Study Of The Motion Of Charged Particles And The Formation Of Dust Crystal In Radio-frequency Plasma Sheath

Dusty plasmas, which can be loosely defined as plasmas containing micro-sized charged particles, are ubiquitous in both our astrophysical environment and various gas discharge generated plasmas on earth. In recent years, this field has attracted much attention all over the world. However, people pay attention to it with completely different purposes. In the plasmas of fusion energy schemes and semiconductor processing, the existence of the charged particles will always make trouble. So there, people always try their best to avoid them as well as to control their motion. Whereas in plasmas of astrophysical environment and laboratory, the appearance of charged particles often brings us some new and surprising phenomena, among which the observation of the dust crystal formation in laboratory should be the most typical one.The present thesis aims mainly at studying the motion of charged particles and dust crystal formation in laboratory dusty plasmas. Considering the fact that in a typical dusty plasma experiment the micro-sized particles always levitate at the sheath edge, where the sheath field and ion flow always play important roles to the property of dusty plasma. So firstly, three different radio-frequency (RF) sheath models are established, depending on the problems to be discussed in the following. They are respectively the one-dimensional (1D) RF sheath, 2D (two-dimensional) RF sheath and 2D magnetized RF sheath model. All these sheath models are in a self-consistent manner by adopting a sheath equivalent-circuit model and by taking into account the ion-neutral collision effect.Secondly, the charging processing and levitation of an isolated dust particle in an RF sheath are studied systematically. In particular, the nonlinear phenomena, such as secondary resonance and hysteresis in the vertical oscillation of a charged particle in an RF sheath are studied in detail, by solving its Newton's equation, in which various forces acting on the particle are taking into account. The results reproduced the recent observation of Ivlev et al[Phys. Rev. Lett., 85, 4060 (2000)]. very well, In addition, it is found that the nonlinearity is related to the particle charge, sheath field, and excitation force, as well as the ion drag force and neutral-gas friction on the particle.Thirdly, the formation and structure transition of 2D dust crystal are studied based on the 2D RF sheath model. The results show that for those small crystals their configurations exhibit strong periodical dependence on the particle number. Then by using wake theory, the formationof 3D dust crystal is studied. It is found that the ion flow induced wake effect will generate an oscillatory potential behind the charged particle, which may trap other particles below it and Jeads to the formation of vertical alignment in 3D dust crystal.Fourthly, the formation and rotation of 2D dust crystal under an axial magnetic field are simulated based on the 2D magnetized RF sheath model. The dust particles are initially placed randomly inside the sheath, and then their motions are tracked by a molecular-dynamics method until stable, ordered 2D structures are formed, which rotate in a plane perpendicular to the magnetic field, driven by the E × B induced azimuthal ion flow. The rotation patterns are found to depend, in a complex way, on the particle number, the crystal structure, and the discharge parameters, such as discharge pressure and magnetic field. However, the typical rotation frequency is in the order of 10-2 Hz, which is conformable to recent experimental observation, and consequently the results confirm that the observed rotations are driven by E × B ion flow.Fifthly, a 2D hydrodynamic model for a monolayer of dust particles is used to study the Mach cones excited by a moving laser beam through dusty plasmas. Numerical results for the density perturbation and the velocity distribution of dust particles exhibit both compressional and shear-wave Mach cones. It is found that the compressional Mach cones exist in cases of both supersonic and subsonic excitations...