The Effect Of Dust Size Distribution To The Dust Charge And The Characteristic Of Waves

The rapid development of science and technology provides an important approach for the study of nonlinear physics. The new nonlinear phenomena and their laws were discovered continually. Nonlinear wave is an important part of it. In the last several years, there have been great interests in the investigations of the physical processes in dusty plasmas because of their applications in the space environment and industrial manufacture as well as in fusion reaction. In the environment of plasmas, the dust particles become electrically charged due to interactions with the electrons and the ions. The presence of highly charged and massive dust particles in the usual plasma can have a strong influence on the characteristics of the usual plasma. Furthermore, new wave modes can be excited, such as dust acoustic wave and dust ion acoustic wave etc.. Nowadays, linear and nonlinear waves in dusty plasmas has been one of the interesting topics.In this paper, we investigate the effect of the dust size distribution to the dust charge of the particles in dusty plasmas. We study the DAWs by using reductive perturbation technique and considering the different dust size distribution and adiabatic dust charge variation. It is shown that the presence of adiabatic dust charge variations and the dust size distribution can significantly influence the characteristic of dust acoustic wave. We also investigate the dust acoustic wave in a magnetized dusty plasma. The dispersion relations for dust acoustic waves in magnetized dusty plasma consisting of mono-sized and different size dust grains have been obtained. Moreover, we theoretically investigate linear and nonlinear dust lattice waves in 2D hexagonal crystal. For linear waves in a 2D hexagonal lattice, it is found that the dispersion relation depends on the orientation of the lattice vector with respect to the waves vector, especially for the short wavelength. For nonlinear waves in this system, they are stable when there are some higher order transverse perturbation.