Linear and nonlinear EMP diffusion through a ferromagnetic conducting slab

The penetration of an EMP field, such as a plane-wave incident upon and a surge-arrestor current terminated at a shielding plate, through a ferromagnetic conducting slab made of iron or steel is investigated. The diffusion of the electromagnetic field in the highly conducting slab is complicated by the presence of the nonlinear saturation of the ferromagnetic permeability\mu, due to the large amplitude of the incident EMP. Such a saturation, compared to the no-saturation constant\mucase, makes the field diffuse faster in the slab and admits a stronger penetration field inside the shielding if the slab is thin and the pulse duration is long, as expected. On the contrary, if the slab is thick and the puslewidth is short, as the practical cases are, the saturation reduces the penetrated field but maintains its time shape. In this report, first we solve analytically the one-dimension plane-wave incidence problem for a slab with a constant\mu. Then we use the results to partly predict and to interpret the numerical values obtained by using a finite difference code for the case of a nonlinear\mu. These comparisons reveal excellent agreement. Second, we solve the constant\mu, cylindrical-wave incidence problem by an approximate but extremely useful analysis, with its validity parameters clearly established. The results, shown to bear a simple relationship to those for the one-dimension problem, enable one to make use of the one-dimension results and predict easily the penetrated fields caused by a cylindrical incident current. Then for the nonlinear-\mucase, we justify and extend that relationship by which the behaviors of the cylindrically diffused fields are obtained from those numerical results of the one-dimensional problem.