Numerical Solution of the “Ellis Window” Problem

Abstract

THE technique of complex ray tracing for studying problems of radio wave propagation in the ionosphere has recently been put forward1,2. A particular application of this technique is the determination of the angular diameter of the “Ellis window”. Ellis3, 4 investigated the conditions under which an upgoing ordinary wave is converted, through a coupling process, into an upgoing extraordinary wave in the Z mode. This occurs for a radio wave incident on the ionosphere from below with its wave normal close to a critical direction which is in the magnetic meridian plane at an angle θc to the vertical. Here sin θcl{Y/(Y+1)}1/2 where l is the sine of the angle Θ between the Earth's magnetic field and the vertical and Y and X are the standard symbols of magneto-ionic theory (see Ratcliffe5). A level near X=1, or just below, in the ionosphere is normally a complete reflector for the ordinary wave, but is semitransparent for a cone of angles centred on the critical direction. This cone is called the “Ellis window”. Its diameter is defined to be the range of wave normal angles within which more than half the incident energy flux is transmitted through this level.