Very-low-frequency radio propagation in the ionosphere

Equations describing the propagation of radio waves in a horizontally stratified aniso tropic ionosphere were developed by considering the limit.ing case of a large number of in finitesimally thin slabs of constant electron density a nd collision frequency. The quasi longitudinal approximation was used. The propagation equations appeared as four coupled first-order linear differential equations, coupled by gradients in electron density and collision frequency. The quasi-longitudinal approximation permitted use of particularly simple forms for t he coupling coefficients, t hese forms being amenable to simple analysis. Coupling between two ordinary or two extraordinary modes was found to be considerably stronger than cross coupling between ordinary and extraordinary mode . Cross coupling was related to the rate of change of the direction of the phase normal. It was found that the reflection of VLF radio waves from t he daytime ionosphere is relatively insensitive to t he angle of incidence on the ionosphere except for highly oblique propagation. "Vhistler penetration was also found to be insensitive to the angle of incidence on the ionosphere.