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 spherical ionosphere when the effects of the Earth's magnetic field are ignored. Furthermore, its use in analytic ray tracing has been extended recently by developments in which real ionospheres are described by fitting quasi-parabolic segments (QPS) to measured vertical profiles. While numerical ray tracing is required to take account of the range of horizontal gradients that occur in the ionosphere, in some real-time applications, analytic results are still preferred because of the shorter computation time. Even though the QPS approach has greatly extended the 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 this paper the QCS model is described, and analytic solutions are derived for range, group, and phase paths. An example of an application is presented in which the QCS model was used to check the performance of a numerical ray tracing code.