Upper and Lower Beam Functionals in Calculating the Radio Paths in the Model Ionosphere

Abstract

The problem of using the direct variational method was considered for seeking all possible types of solutions to the problem on the propagation paths of shortwave radio waves in the model ionosphere with given boundary conditions. An express analysis procedure was described, which makes it possible to study the radio beam functional based on the dependence of the optical path on the shape of the chosen trajectory. As a medium for numerical calculations, a two-dimensional isotropic model of the ionosphere was used, where the electron concentration profile was given in the form of a parabolic layer. The potential of express analysis for automatic determination of radio path types was demonstrated. The fundamental difference between the upper and lower ionospheric rays and prospects for using the direct variational method for their determination were discussed.