Ray theory of wave propagation in nonuniform refraction waveguides: Mode conversion and width build up for waveguide channels

Abstract

A ray approach to the description of conversion of normal modes in nonuniform sections of refraction waveguides is proposed. The introduction of discrete ray parameters in the waveguide (the coordinates of the lower and upper turning points of the ray) makes it possible to reveal the phenomenon of width build up of the waveguide channel. Analytic estimates are obtained for the amplitude of the width oscillations of the channel. Width build up for a symmetrical channel with a parabolic profile is illustrated by a numerical example. A simple estimate is obtained for the number of normal waves excited after a nonuniform section. Two effects are pointed out that can cause additional loss of the energy trapped in the wave channels (besides ordinary absorption). In the first place, there is "spilling" of rays from the channel as a result of width build up, if the waveguide is bounded by a relatively low barrier (as is the case of the betweenlayer FE channel in the ionosphere). Second, part of the primary wave energy may be transformed into modes with greater absorption, something that can be a significant factor for elf signals in the earth-ionosphere waveguide.