Studies Of Dynamical And Mechanical Propetries Of Two-dimensional Yukawa Sytesms Using Simulations

Dusty plasma refers to the mixture of solid particles(dusts)and a plasma,which contains free electrons,ions,and neutral gas molecules.In a laboratory plasma,due to the higher mobility of electrons than ions,dust particles are rapidly negatively charged,with thousands to tens of thousands of elementary charges.As a result,the interaction between dust particles is strongly coupled,and the collection of these dust particles exhibits typical properties of solids and liquids.Due to the screening effects of free electrons and ions,the interaction between dust particles is the Yukawa(or Debye-Huckel)repulsion.In dusty plasma experiments,the motion of dust particles can be directly recorded using high-speed cameras and tracked individually,so that many physical processes of solid or liquid can be studied in dusty plasmas at the "atomistic"and kinetic level.To mimic experiments,simulation methods have also been developed to study dusty plasmas,such as the equilibrium molecular dynamics simulation and the Langevin dynamical simulation.In this thesis,Langevin dynamical simulations are performed to mimic two-dimensional(2D)Yukawa solids and liquids.A few dynamical and mechanical properties of 2D dusty plasmas are investigated.First,dynamical heterogeneities have been widely studied in the overdamped colloids in the glassy transition and the granular materials in the jamming transition.However,dynamical heterogeneities in underdamped dusty plasmas have not been reported.Here,dynamical heterogeneities of 2D dusty plasma at different temperatures are investigated systematically using Langevin dynamical simulations.Based on the positions and velocities of simulated dust particles,various heterogeneity measures are calculated,such as the trajectories of dust particles,the distance matrix,the averaged squared displacement,the non-Gaussian parameter,and the four-point susceptibility.It is found that,for 2D Yukawa liquids at a low temperature close to the melting point,both the spatial and temporal heterogeneities in dynamics are more severe.It is also found that the calculated non-Gaussian parameter of 2D Yukawa liquids consists two peaks at different times,indicating the most heterogeneous dynamics.Compared with the calculated mean-squared displacement(MSD)and intermediate scattering function(ISF),these two peaks are attributed to the transition of different motions and the ?-relaxation time,respectively.Second,the modulation of the external potential arrays on the static structures and dynamics of dusty plasmas is studied.Langevin dynamical simulation is performed to mimic 2D dusty plasma(2DDP)in the presence of a one-dimensional(ID)periodic substrate(1 DPS).Both the pair correlation function perpendicular to the substrate modulation and the MSD of dust particles are calculated.It is found that both the structure and dynamics of 2DDP exhibit strong anisotropic effects,due to the applied 1DPS.As the substrate strength increases from zero,the structure order of dusty plasma along each potential well of 1DPS increases first,probably due to the competition between the interparticle interactions and the particle-substrate interactions.Then this structure order decreases gradually,which may come from the reduced dimensionality and the enhanced fluctuations.In addition,the obtained MSD along potential wells of 1DPS clearly exhibits three processes of diffusion in our studied 2DDP.Between the initial ballistic and finally diffusive motion,there is an intermediate sub-diffusion discovered here,which may result from the substrate-induced distortion of the caging dynamics.Third,a new method of calculating the shear modulus of 2D dusty plasma is developed.Shear modulus is an important quantity to measure the stiffness of materials,which is defined as the ratio of the shear stress and shear strain.While undergoing the shear stress,some materials exhibit the time-dependent shear strain,so that the ratio of the shear stress and this time-dependent strain is called the shear relaxation modulus.Shear stress autocorrelation function can also be used to calculate the shear relaxation modulus.For 2D Yukawa systems,the shear stress can be divided into two parts,the kinetic and potential terms,so that the shear relaxation modulus G(t)consists of the kinetic,potential,and cross portions.Due to their viscoelasticity,2D Yukawa liquids exhibit the typical elastic property when the time duration is much less than the Maxwell relaxation time.As a result,the infinite frequency shear modulus G?(i.e.,the shear relaxation G(t)when t=0)of a 2D Yukawa liquid should be related to the shear modulus of the corresponding 2D Yukawa solid.Due to the thermal motion of dust particles,the infinite frequency shear modulus contributed by the kinetic portion should be removed,equivalent to the situation when all particles are suddenly frozen at their locations,so that,in principle,the potential portion of the infinite frequency shear modulus for 2D Yukawa liquids should be the same as shear modulus of cold 2D Yukawa solids.Following this idea,the shear modulus of cold 2D Yukawa solids calculated from only the potential portion of G?,agree well with the shear modulus derived from the transverse sound speed of 2D Yukawa crystals,which indicates that this method developed here is reliable.Finally,to contribute to the project of Ministry of Science and Technology of China undertaken by our group,various experimental methods of dust injection into tokamaks are reviewed and investigated.Here,these dust injection methods are compared,and the method of the rotary impeller accelerator to inject dust is finally chosen for our project,according to our experimental requirements.In addition,regarding the compatibility of dust and tokamak fusion plasma,the upper limit of the amount of the dust with different materials injected into HL-2A is estimated,assisting the related project implemented successfully.