationship between the predefined magnetic fi eld and the searched current density has been established. So, this inverse problem formulation provides the magnet modeling through its equivalent cu rrent density. The discrete approach consists in modeling this current dens ity by a list of values corresponding to a mesh of the magnet support surfa ce. Furthermore, the use of the spherical harmonic expansion of the predefi ned magnetic field leads to a compact formulation of the inverse problem. T he proposed matrix methodology has been developed on any magnet having a re volution axis (conical magnets). The matrix shape of this general methodolo gy permits to formulate and to solve the inverse problem with optimal crite ria. A computer code, which uses both approaches, has been developed and ap plied to Magnetic Resonance imaging (MRI) magnet design. This code leads to good simulation results, showing great opportunities to new magnet design.