Study Of Strongly Coupled Dusty Plasmas

Strongly coupled dusty plasma crystal is a new class of soft condensed matter. Grains in plasma crystal are of macroscopic size compared with atom in atomic lattice. So, it is easy to observe and control over a wide range of parameters(including plasma density, temperature and particle size). There is growing world-wide theoretical and experimental effort to investigate the dusty plasma crystal. The detailed study of this entirely new material could well lead to a better understanding of phase transition, phono propagation, sublimation, annealing and lattice defects. There are many complicated kinetic forms and transport modes of energy in plasma crystal, for example, oscillation and wave. The wave can represent an object connecting theory and experiment. The investigation of wave is important since fundamental parameters of dusty plasma can be obtained from the analysis of wave propagation.In this paper, we investigated linear and nonlinear waves in two-dimensional(2D) simple cubic lattice and three-dimensional (3D) simple cubic lattice, and derived dispersion relations of linear waves and solitary-wave solution. Because the average interparticle distance is larger than the plasma shielding length, the individual dust particle in a dusty plasma crystal interact only with a few neighboring particles. For simple cubic lattice consisting of the same grains, we discussed the dispersion relations in dust lattice. It is found that there are two modes in a certain direction of 2D lattice. One is longitudinal wave, and the other is traverse wave. Three modes are sustain in a certain direction of 3D lattice. Similarly, one is longitudinal mode, and the others are traverse modes. However, there are two longitudinal waves and two traverse waves in 2D dual lattice. Furthermore, by using reductive perturbation technique, we investigated solitary waves in some special directions. It is indicated that there are different amplitude and width when the soliton propagate in the different directions. The values of the soliton amplitude and width depend on the interaction potential between two particles. We also investigated nonlinear acoustic wave propagating in inhomogeneous plasma and obtained a KdV-type equation and its analytical quasi-soliton solution. By neglecting the reflection, it is found that the amplitude of soliton will change when it propagates into the discontinuous interface.