An analytical study of the oblique echo model for the topside upper hybrid resonance

Abstract

The oblique echo model for the resonance near the local upper hybrid frequency fT 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 using the WKB technique introduced by Fejer & Yu. The resulting set of saddle-point equations is solved by a method which can, unlike previous work, be applied to both the ‘strong’ resonance (for which fT < 2fH where fH is the electron gyrofrequency) and to the ‘weak’ (fT 2fH) resonance. Throughout the calculations the validity of the approximations made is checked. It is found that the weak resonance solution is not valid for typical topside parameters. A condition is derived for the existence of intercepting ray paths and for the maximum time delay which occurs when they do exist. For the strong resonance the electric field of a small pulsed dipole is calculated. Expressions are found for the frequency of the two echoes which are received by the sounder and the frequency of the beating between them. Although they are only strictly valid for times longer than typical observation times, they yield results that agree well with the corresponding results from ray- trajectory computations.