Nonlinear diffusion and internal voltages in conducting ferromagnetic enclosures subjected to lightning currents

The voltage inside a conducting ferromagnetic enclosure, excited by direct attachment of lightning, is determined. A nonlinear approximate model is constructed and solved analytically to model the magnetic field diffusion through the enclosure wall excited by a filament current. This model gives the internal voltage waveform (at very early times it forms a rough approximation to the solution). The solution (including the early time behavior) for an attached current carrying conductor of large radius is also given. The model is constructed by use of known nonlinear saturation front theory. The paper also considers nonnegligible magnetic flux behind the saturation front (in the saturated region), and shows that this saturated flux results in a simple additive time shift to the penetration of the front