Surface fields excited by a vertical electric point source located on a conducting concave spherical surface

With the appearance of dome antenna in recent years, the necessity for analyzing the electromagnetic fields produced by a wave source placed on the concave side of a solid conducting surface has arisen. Some research on this problem for a conducting concave cylindrical surface has beem reported. However, no research which is of practical importance, has been conducted on the concave sphere. This paper describes the result of an analysis of the surface magnetic field produced by an electric point source placed on the concave side of an open conducting sphere. The analytical technique is based on the case of a concave cylindrical surface. First, a wave component traveling along the boundary is obtained from a representation of the field inside a closed conducting sphere and the field representation for an open sphere is derived. Next, the surface magnetic field for the case where the radius of the sphere is sufficiently large compared to the wavelength is represented in the form of the fields of geometrical optics and integrals. As in the cylindrical case, the result of concrete calculation shows that the resulting field agrees with the field near the wave source in the case of a vertical electric point source placed on an infinite ground plane and that a complicated interfering pattern is produced at a distance far from the wave source. Also, the appropriateness of this analytical result is confirmed through an experimental study.