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 allow to represent the sources as equivalent multipoles whose order is associated with a specific 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 model to replace the spherical harmonic functions when the measurements are inside the Brillouin sphere. This representation corresponds to a harmonic basis of equivalent charges on a surface that reproduces the multipolar decomposition of the magnetic field outside the Brillouin sphere while being valid inside. We demonstrate here the ability of this model to identify and extrapolate the field from very close measurements.