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Electromagnetic shielding by thin, perfectly conducting, two dimensional cylindrical shells over a lossy earth is investigated. The temporal frequency response of the exterior field due to a line source within the shell is computed for a shell described by a three sided, rectilinear structure whose opening faces the earth. The formulation allows shells of arbitrary cross-sectional shape to be analyzed. The earth is modeled as a homogeneous half-space with a planar boundary and frequency dependent electromagnetic properties. Two solution techniques are presented. In the first, the induced current is obtained through a numerical solution of the electric field integral equation (EFIE) at many discrete frequencies. It is found that the applicability of this formulation is limited since in the case of effective shielding, fields calculated from the EFIE are very sensitive to numerical errors. In the second technique the EFIE is again solved for the currents induced on the shell. The induced currents are used to calculate the electric field in the aperture which is used to solve a combined-source integral equation (CSIE) for the external fields. It is found that the CSIE does not suffer from the numerical ill-conditioning that plagues the EFIE, and is well behaved at all frequencies. Numerical results are presented which indicate that the shell-earth combination is very effective in shielding the internal source. Interior modes are weakly transmitted to the interior for the case of a purely dielectric earth. For a lossy half-space the resonances of the closed shell are enhanced. The related topic of scattering by perfectly conducting objects over a lossy earth is addressed. Numerical formulations for the solution of the integral equations are presented which deal with several troublesome aspects of the problem, including the incorporation of the correct edge singularities.

The electromagnetic response of infinitely long, thin wires over a flat earth is presented for two different applications: the shielding properties of an ensemble of parallel wires excited by a plane wave and the electromagnetic coupling of two perpendicular wires excited by a dipole. The shielding study begins with the formulation of the boundary value problem for N wires over a lossy half space. A suitable axial impedance operator is applied to obtain a system of equations whose unknowns are the currents flowing on each wire. Once the currents are determined, the aggregate field produced by the ensemble can be computed by summing N Fourier type integrals. For the specialized case of the infinite planar grid, Floquet's Theorem and Poisson's Summation Formula are invoked, transforming the linear system of equations into a closed form expression for the current flowing on each wire. We show that the electromagnetic response of the planar grid of finite extent and the grid of infinite extent are similar. For non-planar configurations, such as the semi-circular shell, shielding values of 60 dB are possible when the structure is of non-resonant dimensions; otherwise, the performance can degrade to 20 dB. In the case of the crossed wire configuration, the starting point is the development of the integral equations that govern the coupling between wires and the source; the unknowns are the spectral currents flowing in each wire. The equations are given in terms of generalized impedance functions for the situation where the wires are over a stratified earth. However, for the numerical work, only the case where the wires are in an unbounded, homogeneous medium is considered. Two numerical methods, with overlapping regions of validity, are applied: the method of moments and the method of multiple scatterers. By using the method of moments, we can obtain a matrix equation that will determine the spectral currents for any wire spacing. The multiple scatterer method leads to a more convenient matrix series solution and shows that the coupling strength is proportional to 1/d², where d is the wire separation, plus higher order inverse terms.

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