Studies on nonlinear waves in plasmas and hydr omagnetic free and forced convection flow

Abstract

In this thesis, we have made a systematic study of nonlinear waves in plasmas under different physical situations. We have, however, discussed a problem of hydromagnetic flow in the last chapter of this thesis. One of the most important results of nonlinear effects in plasma oscillations is to cause steepending of the leading edge of the wave. Unlike the case of ordinary gas dynamics, where dissipative effects are important for short wave length waves, in plasma dynamics it is often found that dispersion effects become significant as the steepness of the wavefront increases. An exact balance between nonlinearity and dispersion leads to the formation of ion acoustic solitary wave. We have investigated the effects of a colder electron species on the propagation of weakly nonlinear ion acoustic waves in an unmagnetized plasma in cylindrically and spherically symmetric geometries. Depending on the densities and temperatures of the two electron components and ion temperature of a collisionless plasma, the ion acoustic wave has been found to be either a hump or a dip. Similarly, the shock amplitude of the cylindrical shock wave in a multi-species collisional plasma has been found to be either hump or a dip depending on the same. Higher order contributions to ion acoustic solitary waves in a plasma in presence of a colder electron component and trapped electrons have been discussed. It has been obtained that the ion acoustic wave propagates either as a soliton or as a hole depending on the densities and temperatures of the two electron species and ion temperature. The density of the trapped electrons, which interact strongly with the wave during its evolution, can not be described by a Boltzmann distribution. The distribution of the electron density in the resonant region has been found to be flat-topped or vortex type depending on the number of trapped electrons. In the above studies we have used the reductive perturbation method. It is, however, possible to find out the solitary wave solution without any perturbation...