Study On The Stability Of Dusty Plasmas With Dust Charging In Bounded Space

In recent years, there has been great interesting in studying dusty plasmas, such as the stability of low frequency waves and the properties of nonlinear coherent structures (solitary wave) et al. The effects of dissipation et al. are produced by the dust charging in a dusty plasmas, this will strongly influence the stability of the dusty plasmas. Nowadays, dust charge fluctuation is one of interesting topics in studying plasmas. 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 another focus in studying plasmas.In this paper, by carrying out a normal mode analysis, the effects of dust charge fluctuation et al. on the dispersion relation of low frequency electrostatic waves are investigated. Moreover, the features of a 3-D dust acoustic solitary waves in a dusty plasmas are also studied by using the reductive perturbation method.In the present thesis, firstly, the dispersion relation of an infinite dusty plasmas is studied, it is found that the effects of adiabatic variation, the external magnetic field, the particle collisions and the obliqueness have strong influence on dusty low frequency waves. Secondly, the dispersion relation of dust acoustic wave in a bounded dusty plasmas is discussed, it is shown that the radial wave number is discrete because of the boundary effect, and the dust acoustic wave is obviously affected by the effects of adiabatic dust charge fluctuation, the particle collisions and the dust grain size. Furthermore, the influence of the boundary effect, nonadiabatic dust charge fluctuation, magnetized field and fast ions etc on the low frequency waves in a dusty plasmas is analyzed. It is observed that there exist two different wave modes. Lastly, we studied the properties of a 3-D dust acoustic solitary waves in a dusty plasmas. It is clear that the rarefactive solitary waves only exist, arid the external magnetic field and collisional frequency just modified the width of the waves.