Finite Length Cylindrical Scatterer Near Perfectly Conducting Ground-A Transmission Line Mode Approximation

A Pocklington type integro-differential equation, possessing an exact kernel, is formulated in terms of a complex frequency for the current induced on a thin finite-length cylindrical scatterer which is above, near, and parallel to a perfectly conducting ground plane. The circumferential variation of the axial current is assumed to be described by a transmission line mode approximation when the scatterer is near the ground plane. The integro-differential equation is reduced to a system of algebraic matrix equations through application of the method of moments. The singularity expansion method is utilized to determine the transient current response of the cylindrical scatterer to a unit step incident plane wave. Complex natural frequencies, natural mode vectors, nonnalization coefficients, and induced currents are compared to those found through a similar procedure with an approximate kernel, which assumes uniform circumferential variation of the axial current. The exact kernel with an assumed circumferential variation of the axial current is shown to be necessary when the thin cylindrical scatterer is near the ground plane.