Electromagnetic response of thin wires over an homogeneous earth.

Abstract

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.