Studies Of The Substrate Dynamics Modulation Mechanism Of Dusty Plasmas Using Simulations

Dusty plasmas refer to the mixed system containing neutral gas atoms/molecules,free electrons,ions and charged dust particles.In the typical laboratory conditions,the electrical field in the plasma sheath above the lower electrode can suspend and restrain these charged dust particles,so that they can self-organize to a two-dimensional dust crystal,i.e.,a 2D dusty plasma(2DDP).Due to the shielding effects of electrons and ions,the interaction between dust particles can be accurately modeled as the repulsive Yukawa potential.Due to the extremely low charge-to-mass ratio of these dust particles,the potential energy between adjacent dust particles is greater than their kinetic energy,so that they are strongly coupled with each other,exhibiting typical properties of liquid or solids.Since the detailed trajectories of individual dust particles can be recorded by high-speed cameras in experiments,dusty plasma is an excellent experiment model system to study many fundamental physics processes in solid and liquid at the kinetic level of individual particles.In the past three decades,the collective behaviors of dusty plasmas without external fields have been widely studied in experiments and simulations.Through the laser interference or other experiment methods,the substrate,i.e.,the array of potential wells related to the locations,can be introduced into the dusty plasma system,which would generate abundant dynamic behaviors.On the other hand,the equation of state(EOS)of dusty plasmas has been found in recent years,which is of great significance in the study of the physical properties of dusty plasmas.In this paper,the EOS and the substrate dynamics modulation mechanism of 2DDP are studied systematically using Langevin dynamics and molecular dynamics simulation methods.First,the effects of one-dimensional(1D)periodic substrates on the static structure,diffusive motion and wave propagation of 2DDP are studied using Langevin dynamics simulations.Based on the positions of the simulated dust particles,the 2D distribution function and mean square displacement describing the structure and diffusion behavior of system are calculated.The results show that,when the substrate width increases,the order degree of dust particles arrangement first decreases,then increases,and then decreases again.The initial decrease in the structural order due to the transition from the single row to the double row arrangement within one potential well.When the substrate width increases to a certain value,the stable zigzag arrangement with the highest order degree is formed within one potential well.In addition,the oscillation-like diffusion behavior is found to happen in the longtime diffusion with the increase of substrate width,probably due to the stable zigzag arrangement of dust particles within each potential well causing the least diffusive motion.Based on the positions and velocities of the simulated dust particles,the phonon spectra of the 2DDP are calculated to study the wave propagation.The results show that the waves perpendicular to the potential wells are unable to propagate further,due to the confinement from the substrate.With the narrow or deep substrates,the dust particles would form to a 1D chain at the bottom of each potential well,so that the wave propagation along the potential well is mainly dominated by the longitudinal motion of dust particles.With the wider or shallower substrate,the dust particles would buckle into the zigzag structure,so that the corresponding spectra would develop into two branches.The low-frequency branch would correspond to the sloshing motion,while the high-frequency branch would correspond to the breathing motion.In addition,the pure repulsive interaction between dust particles would generate the backward propagation of the sloshing motion for the transverse wave along the potential well for small wave numbers.Second,the depinning dynamics of 2DDP under 1D periodic substrates is studied.Using the obtained positions and velocities of the simulated dust particles from Langevin dynamics simulations,the collective drift velocity,static structure factor,particle trajectories,mean square displacement,kinetic temperature and other diagnostics are all calculated.The results show that,for a specific range of substrate strengths,as the DC driving force increases from zero,the system would experience the pinned state,the plastic flow state,and the elastic flow state.For deeper substrates,as the DC driving force increases from zero,the system would change directly from the pinned change to the elastic flow state.When the DC driving force is large enough,for any substrate strengths,the drift velocity would follow the same linear relation with the DC driving force.Third,the EOS of 2D liquid dusty plasmas is studied using equilibrium molecular dynamics simulations.Based on the obtained positions,velocities of dust particles,as well as the interaction between dust particles,the pressure of 2DDP is obtained from the diagonal element of stress tensor.Thus,an analytical expression of the relationship between the pressure and internal energy of 2D liquid dusty plasmas is obtained.The expression indicates that,the relationship between pressure and internal energy is much more complicated for 2D liquid dusty plasmas than that in ideal gas.Especially in the conditions of lower temperatures and larger shielding parameters,this relationship between pressure and internal energy deviates much more from that of the ideal gas.This result completely solves the questions in the previous paper[Oxtoby et al.,Phys.Rev.Lett.111,015002(2013)].In addition,based on the obtained EOS of 2D liquid dusty plasmas,the isothermal bulk modulus of elasticity of 2D liquid dusty plasmas is derived,and next the longitudinal sound speed in this system is derived using this bulk modulus.The obtained sound speeds here are well consistent with the previous results from other methods in this field.Finally,to carry out the project from the Ministry of Science and Technology which is being undertaken by our research group,a series of rehearsal experiments of 3D trajectory reconstruction for dusts have been performed to seek the optimized choice of various parameters in the 3D reconstruction,and under this condition,the effect of the placement of the measured object on the error of the experimental results is studied.These results provide the technical supports in the designing and application of the calibration and periscope systems of the stereo camera.