Investigations Of Optimizing Particle Tracking Algorithms For Charged Dusts In Complex Plasmas

Dusty plasma refers to a mixed system consisting of dust particles and plasma.In the laboratory conditions,dust particles are charged negatively in the RF discharge plasma,containing thousands to tens of thousands elementary charges each in the steady state,as a result,these dust particles repel each other.Due to the strong electric field in the plasma sheath above the lower electrode,the downward gravity of each particle is balanced by the upward electric field,so that these charged dust particles can self-organize into a quasi-twodimensional single layer suspension in the sheath.Due to the extremely low charge-to-mass ratio of dust particles,the motion of dust particles is slow enough,and the interparticle distance is large enough.As a result,the detailed trajectories of dust particles inside the fieldof-view can be recorded directly using high-speed cameras.Therefore,in dusty plasma experiments,the particle tracking velocimetry(PTV)can be exploited to analyze the microscopic dynamics mechanism of many physical processes in dusty plasmas at the kinetic level of individual particles.Particle tracking velocimetry is a systematic data analysis method,which generally includes the particle identification from the image of each frame,the precise position calculation for all identified particles,the particle tracking between different frames,and finally the particle velocity calculation from their positions in different frames.While a PTV method is being used,various systematic and random errors are inevitably introduced in the calculated particle velocity.It is extremely important to reduce these errors when using these PTV methods to analyze dusty plasma experiments,which is the topic of this thesis.Similar to PTV,particle tracking acceleration(PTA)is to calculate the acceleration data of particles identified in each frame,which is also introduced into the data analysis of dusty plasmas.To reduce systematic errors while optimizing PTV and PTA methods,various particle tracking algorithms are introduced in this thesis.To quantify systematic errors,computer simulations of two-dimensional dusty plasmas are performed to achieve abundant particle position data,which are used to calculate various dynamical diagnostics.Thus,the advantages and disadvantages of these particle tracking algorithms can be compared,which provides an effective basis for the determination of the best particle tracking algorithm for the data analysis of dusty plasma experiments.First,Langevin dynamical simulations of two-dimensional dusty plasma liquids are perform to generate trajectories of thousands of particles.Next,to generate synthetic data to imitate the particle position data from experiments,an artificial error comparable to the error of the calculated particle positions in the experimental data analysis is added to each coordinate of the obtained particle position in the Langevin dynamical simulations.The systematic errors of these PTV methods can be quantified after analyzing these synthetic data using these PTV methods to calculate the velocity data and then comparing them with the velocity data directly from Langevin simulation.Thus,the best choice of the PTV method is determined.Besides the most commonly used two-frame linking,the polynomial fitting and spline interpolation are also introduced in the investigation of this thesis,and these tracking methods are based on the average of the position information in the several consecutive frames to reduce the systematic error.To describe the trajectories of particles,instead of assuming straight lines between frames in the two-frame linking,the polynomial fitting method uses a polynomial fitting expression to describe trajectories between several frames,while the spline uses smooth curves of the piecewise functions exactly going through all measured positions.For the synthetic data obtained by artificially introducing errors in the particle position data from simulations of magnetized two-dimensional dusty plasmas,the magnitude of magnetic field,the amplitude of particle position error,and the time interval between two consecutive frames are all easily adjusted.Then,the particle velocity data are calculated using various PTV methods with the synthetic data,so that the two dynamical diagnostics of the probability distribution function for the velocity and the velocity autocorrelation function are calculated,which are compared with these two diagnostics calculated from the "real" particle velocity data(i.e.,which are directly from the Langevin dynamical simulation without adding any noise).Thus,the most desired PTV method just corresponds to the diagnostic closest to that of the true velocity.Furthermore,in this way,the systematic errors of various PTV methods are effectively quantified,and the variation of systematic errors of these PTV methods with the experiment conditions can be easily analyzed.It is found that,with the increase of the measurement uncertainty,the probability distribution function of the calculated velocity from these PTV methods are dispersed further away from that of the true velocity.As the time interval between two consecutive frames gradually increases,the velocity data calculated from these PTV methods mostly tend to result in smaller velocities.The best choice of PTV method is not fixed,which directly depends on the experiment conditions.At the same time,these trends are more significant under a stronger magnetic field.A demonstration of using these PTV methods with the experimental data of two-dimensional dusty plasma is also performed,with the experiment results well agreeing with the simulation results above,further confirming that the suggested practical procedure of determining the best choice of PTV methods using computer simulations is reliable.Second,due to the importance of the acceleration data in the related studies,investigations of determining the best choice of the PTA method is also performed under various conditions here.Similar to the previous PTV investigations,polynomial fittings and spline interpolations are also introduced into the PTA investigations here,and the two diagnostics of the probability distribution function for the acceleration data and the acceleration autocorrelation function are used to quantify the systematic errors of various PTA methods,which are compared to determine the best choice of the PTA method.The results from the simulation and synthetic data show that the best choice of the PTA method depends on the experiment conditions.Furthermore,the best choices of the PTV and PTA methods may not be the same,even if the conditions are the same.However,by comprehensively considering the results of these PTV and PTA diagnostics,the selection of the PTV and PTA methods within the acceptable range of errors can be achieved,so that the obtained velocity and acceleration data are self-consistent.