Parametric instabilities in inhomogenous plasmas
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This thesis will deal with certain problems of parametric instabilities in the inhomogeneous plasma. A large amplitude, 'pump' wave can deposit some of its energy into the plasma through resonance with two lower frequency waves (which may be damped). This type of process is a parametric decay of the pump wave and has applications in many fields. We consider, predominantly, that of laser fusion, in which the pump wave is electromagnetic and incident on the plasma. The objective is to deposit as much energy as possible within the plasma. Instabilities reducing this energy input are therefore of importance and it is, mostly, to these that this thesis will turn. They are mostly scattering processes in which one of the decay modes is electromagnetic. We examine the stimulated Brillouin backscattering process (the other decay mode being an ion accoustic wave) from a reference frame in which the plasma is streaming outwards. It is found that, if this velocity is near the sound velocity, the ion acoustic wave has a frequency Doppler-shifted to zero, the electromagnetic waves then having equal frequencies. In such a situation, any reflection of the pump wave at the critical surface will enhance the initial level of the backscattered wave. We find that, allowing for this, there is considerable enhancement of backscatter from the plasma, with consequent energy loss to the pump. Since the effect is noticeably unaffected by 'off- resonance' situations, it is felt that this process could mount a barrier to possible applications. We next consider the stimulated Compton scattering process, where the pump is scattered off the 'bare' or thermal electrons in the plasma. It is found that this rather weak instability occurs predominantly only when electron plasma waves are heavily dampled. Substantial reflection only occurs for high pump powers. Whilst there is little loss to the pump energy, there is substantial perturbation to the background distribution function. However, at the high powers involved filamentation and modulation of the pump can occur with a resulting enhancement of the scattering. Finally, we consider the effect on the decay instability (photon → plasmon + phonon) of the presence of substantial filamentation of the critical surface. It is found that the growth rate is substantially reduced.
Thesis, PhD Doctor of Philosophy
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