Propagation of VLF radio waves in the earth's ionosphere

The paper considers the rigorous solution to the problem of VLF wave transmission through a plane-stratified magnetically active ionospheric plasma with arbitrary mutual orientation of the wave normal and the geomagnetic-field vector. The angular, frequency, latitudinal, and azimuthal dependences of the transmission coefficient for VLF waves propagating through the lower ionosphere are analyzed. For the case of vertical wave incidence on the ionosphere, an approximate method is developed for calculating VLF wave transmission, and analytical solutions to the problem are obtained for the model of the lower ionosphere with exponential electron-density and effective-collision profiles. Calculations of the ionospheric field intensity of a ground-based VLF transmitter are made on the basis of the ray treatment of a field in the earth-ionosphere waveguide. Results of theoretical investigations are compared with experimental data obtained by two satellites.