Analytic treatment of field diffusion into hysteretic magnetic materials

This paper reapproaches the very classic problem of the analytic study of nonlinear diffusion of electromagnetic fields in conducting media. Significant contributions that appeared in the literature on this topic are cited in order to highlight the interest and the efforts provided by the scientific community on this topic as well as the aim and the main results of this work. The capabilities of two analytic procedures for estimating the energy losses in magnetic materials with hysteresis are shown and discussed. One formulation reduces the full nonlinear diffusion problem to a linear problem through an optimization procedure and is suited for thick cores. A second formulation approximates the magnetic field behavior by means of polynomials and provides good results for thin laminations. Energy losses are evaluated for magnetic materials with different B-H relations operating in wide frequency intervals. A scalar Preisach model, numerically treated, is used as a benchmark and, finally, calculations are compared with experimental data provided by other authors.