The ray tracing treatment of the oblique echo model for the topside upper hybrid resonance

The oblique echo model for the resonance near the local upper hybrid frequency f T observed by topside sounders involves the propagation of slow waves away from the sounder, which later return as echoes after refiexion due to an electron density gradient. The model is investigated by using ray tracing techniques. Use of Poeverlein constructions gives some idea as to the qualitative nature of the rays which contribute to the resonance. A quantitative description requires the use of ray-trajectory equations. By using a simple approximate warm electromagnetic dispersion relation (which, nevertheless, retains all the important features of the exact dispersion relation), the ray-trajectory equations are integrated analytically for the case of a stratified plasma with a linear density gradient. These equations are used to investigate the behaviour of the frequency of the received echoes as a function of delay time. The resonance exhibits strikingly different characteristics for f T <2f H and f T >2f H respectively, where f H is the electron gyrofrequency. For f T <2f H the resonance is ‘strong’, the receiver observing a continuous response consisting of two echoes which interfere to give a fringe pattern. Some typical ray paths are illustrated. For f T <2f H the resonance is ‘weak’ and without fringes. A condition is derived for the existence of intercepting ray paths and for the maximum time delay that occurs when they do exist.