Fields near a caustic and cusp in an isotropic ionosphere

Abstract

A previous paper showed that 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 which some focusing of the rays occurs. Two branches of the caustic surface can meet in a cusp where the focusing is even greater. The field strength at a point distant from these focusing regions within or below the ionosphere is now found by applying the method of steepest descents to the integral that expresses the field as an angular spectrum of plane waves. The result is equivalent to the use of a simple ray theory. A method is then given for finding the field strength near a caustic or cusp where ray theory fails. Some examples for two different model ionospheres are presented and discussed. Some possible practical consequences are reviewed.