Influence Of Dust Particle Size Distribution On Shock Waves In Inhomogeneous Dusty Plasmas

In recent years,the study of dusty plasma has always been the focus of people's attention.The study of the composition of dusty plasma and its physical properties plays an important role in space exploration,experimental analysis and industrial processing,and also has an important reference value for new interdisciplinary subjects.In this paper,based on the importance of dusty plasma research,combined with the relevant knowledge of nonlinear science,the theoretical analysis and numerical simulation of different dusty plasma models are carried out,and the relevant conclusions are obtained,which has important reference significance for space exploration,experimental research and industrial fields.Dusty plasma is mainly composed of ions,electrons,charged dust and neutral particles.From the macroscopic point of view,the moving electron,ion and charged dust can be approximately regarded as an ideal fluid.By using the continuity equation,momentum equation and Poisson equation in fluid mechanics,a set of equations describing the dust plasma wave is established.Among them,the size distribution of dust particles obeys the Power Law Distribution(PLD),ion obeys the non-thermal distribution,and electron obeys the Boltzmann distribution.In general,for equations describing different physical models,different methods can be used to solve them,such as reduced perturbation method,similar transformation method,trial function method,special transformation method,etc.In the third chapter,the propagation characteristics of three dimensional nonlinear shock waves in magnetized dusty plasmas are studied.By using the reduced perturbation method,the Korteweg-de-Vries Burgers equation is obtained,and the approximate solution described the shock wave structure is obtained.Through numerical simulation of different parameters,the effects of inhomogeneity,dust particle size distribution and external magnetic field on the propagation characteristics of shock waves in plasma are studied.The numerical simulation shows that when the dissipation effect caused by the viscosity parameter is much larger than the dispersion effect,the shock wave will change from oscillating structure to smooth structure.In addition,The oscillation intensity and amplitude of dust shock waves with the same size of dust particles are much larger than those with different size of dust particles.In the fourth chapter,the stability of linear dust wave in magnetized dusty plasma is studied.The linear dispersion equation describing the stability of dust acoustic wave is given by Fourier analysis method.The frequency and damping rate under different parameters is obtained by numerical simulation.The effects of particle size distribution,non-uniformity and external magnetic field on dust acoustic stability is studied.The numerical results show that the thermal ion density parameters,minimum radius,radius of maximum and minimum radius ratio,dust charge number index,and magnetic field enhance the damping rate,but the dust density parameters,the boltzmann electron density parameters,the power-law distribution index,along the x direction of wave number and inhomogeneity weaken the damping rate.