The Study Of Collective Excitations In The Dusty Plasmas

In recent years, there has been great interesting in studying new wave modes that result from the presence of micron-sized, charged dust particles in plasmas, i.e. the stability of low frequency waves and the properties of nonlinear structures (solitary wave)etc have been studying extensively. Recently Khrapak and Morfill considered a two component electron-dust plasma. Here the dust grains are charged positively due to ultraviolet(UV)photoelectron emission or thermal emission. However, most of these investigations are only concerned with a dusty plasmas of infinite extent. As is well known, the boundary is the distinct character in experiment plasmas, moreover, various localized structures are automatically formed in space plasmas environments. Plasmas wave spectrum is discrete due to the boundary effect. So the boundary effect is a focus in studying plasmas.In this paper, by carrying out a normal mode analysis, the effects of dust charge fluctuation and the boundary effect etc. on the dispersion relation of waves in electron-dust plasmas are investigated. Moreover, the formalism of a solitary wave in a electron dusty plasmas are also studied by using Pseudopotential approach.In the present thesis, firstly, by carrying out a normal mode analysis, we obtain the dispersion relation of waves in electron-dust plasmas. Furthermore, the numeric analysis of the dispersion relation is presented and some limiting cases are discussed. It is observed that there exist two different wave modes, and the waves in the electron-dust plasmas are obviously affected by the effects of adiabatic dust charge fluctuation, the dust (electron) number density, the particle collisions and the dust grain size etc. Moreover, it is shown that the radial wave number is discrete because of the boundary effect and the boundary effect has significant influence on the waves in the two component electron-dust plasmas. The boundary effect not only modify the frequencies of the two wave modes but also has significant influence on the damping rate of the long wave. Lastly, we consider the problem of arbitrary amplitude nonlinear wave propagation with the help of a pseudopotential formalism taking care of the boundary condition on the surface of the cylindrical wave guide. It is shown that there exist solitary wave in the electron-dusty plasmas and the boundary effect has significant influence on the solitary wave.