A differential magnetic permeability model for pulsed magnetic field calculations

Problems involving intense pulsed magnetic fields in soft ferromagnetic materials require the solution of nonlinear partial differential equations with a field-dependent relative differential permeability that must represent the major magnetic properties of the material over an extremely wide range of magnetic fields. With the assumption that hysteresis can be neglected, a simple mathematical model with two exponential terms is described in which four constants can be used to model the magnetic properties of interest in a given problem. The model is constrained to match the initial value, the maximum value, and the saturation flux density. The analysis presented here shows that there are limitations and that not all values of the magnetic properties can be accommodated simultaneously