Caustics and cusps in an isotropic ionosphere

Physics

Scientific paper

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Ionospheric Propagation, Radio Wave Refraction, Ray Tracing, Cusps, Isotropic Media, Radiant Flux Density, Radiation Distribution, Radio Signals

Scientific paper

The paper shows how to locate caustics and cusps in a horizontally stratified isotropic ionosphere and to describe their basic properties, which is of great significance in calculating the strength of the signal received from a radio transmitter either at a point within the ionosphere or in the free space below it. Some specific simple examples are given, and the effects of the earth's curvature, geomagnetic field, and electron collisions are mentioned. Two caustic surfaces can meet in a singularity which is a cusp where the ray focusing is even greater than near a simple caustic. The equation of these focusing regions is found by applying the method of stationary phase to the integral expressing the field in the ionosphere as an angular spectrum of plane waves. A discussion of the phenomenon of skip distance indicates that for some electron distributions there can be a reversed skip and a second cusp, where the two cusps can coalesce under certain conditions. Caustic-cusp configurations are classified using the number of real rays reaching a given point. For a loss-free ionosphere the caustics and cusps occur at real heights.

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