Chapter 3 - Infinite Conducting Cylinders: TDIE Solution

Abstract

This chapter discusses the numerical solution methods to solve the time domain (TD) integral equation for infinitely long, conducting cylinders of arbitrary cross-section illuminated by a Gaussian plane wave pulse. The chapter considers both the transverse magnetic (TM) and transverse electric (TE) solutions to this problem. The solution to the infinite cylinder problem, also popularly known as a two-dimensional problem, provides a precursor for the more difficult three-dimensional finite body solution. Here, we use simple square patches to model the surface of the cylinder. For this purpose, the contour of the cylinder by straight line segments is first approximated. Then, the length of the cylinder is divided in a similar manner to develop the square patches. Details of the modeling are discussed further in the chapter. The numerical solution procedure is obtained using the well-known method of moments (MoM). In the following sections, the mathematical equations to calculate the current at a certain time instant as a function of currents of past instances and the incident field are derived. The electric field integral equation (EFIE), obtained by enforcing the boundary condition on the tangential component of the electric field, is used for both TM and TE incidence. The chapter also discusses the magnetic H-field integral equation (HFIE) obtained by enforcing the boundary condition on the magnetic field for TE incidence whose solution is useful in dealing with dielectric scatterers.