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

Citation

Lam, John Ling-Yee (1967) Radiation of a Point Charge Moving Uniformly Over an Infinite Array of Conducting Half-Planes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1BR2-6A78. https://resolver.caltech.edu/CaltechETD:etd-09252002-122649

Abstract

The problem of 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. It is treated as a boundary value problem for the potentials of the diffracted electromagnetic fields. The formulation of this problem makes use of the well-known conditions on the electromagnetic fields at a metallic boundary. A method is used to translate these boundary conditions on the fields into boundary conditions on the potentials. In this way the problem is formulated in terms of a set of dual integral equations for the current densities induced on the plates by the point charge. These integral equations are exactly soluble by the Wiener-Hopf technique. The solutions are found to satisfy the famous edge conditions for diffraction problems, and are therefore unique. From these solutions exact expressions for the diffracted fields are derived in the form of Fourier integrals. It is seen that these fields represent a radiation of electromagnetic energy. The method of steepest descent is then used to obtain expressions for the radiation fields, the Poynting vector, the frequency spectrum and the radiation pattern. The radiation shows that the array of plates behaves both like a diffraction grating and a series of parallel-plate waveguides.

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