Investigation of Parametric Instabilities in Plasmas Induced By Stochastic Pumps.

Abstract

The purpose of this thesis was to investigate the effect of stochastic pumps on the parametric instabilities in plasmas. The parametric instabilities can be interpreted simply as the decay of a pumping mode into two other unstable plasma modes. The stochastic coupled-mode equations describing these instabilities are derived from Maxwell's equations, the continuity and momentum equations of the two-fluid description for a homogeneous unmagnetized plasma. The equations for the "mean" are obtained by taking the ensemble average of the stochastic coupled-mode equations and employing the Bourret-approximation to close the set of hierarchical equations. Therefore the effect of the stochasticity of the pump is correctly taken into account in the mean-value equations. In the previous work only one aspect of the effect of the stochastic pump on parametric instabilities was considered which is the pump b and width effect for perfect frequency matching. The common result of these works is that the increasing pump b and width increases the threshold for instability and as a conclusion of this the undesirable instabilities could effectively be controlled by increasing the b and width of the pump. We have considered the combined effects on the parametric instabilities of the pump b and width in the presence of imperfect frequency matching, the pump amplitude fluctuation and the plasma temperature fluctuation due to the pump fluctuations. We have obtained some surprising results. Contrary to what is known in the literature, the threshold for instability can initially decrease with increasing pump b and width and reach a minimum. A physical explanation of this minimum is given. The pump amplitude and the plasma temperature fluctuations compete with the pump b and width and decrease the threshold for instability. Even for large pump b and width, the threshold for instability for a pump with r and om amplitude is always lower than the coherent one. Our general conclusion is that in studying the effect of stochastic pumps on parametric instabilities one actually may have to take into account in addition to the pump b and width, a number of other phenomena like imperfect frequency matching, the fluctuation induced in plasma parameters and the amplitude fluctuation of the pump itself.