Study On Dust Lattice Waves And Dust Sheath Under Non-debye Interaction Potential

Dusty plasma is also called complex plasma,is an important branch of plasma physics.Due to the presence of dust particles,the collective behavior of dusty plasma is quite different from that of classical plasma.This thesis focuses on the collective behavior of dusty plasma,including linear waves?dust lattice waves?and nonlinear structures?dusty plasma sheath and dust acoustic solitary waves?.Based on Newton's equation of motion and fluid theory,the propagation of dust lattice waves in a one-dimensional dust ring,a binary dust chain and a two-dimensional hexagonal crystal,as well as the sheath structure of dust plasma and dust acoustic solitary waves are investigated.The dispersion relations of the dust lattice wave,the physical images of sheath structure and dust acoustic solitary wave are obtained.Our results further broaden the research scope of dusty plasma physics,and also provide theoretical support for explaining and observing relevant experimental phenomena as well as computer simulation.Firstly,the research background of dusty plasma is introduced,including the source,formation,characteristics and related applications of dusty plasma,as well as the main research methods of dusty plasma,charging process of dust grains,wave propagation,properties of dust crystals and dust lattice wave.Secondly,starting from the strong coupling system,considering that the binary dust chain is composed of two kinds of dust particles with different mass and charge,the structure of the binary dust chain is…/A/B/A/B/….The dispersion relations of longitude and transverse waves in the binary dust chain are obtained by solving the motion equations.It is found that the first Brillouin region of binary dust chain is reduced by half compared with that of single particle dust chain,and for each longitudinal wave in binary dust chain,it is divided into two branches:longitudinal optical mode and longitudinal acoustic mode,and there are transverse optical mode and transverse acoustic mode in transverse waves.The movement direction of dust particles in binary dust chain is also analyzed in detail.On this basis,the propagation of dust lattice waves in one-dimensional dust rings and two-dimensional dust hexagonal crystals under non-Debye potential is studied,the corresponding dispersion relations are obtained,and the effects of relevant parameters on the dispersion relations are analyzed,as well as the instability of transverse waves is studied.In two-dimensional hexagonal dust crystals,due to the symmetry of hexagonal crystals,waves with a difference ofp/3 in propagation angle are the same.Considering the plasma adsorption effect,the temperature effect will increase the frequency of dust lattice wave,while the spatial effect will reduce the frequency of dust lattice wave.Thirdly,based on the fluid equation of dusty plasma,the effects of polarization and charge gradient force on the dust sheath formation are studied.The corresponding new Bohm criterion for the dust sheath is obtained.By analyzing the Sagdeev potential numerically,it is found that the width and depth of the Sagdeev potential increase with of polarization parameters P_R and Mach number M.The critical Mach numberM_cr decreases with the increase of polarization parameters,while M_cr increases with the increase of charge gradient force parameters.Furthermore,the effects of the polarization and charge gradient forces on the dust solitary wave are studied.The modified KdV equation under the polarization force and charge gradient force is obtained by using the reduced perturbation method.The static solution of KdV equation is obtained by deforming the spatial variables,and the images of dust acoustic solitary wave evolving over time are obtained.With the increase of time,the solitary wave propagating to the right,the amplitude and width of the solitary wave are fixed during the wave propagation.In addition,if the polarization force effect is considered,the amplitude of the solitary wave increases with the increase of the polarization parameters,while the effect of charge gradient force on dust acoustic solitary wave is just opposite to polarization force,the amplitude of the dust acoustic solitary wave decreases with the increase of the charge gradient parameter.Finally,the whole dissertation is briefly summarized and the future work is prospected.