Identification of an Arbitrary-Surface Harmonic Magnetic Model from Close Measurements

Decreasing spherical harmonic functions are widely used to identify and extrapolate the magnetic field produced by various devices. These functions are equivalent to a multipolar decomposition which orders the field according to its spatial decreasing rate. However this representation is not valid inside the Brillouin sphere, the smallest sphere enclosing the device. We introduce here the use of an alternative representation to replace the spherical harmonic functions when the measurement are inside the Brillouin sphere. This representation uses a basis of equivalents charges on a surface to reproduce the multipolar decomposition while being valid inside the Brillouin sphere. We demonstrate here the ability of this model to identify and extrapolate the field from very close measurements.