Induced currents on vibrating perfect surfaces under the illumination of electromagnetic waves: One-dimensional simulation

Abstract

One-dimensional numerical results of the induced currents on traveling and/or vibrating perfect conductor surfaces are presented in this report. The computational data are obtained using the method of characteristics with the application of the characteristic variable boundary conditions and the relativistic boundary conditions. The perfect plane may travel at a constant speed and/or vibrate sinusoidally or in zigzag with a constant frequency and a constant amplitude. The Doppler effects on both magnitude and frequency of induced currents were investigated by comparing computational results with the theoretical double-Doppler shift values. Good agreements were found. It is also found that when conductor travels and vibrates simultaneously, modulation on the magnitude of induced current is dependent on the combined instantaneous velocity while that on frequency is on the translational velocity. The scattering of electromagnetic waves from perfectly conducting objects in motion has been attracting significant attentions of many researchers since the 60s. This arouse from the need of knowledge for such as target identification. Kleinman and Mack (1), Cooper (2), and Harfoush et al. (3) developed analytical expressions for the electromagnetic wave scattering by either moving or vibrating bodies with the following conclusions. Object undergoing translational motion results in double-Doppler shifts in the reflected fields. An oscillating perfect electric conductor changes both phase and magnitude of the scattered fields. Though theoretical studies are available, the objective of the present effort is to develop an accurate numerical approach for electromagnetic scattering problems. The validation of the present numerical technique is carried out by the comparison of computational results with analytical values. Among variety of computational methods that provide numerical approximations to the solutions of the scattering of electromagnetic waves, the method of moment (MoM) and the finite-difference time-domain (FDTD) technique are the two most popular approaches. The method of characteristics is a recently developed numerical solver for like purpose. Whitfield and Janus applied the method of characteristics to solve fluid dynamic problems in the early 80s (4). By incorporating the explicit centered finite-difference scheme into the method of characteristics, Shang directly approximates the time-domain Maxwell curl equations (5) in the early 90s. In reference (6), the method of characteristics was formulated as an implicit numerical solver and found to have good agreement with the FDTD method. In contrast to the FDTD method where fields are allocated at node points, in the method of characteristics all field variables