Two Dimensional Implicit IFE-PIC Plasma Numerical Simulation And Its Application

Low temperature plasma has been widely applied in many industrial fields,however,the research methods for plasma science are very limited in numbers.The cost of experimental methods is huge,and the behavior of microscopic plasma can not be observed.The cost for numerical simulation is relatively less,but fluid model which treat the electron and ion as the fluid is still unable to observe the microscopic plasma,and particle model can get all the microscopic and macroscopic plasma behaviors accurately and consistently.Nevertheless,particle model is time-consuming,which is not suitable on the simulation of large-scale plasma physics or engineering problems.The main reason for the low efficiency of the particle model is due to the explicit particle-in-cell(PIC)model,the performance of this model is limited by the stability conditions and can not use larger temporal and spatial step sizes.As a result,the cost of total simulation time is high.Thus,it is necessary to develop a high efficiency particle model for the research of low temperature plasma.This thesis developed a two-dimensional implicit PIC model based on an immersed-finite-element(IFE)method,which can significantly improve the computational efficiency,especially for the large-scale and long-time evolution plasma problems with complex interface.Then,the implicit IFE-PIC model was used to simulate the electric thruster.Compared with previous works,the biggest advantage of the model is that it uses real physical parameters,and does not scale the physical space or mass,which makes the results more accurate and reliable.The main research content of this paper can be divided into two parts.The first part is the method research of the implicit IFE-PIC model,including Chapter 2 and Chapter 3.The second part is the simulation research of electric thruster,including Chapter 4 and Chapter 5.First of all,this thesis used the full particle model based on particle-in-cell(PIC)to simulate the plasma to obtain the microscopic and macroscopic behaviors of plasma with reasonable accuracies,and used the regular grid to discretize the calculation domain to adapt to the particle model.Thus,this thesis chose the immersed-finite-element(IFE)method to solve the problems with complex interface in regular grid.So,the main simulation method of this thesis is based on the immersed-finite-element particle-in-cell model(IFE-PIC).This work first give a detailed description of the IFE method and the PIC model,and introduce the setting method of various boundary conditions.The accuracy of the IFE-PIC model is verified by numerical examples.Secondly,the cost of explicit IFE-PIC model is too high to satisfy the current application requirements in physics and engineering problems,so the implicit IFE-PIC model was developed in this thesis.With the implicit PIC algorithm,the traditional Poisson's equation becomes a non-isotropic equation,thus this thesis developed an anisotropic IFE method firstly,and verify the accuracy and convergence by numerical examples.Then,incorporating the anisotropic IFE method into the direct implicit PIC method,a complete implicit IFE-PIC method was constructed.Finally,this work provided some plasma sheath examples to illustrate the accuracy,stability and applicability of the implicit IFEPIC method.The results indicate that the method can efficiently and accurately simulate plasma problems with complex interface based on structured grids and large step sizes.Thirdly,the Radio-Frequency(RF)biased grid system of ion thruster was studied based on the implicit IFE-PIC model.This work built a two-dimensional numerical model of the RF biased grid system firstly,and simulated the accelerating process of RF biased grids.The results showed that electrons can enter the downstream through the acceleration grid only when the RF voltage reaches the minimum.Furthermore,the law of plasma motion was further explained based on the spatial velocity distribution of electrons and ions.Then,the working conditions of different RF voltage,RF frequency and upstream plasma density were discussed in detail,it was found that these physical factors have a great influence on the plasma acceleration process,especially on the downstream average neutralization rate and the impact current of the acceleration grid.As a whole,the average neutralization rate and the impact current decreased with the increase of voltage,the average neutralization rate and the impact current decreased with the increase of RF frequency,and the average neutralization rate and the impact current increased with the increase of upstream plasma density.Finally,the two-dimensional annular channel exit and the circumferential channel cross section of the Hall thruster were simulated by the implicit IFE-PIC model.All the physical parameters used in these simulations are real values which without any human scaling operation.The simulation results showed that there is an obvious periodic fluctuations in electrical potentials in the annular channel,and the rotating frequency is about31.25 KHz,which is close to the azimuthal low frequency oscillation(Rotating Spoke).In the annular channel,the distribution of plasma in the radial direction was not completely symmetrical,and the number of various kinds of particles impacting on the inner and outer walls showed spatial heterogeneity,which indicated that the plasma impact on the wall is not uniform,this simulation result was consistent with the corrosion morphology of the wall of Hall thruster.Compared with the two-dimensional rectangular expansion model,the annular channel was obviously affected by the centrifugal motion and the change of magnetic field curvature.The simulation results of the circumferential channel showed that the plasma density reaches the maximum in the acceleration region,and the plasma density showed obvious oscillations in the axial and circumferential directions.The analysis of the axial and circumferential oscillations on the exit section showed that the axial oscillation is related to the ion transmission time,while the rotation speed of the circumferential oscillation is small.