Electromagnetic Pulse Transmission Through a Thin Sheet of Saturable Ferromagnetic Material of Infinite Surface Area

The symplectic finite difference time domain method

“…And the constitutive relations are (3) and (4) where and are permeability and permittivity, respectively. Variational formulations of Maxwell Equations in terms of the scalar and the vector potential and are well known.…”

“…Many such attempts to extend the FDTD method to higherorder methods [2], [3] or implicit methods [4] have been made. But they have not worked well because they destroyed the symplectic structure (energy, helicity, etc.)…”

Ferromagnetic Mitigation of Electromagnetic Pulse Effects

“…Although this earlier work clearly demonstrates the utility of ferromagnetic shields devised from off-the-shelf materials, a realistic understanding of the behavior of such shields is indeed lacking. This deficiency is principally due to the nonlinear nature of the problem which led earlier workers [1][2][3][4][5] to analytic solutions which oversimplify the magnetization processes involved. Such oversimplifications include models which assume constant or a limiting value of the magnetic permeability.…”

Shielded Enclosure Test Bed Requirement.

“…Analytical work 5 ' 6 has been done to calculate the effect of magnetic saturation on the propagation of a pulse through a flat sheet of infinite extent. Both experimental work and analytical modeling are required to extend the results to the case of saturation fields over a box-like shield.…”