QUASI-LINEAR THEORY OF TRANSVERSE PLASMA INSTABILITIES WITH APPLICATIONS TO HYDROMAGNETIC EMISSIONS FROM THE MAGNETOSPHERE

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Abstract
Transverse instabilities in two magnetoactive plasma streams are investigated theoretically. The approach taken is to investigate how a small signal transverse electromagnetic wave, which, in a zero temperature background plasma, can be propagated as a circularly polarized sinusoidal wave (with the two possible modes, electron and ion cyclotron) along the external magnetic field, behaves under perturbations arising from the existence of the streaming plasma and the nonlinear terms in the Boltzmann equations describing the plasma particle distribution. The perturbation method originally given by Bogoliuboff et al. and since developed into the so-called multiple time-scale method by Frieman et al. (1963) is employed to solve the problem. The cyclotron instability is rediscovered as the effect of the lowest order (viz., the most effective) among all possible instability processes. The wave amplitude is found to grow gradually with time in the vicinity of the cyclotron resonance frequency because of the instability. The effective wave frequency is also found to change gradually in time. The growth rate of the signal intensity and the rate of the time change in the frequency are calculated for a case of geophysical interest, viz. the instability in the ion cyclotron mode of waves by a proton stream proposed as the generation mechanism for hydromagnetic (hereafter hm) emissions. The location of the occurrence of the instabilities is taken to be the equatorial region in the outer magnetosphere. A model is considered where the instabilities occur in the region with L value equal to about 5.6. The growth rate of the signal strength calculated with reasonable values of the geophysical parameters involved is in agreement with the observations. Calculations of the rate of the time change in the wave frequency show that the frequency is seen to increase with time, and the rate, which is of the order of 0.1 c.p.s./minute, is comparable to that obtained from observations, showing that the process proposed for hm emissions may be correct.