WAVE PROPAGATION AND INSTABILITIES IN CERTAIN PLASMA CONFIGURATIONS

Abstract

The thesis entitled "WAVE PROPAGATION AND INSTABILITIES IN CERTAIN PLASMA CONFIGURATIONS" is presented in seven chapters. Chapter 1 is introductory in which the subject matter of the thesis has been introduced along with the history of plasma physics. It also provides the perturbation methods in nonlinear wave theory used in the problems investigated. The contents of the thesis which form the main contribu- tions are divided into parts A and B. Part A contains four chapters dealing with the investigations carried out using linear theory of MHD and plasma waves including certain micro- scopic effects. Part B consists of two chapters dealing with nonlinear behaviour of Alfven waves in certain plasma configu-rations. The brief outlines of the research work presented in the thesis chapterwise are as follows: Chapter 2 deals with the effect of neutral gas friction, on Alfven surface waves propagating along an infinitely conduct-ing viscous plasma vacuum interface. A dispersion relation vc is obtained for such waves. For S = = 0.0, 0.01, 0.2 and 0.8, the variations of real and imaginary part (kr andk1) of wave number k with V(= 111w ) 2 PolvA 2 B22 for R =pd B2 = 0.2 and ao = = Bol 0.5 are shown graphically. The results are compared with previous ones. It is concluded that three mode structure of ii Alfvn surface waves results due to the neutral gas friction. It is suggested that our results are useful for both laboratory and astrophysical plasma e.g. photospheres, chromospheres and cool interstellar clouds. Chapter 3 is devoted to the study of stability of an inhomo-geneous two component plasma with magnetic viscosity. The stability of a semi-infinite quastineutral plasma has been discussed by using JWKB approximation in which the parameters are regarded slowing varying. Dispersion relation is obtained and discussed. It is found that the inhomogeneous system is unstable for all perturbation with ky = 0. A dispersion rela-tion for homogeneous plasma is also obtained and discussed. It is shown that the fast and slow-MHD waves propagate in the homogeneous plasma in the limit of almost perpendicular propa-gation under certain condition. In Chapter 4, effect of large Larmor radius on the stabi-lity of an infinitely conducting infinitely extended inhomo-geneous plasma with rotation of magnetic field has been studied. A dispersion relation is obtained and discussed in two cases when kx = 0, V2 (sound speed) = 0 and kx = 0, Vs2 co. It is found that the inhomogeneous system is unstable in both the cases. A dispersion relation is obtained for the homogeneous system and it is found that it is stable and MHD waves propa- gate.Thevaluesofwrandw.have been computed numerical-1y and are given in Tables 4.1-4.8. iii In Chapter 5, the problem of gravitational instability of an infinite homogeneous self gravitating medium carrying a uniform magnetic field has been investigated taking into account the Hall effect. The dispersion relation has been obtained. It has been found that the Jeans's criterion for gravitational instability remains unaltered in the presence of Hall effect. In Chapter 6, the nonlinear behaviour of azimuthally symmetric Alfven waves propagating along the axis of a cylindri-cal ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrodinger equation. Modulational instability for fundamental (m = 1) radial mode is 2 YPo discussed for a = - 0.1, 0.2, 0.3 and different values of Po k. Alfven waves are modulationally stable for andd w3 for all values of k and a2 = 0.1, 0.2, 0.3. They are modulationally stable for w2 and w4 for all values k except for k'= 0.1-2.5 for a2 = 0.1, k = 0.1-2.8 for a2 = 0.2, and k = 0.1-3.5 for a2 = 0.3 for which they are modulationally unstable. The amplitude-dependent frequency and wave number shifts are calcu-lated and their variations with wave number are shown graphic-ally. In Chapter 7, we have studied the effect of large Larmor --r-ad-i-u-s—on—t-h-e—n-o-n-l-i-n-ea-r be o f xl-tv4 n w a-v r-cl pa g a ti-ng- parallel to a uniform magnetic field in a compressible fluid using LLR-MHD equations. A reductive perturbation expansion method is applied to investigate the nonlinear behaviour of iv Alfv6n waves propagating along the magnetic field. It is shown that asymptotic evolution of these waves is governed by the modified nonlinear Schrodinger equation. The dispersion is provided by the large Larmor radius effect in magnetic field equation. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in both laboratory and space plasmas, e.g. imploding e pinches, laser-blowoff plasma experiment, recent barium releases in the magnetosphere, plasma flow near small planetary bodies such as comets and plasma dynamics near collisionless shock fronts.