Abstract
When rays from a point transmitter enter a horizontally stratified inhomogeneous ionosphere they comprise a family of curves, whose envelope is a caustic surface. Near it, adjacent rays cross, and the ‘ray density’ is large so that there is some focusing, sometimes called edge focusing. 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 within and below an isotropic ionosphere is found by applying the method of stationary phase to the integral that expresses the field as an angular spectrum of plane waves. It is shown how the parameters of the caustic and cusp can be related to the ionospheric model and some examples are presented. For a loss free ionosphere the caustics and cusps occur at real heights. When collisions are included they are at complex heights.
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