On Landau Damping And Instability Of Dust Acoustic Waves In The Plasma With Nonextensive Distribution

The dust particles are widely distributed in space, and99%of the visible matter of universe is the plasma state, so that dusty plasmas are throughout every corner of the universe. Distribution breadth of the material form itself constitutes the reason to study it. Plasma is a complex system, with kinetic theory to examine the Landau damping and instability, which is an important issue, with which to deal based on statistical mechanics is a large class of methods. Nonextensive statistical mechanics is an emerging discipline. There is increasing evidence that the nonextensive statistical mechanics (NSM) can be considered as the more appropriate basis of a theoretical framework to describe the complex systems. So there is a great significance to examine the effect of nonextensive parameter on Landau damping and instability of dust acoustic wave in dusty plasma.In this thesis, the general longitudinal dielectric function in a collisionless, unmagnetized, isotropic plasma is given based on the kinetic theory, firstly. Then according to this expression gives the dispersion relation and Landau damping rate of dust acoustic waves. In chapter2, we consider a dusty plasma modeled by a nonextensive distribution for electrons and ions, and a Maxwellian distribution for dust grains. And find that Landau damping is dependent on the nonextensive parameter as well as the ratio of ion density to electron. In the extensive limit, the result based on the Maxwellian distribution is recovered. The maximum Landau damping rate is found to be enhanced as the population of the electron density decreases.In chapter3, we promote the model in the chapter2. The nonextensivity of dust grains is considered, and the nonextensivity parameters of nonextensive distribution for three plasma components are different from each other, and electrons and ions with different drift velocities is assumed. After this generation, we find that there is the instability growth rate but not the Landau damping rate, and the instability growth rate is dependent on the nonextensivity parameters as well as on the ion-electron number density ratio. In the extensive limit, the result in Maxwellian distribution plasma is reproduced, and the instability growth rate decreases as the population of suprathermal electrons and dust grains increases, but enhances when the number of suprathermal ions increases and electron density decreases.