Study On The Two-dimensional Numerical Simulation Algorithm For Plasma Diffusion Equation In Hall Thrusters

With the deepening of space exploration,electric thruster has become a necessity for the development of national space industry.Hall thruster has been widely used in space system because of its superior performance.In order to better understand the internal physical mechanism of Hall thruster and to further optimize and improve the performance of Hall thruster,it is usually necessary to simulate the operation process of Hall thruster.At present,it is the full Particle-in-Cell simulation method that is mainly used to simulate in our country.However,the full Particle-in-Cell simulation method has great limitations for its slow calculation speed and the small range of applicability to particles.In order to solve this problem,a hybrid PIC simulation method is proposed to simulate and analyze Hall thruster.Based on the basic principle of plasma physics,a hybrid PIC simulation model of Holzer thruster is established.In this hybrid PIC simulation model,the ions and electrons in Hall thruster are processed by different methods.The dynamics and kinematics of ions in Hall thruster are analyzed.The PIC method is used to track the movement of ions after each time step.After obtaining the position of ions at each time step,the density distribution of plasma is obtained by Cloud-in-Cell method.According to the current conservation equation,diffusion current equation and plasma density distribution of electrons in the channel,the new potential distribution in Hall thruster can be obtained after a single time step.With the time overlying and the continuous cycle of the program,the final motion state of the plasma in the Hall thruster can be obtained by this method.In the hybrid PIC algorithm,it is mainly divided into two parts: the ion propulsion part and the solving electron diffusion equation.In the part of ion propulsion,PIC method is successfully used to simulate the particle movement in Hall thruster.For solving the electron diffusion equation,a finite element numerical solution algorithm is built to solve and analyze it.In the process of building the solver for finite element numerical solution,the following four steps have been taken: meshing and information storage of finite element,derivation of basis function,discretization of finite element weak format and treatment of boundary conditions.In order to solve the electronic diffusion equation,the finite element numerical solver was upgraded three times after its basic functions were built and verified.Finally,the solver can further solve the anisotropic elliptic equation in Cartesian coordinate system,the isotropic elliptic equation in cylindrical coordinate system and the anisotropic elliptic equation in cylindrical coordinate system.The feasibility and convergence of the sovler are proved by error analysis of the calculating results of the solver.Thus,the solution of the key control equations in the Hall thruster hybrid PIC algorithm can be successfully completed by using the solver.Finally,the integrated model of hybrid PIC simulation of Hall thruster is built,which can be used in the related research work of Hall thruster.