Early-time currents induced on a cylinder by a cylindrical electromagnetic wave

An analytical study of the early-time current response of a perfectly conducting circular cylinder to a cylindrical electromagnetic wave, produced by a parallel filament carrying a unit-step current, is presented. Surface current density expressions for both the shadow and illuminated regions are obtained by applying the Watson transformation to the frequency-domain solution and then evaluating the corresponding integrals separately, in the shadow region by a residue series and in the illuminated region by using the saddle point technique. Analytical results obtained by using a double Laplace transform approach for the shadow region and the Luneberg-Kline expansion approach for the illuminated region are given. Numerical results illustrate the variation of the distribution of current density with time for different locations of the line current with respect to the cylinder, and also allows a comparison of the alternate methods applied by the authors, showing their corresponding range of validity. The response to an impulsive plane wave is derived as a special case