Studies In Radar Cross Sections Xlvi The Convergence Of Low Frequency Expansions In Scalar Scattering By Spheroids

For the scalar problem of the diffraction of a plane wave by a spheroid the exact solution is known, and at low frequencies the expression for the far field amplitude can be expanded in a series of increasing positive powers of ka, where k is the wave number and 2a is the interfocal distance. This is the Rayleigh series, and is convergent for sufficiently small values of ka. To determine the range of frequencies for which this expansion is applicable an essential factor is the radius of convergence, and the discussion is devoted entirely to the calculation of this quantity. Attention is concentrated on the case in which the plane wave is incident nose-on, and the radius of convergence is obtained as a function of the length-to-width ratio for prolate and oblate spheroids, hard as well as soft. For other angles of incidence it can be shown that the radius is not greater than this, and in most instances it would appear to be the same. (Author).