Partially saturated ferromagnetic cylinders

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Abstract
The magnetostatics of a partially saturated ferromagnetic cylinder are calculated for the case where the susceptibility is infinite in the unsaturated region and Ms points along the direction of the internal field Hi for the saturated regions. The boundaries between the regions, the volume charge (∇⋅Ms) in the saturated regions and all the surface charges (n̂⋅M) are found by parameterization of the scalar potential, the surface charge distribution and the interfaces. The parameters are varied to minimize the deviation from Hi=0 in the unsaturated regions and the deviation from ∇⋅[H+4πMsH/‖H‖]=0 in the saturated region. Parameters, such as the distance between the interfaces, follow irrational powers of H0−Hs, where the saturation starts at the applied field H0=Hs. The results are found to explain the somewhat puzzling magnetic response of partially saturated iron whiskers.