A STUDY OF WAVES AND INSTABILITIES IN PLASMAS

Abstract

The thesis entitled "A STUDY OF WAVES AND INSTABILITIES IN PLASMAS" is presented in seven chapters. Chapter I is devoted to the introduction of some basic aspects of plasma physics and a brief summary of history and development of the subject. A brief review of plasma 7 waves and instabilities is provided and general methods to analyse the r. problems are given. The subsequent contents of the thesis, which form the main contributions carried out using linear and nonlinear theory of MHD, plasma waves and instabilities are the following: Chapter 2 deals with the linear stability analysis for the Kelvin-Helmholtz instability in a sheared MHD flow in a compressible. plasma with uniform rotation. The orientation of the magnetic field Bo, velocitsy/o.and the wave vector k is taken In the plane perpendicular to ; the velocity gradient. In this '-chapter, a single second order differential equation including the effect of gravity is obtained, which represents the coupling between K-H mode and the interchange mode. The asymptotic behaviour in x of the Kelvin-Helmholtz eigenfunction for the case of finite compressibility in the presence of uniform rotation is studied and the instability condition is derived. In the incompressible limit a dispersion relation is obtained which has been solved numerically and discussion is made. It is found that the imaginary partsQ.of the frequency Q are greater than zero, which shows that the inhomogeneous system is unstable in the incompressible limit. The values Q. > 0 and the corresponding values of Qr are plotted against the rotational parameter D for different values of shear velocity parameter S1. Chapter 3 is devoted to study the problem of gravitational instability of an infinite homogeneous self-gravitating medium carrying a uniform magnetic field in the presence of Hall effect to include the effect due to rotation. The dispersion relation has been obtained. It has been found that Jean's criterion for the instability remains unaffected when the effect due to rotation is considered in the presence of Hall effect carrying a uniform magnetic field. In chapter 4 the effect of. large Larmor radius on K-H instability in an ideally conducting inhomogeneous plasma with two dimensional magnetic field has been studied. A dispersion relation is obtained for two cases (i) a cold plasma (ii) an incompressible plasma. It is found that the inhomogeneous system is unstable in both the cases. The values of Re (0) and lm(Q) are computed numerically and the variations of Im(ii) ••••••,. C and the correspond)ng'Re(0) with large Larmor radius parameter are shown graphically. Chapter 5 is devoted to study the effect of resistivity on Alfven surface waves propagating along plasma-vacuum interface, A dispersion relation is obtained for such waves. The variations of real and imaginary part (kr and ki) of wave number k with resistivity as well as with viscosity parameters for different values of neutral gas friction parameter are shown graphically. It is concluded that two mode structure of Alfven surface waves results due to the effect of resistivity, viscosity and neutral gas friction. The results discussed in this chapter can have relevance to study of Alfven surface waves in the heating of solar coronal plasma, where it has been noted recently that in the process of resonant absorption of Alfven surface wave viscosity dominates over the kinetic effects. These results are also useful for both laboratory and astrophysical plasmas e.g. photospheres, chromospheres. In chapter 6 an investigation of linear stability of the cometary innersheath, the boundary layer surrounding the ionopause which separates the outflowing unmagnetized plasma from an inflowing magnetized plasma, has been carried out by taking into account the large Larmor radius effects. The structure of the boundary layer is determined by the balance between an outward ion-neutral collisional drag force and an inward magnetic stress. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary ionosphere as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. Certain limiting cases of the wave equations are also discussed. In general, the cometary ionosphere is structurally linearly unstable and the effects of recombination, photoionization, plasma pressure, though stabilizing are unable to quench the instability completely. The large Lamar radius also has a destabilizing effect of the system. The instability of the cometosheath is further proved by Te/Ti assuming a value greater than 30 that is sufficient for the convection of perturbations down into the cavity surface and this is in agreement with the observations of ripples in the ionopause. Chapter 7 deals with the study of nonlinear interactions of two Alfven waves propagating in a cylindrical waveguide filled with hot -iv- plasmas. Two cases are considered (i) The nonlinear interaction of two identical oppositely propagating Alfven waves and (ii) the nonlinear interaction of two Alfven waves with equal group velocities. In the first case the second-order perturbation fields generated through self and mutual interactions of the waves are calculated and their effect on the otherwise formed simple linear standing-wave pattern is studied. In the second case two coupled nonlinear Schrodinger (NLS) equations are obtained in order to describe the nonlinear evolution of the wave amplitudes. Modulational instability is studied for individually excited as well as for simultaneously excited waves.