Studies on the propagation of non linear waves in plasmas

Abstract

The piece of work in the thesis is in relation to nonlinear solitary waves under different physical situations in plasmas. The thesis consists of six chapters including the introduction. In the chapter introduction, a brief description of plasmas as regards how it occurs both in nature and labora-tory is incorporated. Discussion on experimental devices to develop techniques to generate plasma with high temperature and its confinement for fusion reaction, is also made with reference to various tokamaks installed in different parts of the world. Besides, the validity of the fluid model for the study of nonlinear waves in plasmas is explained. It contains an elaborate history of the development of solitary waves (a kind of nonlinear waves arising out of the interaction between nonlinearity and dispersion that moves without changing its shape) with innumerable references. Furthermore different non-linear equationsin connection with the studies of solitary waves have also been discussed together with their methods of solution. In the latter chapters, we use these nonlinear equations in appropriate physical situations of plasmas and try to make physical plausibility and explanations. Interesting results in respective chapters are also cited. In chapter 2, we investigate theoretically the propaga-tion of ion acoustic solitions in a warm plasma in presence of negative ions and Boltzmann distribution of electrons through the modified KdV equation. In the general procedure of deriva-tion on the KdV equation, the physical quantities are expanded in terms of a small parameter E (Eltlt1) retaining only terms upto second order. But for the consideration of higher order nonlinearity and to extract more inner ideas of the phenomena, we take the help of different set of stretched variables and derive the modified KdV equation setting the nonlinear co-efficient of the KdV equation to zero which gives the critical density. We establish the existence of both compressive and rarefactive solitons at different critical densities for...