VLF propagation in a sharply bounded, compressible, isotropic ionosphere

The effect of compressibility on the characteristics of the waves guided by the ionosphere is studied using a simple model which consists of a perfectly conducting flat earth and a sharply bounded and a uniform ionosphere with a sharp rigid boundary, without losses or anisotropy due to the earth's magnetic field. The compressibility of the ionosphere introduces an exponential damping for frequencies greater than approximately the electron plasma frequency for the fast waveguide modes, which in an incompressible ionosphere propagate without any attenuation even above the plasma frequency. Also the propagation range of the slow-wave mode (
n = 0
), which does not propagate above
1/\sqrt{2}
times the plasma frequency in a cold ionosphere, is extended indefinitely beyond that critical frequency. The compressibility is found to have negligible effect on the wave propagation in the VLF band. For a source situated on the earth and radiating in the VLF band, the power transmitted by the slow-wave mode and the first three waveguide modes are evaluated. The excitation of the slow-wave mode is found to be comparable in magnitude to that of the waveguide modes in the lower end of the VLF band but in the higher frequency end the power radiated by the slow-wave mode is shown to be negligible.