THE UPPER CUTOFF FREQUENCY OF NOSE WHISTLERS AND IMPLICATIONS FOR DUCT STRUCTURE

The upper cut-off frequency of whistlers for ducted propagation in a field-aligned enhancement of electron density is determined (i) theoretically not accounting for ambient plasma gradients and (ii) with the effect of ambient gradients for L-values around 3-4, using both ray tracing in a realistic plasmaspheric model and also by using formulae previously derived by other workers. It is found that the minimum enhancement required for a given duct width to guide whistler-mode rays from low altitude (approximately 1000 km) in one hemisphere to a similar altitude in the conjugate hemisphere (corresponding to whistler paths) is significantly larger than previously determined for frequencies close to half the minimum electron gyrofrequency along the path. Three different effects are shown to be important; that is, (i) the finite ratio of plasma frequency to gyrofrequency, (ii) the magnetic field and ambient electron density gradient across the duct in the region of the equatorial plane and long the length of the duct and (iii) the curvature of the field lines. From ray-tracing calculations in uniform enhancement Gaussian cross-section ducts, it is found that for normal whistlers at L approximately 4, a much wider range for the ratio of upper cut-off frequency to equatorial electron gyrofrequency would be expected than is experimentally observed. Possible reasons for this are discussed and it is concluded that either there is an amplitude threshold or df/dt limit for whistler amplification or ducts have a more complicated morphology; an increasing enhancement along the field line or superimposed fine structure. Mechanisms for whistler cut-offs above half the electron gyrofrequency are also discussed, with particular reference to the occurrence of super-whistlers.