Transient radiation in a plane stratified dispersive medium. II. Exponential profile, plasma slab, and plasma gap

Abstract

In a previous paper by the authors, a similarity principle was derived for a class of transient diffraction problems in cold, lossless, isotropic, plane stratified plasmas. In this paper, the similarity principle will be utilized to obtain exact closed-form solutions to three specific problems; the problems of an impulsive point magnetic dipole (the current density is a delta function in space and time) in the presence of (1) a continuously varying plane stratified plasma with an exponential electron density profile, (2) a grounded plasma slab, and (3) a grounded plasma gap. In the case of the exponential electron density profile, the solution to the problem suggests a new type of approximation to cases where the profile is slowly varying but otherwise arbitrary. In the case of the slab and gap problems an interpretation will be given in terms of multiply-reflected rays within the slab. The gap problem is particularly interesting because, if the impulsive time dependence of the source were replaced by a harmonic time dependence, this problem would be distinguished by the presence of a surface wave. Thus an examination of the gap problem serves to illustrate the role played by the surface wave in the transient case.