ANALYTIC RAY PARAMETERS FOR THE QUASI-CUBIC SEGMENT MODEL OF THE IONOSPHERE

Models of the ionosphere giving analytic ray solutions are very useful for the study of ionospheric propagation. Probably the most useful is the quasiparabolic model which gives analytic solutions for a spheric al ionosphere when the effects of the Earth's magnetic field are ignor ed. Furthermore, its use in analytic ray tracing has been extended rec ently by developments in which real ionospheres are described by fitti ng quasi-parabolic segments (QPS) to measured vertical profiles. While numerical ray tracing is required to take account of the range of hor izontal gradients that occur in the ionosphere, in some real-time appl ications, analytic results are still preferred because of the shorter computation time. Even though the QPS approach has greatly extended th e utility of analytic ray tracing, it produces model ionospheres which are continuous in only the first derivative of the refractive index. The lack of continuity of the second derivative can lead to relatively abrupt changes in ray quantities with, for example, elevation angle. This drawback has been addressed by developing a model based on quasi- cubic segments (QCS) which also provide analytic ray solutions. In thi s paper the QCS model is described, and analytic solutions are derived for range, group, and phase paths. An example of an application is pr esented in which the QCS model was used to check the performance of a numerical ray tracing code.