Radiation of a Point Charge Moving Uniformly over an Infinite Array of Conducting Half-Planes

Abstract

The excitation of an infinite array of parallel semi-infinite metallic plates by a uniformly moving point charge is studied by the Wiener-Hopf method. The problem is treated as a boundary-value problem for the potential of the induced electromagnetic field, and is formulated in terms of a dual integral equation for the current density induced on the plates. The solution of the dual integral equation gives exact expressions for the induced current density and the induced field in the form of Fourier integrals. The Poynting vector is calculated, and the radiation shows that the array of plates behaves both like a diffraction grating and a series of parallel-plate waveguides.