A Half-Cell Weighting Method for Multiple-Grid PIC Simulation

Summary form only given. Particle-in-cell (PIC) simulations have been extensively used in recent years for the modeling of plasmas. When there is a need for higher spatial resolution in PIC simulations, it is common practice to reduce the cell size. In situations where detail is needed in one part of the simulation region and not another, one can use two or more grids of differing cell size. This has the advantage of using fewer nodes in the simulation, thereby reducing computation time, without sacrificing detail where it is needed. In a multiple-grid system, a problem arises at the interface between two grids. The case where a coarse grid is joined to a fine grid of half the cell-size is discussed. There are two types of interface nodes, the node (j,k) is one type and the node (j,k+l) is another. The node (j,k) is at the corner of four cells: A, B" C and D". The node (j,k+l) shown is another tvpe of node, it is at the corner of only the A and E cells and not the B" cell. A half-cell weighting method is developed to solve the weighting problem arises at the boundarv. It is shown that the expression for the change of momentum has no weighting function present. The self-force as described in C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985) is eliminated as the question of momentum change is reduced to the properties of the calculation of the electric field from the charge density. The method has been applied to simulate Metal Plasma Immersion Ion Implantation of a sharp cone and a fine tip.