Scattering of electromagnetic fields by a moving boundary: The one-dimensional case

The scattered field is studied that results when a plane wave is normally incident on a perfectly conducting flat plate in motion. The exact solution is analyzed for both periodic and aperiodic motion. The quasi-stationary approximation is compared with the exact solution, and the error is found to be on the order ofβ = υMc⁻¹whereυMis the maximum speed of the moving boundary andcis the speed of light. This error estimate includes a factor which increases as the distance from the plate increases. A uniform quasi-stationary approximation is developed which has an error on the order of of the space variable. By taking into account the Doppler shift, it is possible to construct a uniform approximation to the exact solution on the order ofaMc⁻²whereaMis the maximum acceleration of the boundary.