Identification of Low and High Ionospheric Rays by a Direct Variational Method

Direct optimization of the optical path functional is a promising approach to the point-to-point ionospheric ray tracing problem. The approach involves a systematic transformation of the ray trajectory to an optimal configuration satisfying the Fermat's principle, while the endpoints are kept fixed according to the boundary conditions. Here, a strategy is proposed for the identification of both high and low rays using a direct variational approach. High rays are obtained by minimizing the optical path of ionospheric radio rays. Low rays which correspond to saddle points of the optical path are found using the minimum mode following method, where the saddle points are essentially converted to local minima. The method is applied to a point-to-point ionospheric ray tracing, where the propagation medium is obtained with the International Reference Ionosphere model.