Amplification of whistler waves in the magnetosphere

Abstract

The effect of a succession of narrow band morse pulses, propagating in the whistler mode, on a steady state distribution function of electrons trapped in the Earth's magnetic field is studied. The pulses have the effect of diffusing the particles in both pitch angle and energy, and the corresponding pitch angle diffusion coefficients and energy diffusion coefficients are computed. Because of the definite relation between the change in magnetic moment and energy of a particle which occur at resonance, particles are forced to move on given surfaces in velocity space, so that the diffusion is one-dimensional. The corresponding single diffusion coefficient is computed and a one-dimensional Fokker Planck equation derived. A Kennel and Petschek type initial distribution function is used and a time development of this distribution function is considered. It is found that a slot develops in the distribution function at a velocity corresponding to the frequency of the morse pulses. Growth rates for the modified distribution function are computed, and the behaviour of the growth rates lead us to postulate a mechanism for the explanation of the artificially stimulated emissions. The mechanism explains some of the important observational results for ASE such as the offset frequency and the fact that emissions are often triggered near the equator. An extension of this work may also explain the observed preferential triggering at half the minimum gyrofrequency.