Diffraction of a plane wave by a narrow cone

Abstract

We consider the problem of incidence of a plane waveupon an arbitrary cone Z (see Fig. 1). The wave propagates along the direction -w0. We have the boundary condition on the surface of the cone 07=,(~ is the differentiation in the direction of the external normal of E). We assume thatwhere u ~ is the wave scattered by the cone that satisfies the radiation conditions and the Maixner condition in a vicinity of the cone's vertex C. The wave Gdiff emerges as a result of the diffraction process. It has a spherical front centered at the cone vertex. There is a well known formula for Gdiff:where r is the distance between the point C and the point M(Xl, x2, xa) of observation, w is the unit vector with the same direction as the vector CM,