Transmission of VLF Radio Waves Through the Ionosphere

Abstract

The fields of 10-kHz radio waves propagating into and through the lower ionosphere are calculated by numerical methods, and the attenuation, polarization, and power flow characteristics are examined as a function of height for daytime and nighttime ionospheric electron density profiles with varying angles of incidence, directions of propagation relative to the earth's magnetic iield, and dip angle. The conclusions are that virtually all the attenuation of the wave occurs in the lower D region of the ionosphere, that the transmitted wave is nearly circularly polarized, and that the energy of the transmitted wave is traveling nearly along the magnetic lines of force in agreement with the predictions of "ray theory." The analysis also shows the strong variation in transmission with dip angle and with change from day to night ionosphere in agreement with observed variations in intensity and in frequency of occurrence of "whistlers." lntrodudionThe coupling of VLF radio energy between the earthionosphere waveguide and the exosphere has important bearing on the understanding of such phenomena as whistler propagation and VLF emissions and on the detection and measurement in space vehicles of VLF signals from transmitters on the ground. The theory of the cou.Plillg of such signals through the ionosphere remains the least well understood facet of VLF propagation phenomena, if not qualitatively, at least quantitatively. This is a consequence of the fact that, for the long wavelengths involved, the ionosphere is a medium which changes significantly within a wavelength so that ray-theory techniques are not appropriate. Full-wave solutions are required which cannot be handled with the same· analytic ease that the ray theory allows..With the advent of large, high-speed digital computers, however, tractable numerical methods have been developed for calculating the fields as the wave penetrates into the ionosphere