Particle-in-cell Simulation Of Hall Thruster In Non-orthogonal Structured Grids

The numerical method based on Particle-in-Cell(PIC)is a very effective way to study hall thruster.The current PIC model approximates the boundary with a stepped grid,which is difficult to apply the boundary conditions accurately and brings about certain calculation errors.In view of the development trend of more and more complex geometric models of Hall thrusters at present,the PIC model under non-orthogonal structured meshes is established by generating non-orthogonal structured meshes that are fully compatible with the boundary,which can enhance the adaptability of the numerical simulation platform to complex Hall thrusters.The new numerical simulation platform is used to simulate the hall thruster in the straight channel and the hall thruster in the widening channel to verify its effectiveness.Firstly,the key technology of PIC model in non-orthogonal structured grid is studied.Starting with the particles,the paper first describes how to introduce or arrange the particles in the simulation initialization,then describes how to distribute the electromagnetic field value on the grid nodes to the particles in the non-orthogonal structured grid.Particles begin to move under the action of electromagnetic fields.When they move to a new position,in order to distribute the charge to the grid nodes,the grid of particles must be determined and the interpolation scheme mentioned above is adopted to locate the particles.Particles may collide in the process of motion.After analyzing the mean free path,this paper only considers the excitation,elastic and ionization collisions between electrons and atoms.Finally,in order to reduce the calculation amount,the method of giant particles is adopted,but the atomic density is still two orders of magnitude different from the plasma density,so the method of variable weight is adopted.At the same time,using Szabo method to reduce the ion mass and increase the vacuum dielectric constant can effectively reduce the calculation amount.Secondly,how to solve Poisson equation discretely in non-orthogonal structured mesh is studied.We use the finite volume method to discretize Poisson equations in each grid cell.However,different from orthogonal grids,the diffusion term is divided into orthogonal and non-orthogonal terms by delay correction method,and the delay of non-orthogonal terms is added to the source term processing.Therefore,the solution ofthe whole algebraic equation is divided into inner iteration and outer iteration.For inner iteration,we use the double conjugate gradient stability algorithm to solve the large sparse matrix.For outer iteration,when the inner iteration yields a convergent solution,the resulting solution is used to update the source term until the corresponding conditions are met.Finally,gaussian formula is used to solve the electric field distribution on the grid nodes after the electric potential is determined.Thirdly,the generation technology of adaptive grid is studied.It is important to generate a reasonable grid for numerical computation.Starting from the most typical straight-path hall thruster and wide-path Hall thruster geometric models,the advantages and disadvantages of several grid generation methods are discussed in turn.The methods to generate the proper body mesh mainly include algebraic method and differential equation method,among which the differential equation method can be divided into elliptic equation method,parabolic equation method and hyperbolic equation method.In this paper,an elliptic grid generator is used to generate a fully fit mesh by solving Laplace equation in blocks.Finally,we verify the code.First,test the most basic code segments one by one,including particle motion module,potential solver,electric field solution,etc.,to ensure that each segment of code can achieve the expected function;Then the whole PIC program is tested to verify the effect of the program in the hall thruster in the through channel and the hall thruster in the widening channel.