A new algorithm for charge deposition for multiple-grid method for PIC simulations in r– z cylindrical coordinates

Abstract

A mesh of nodes used in particle-in-cell simulations may be refined in some regions to obtain better local spatial resolution without adding excessive computational cost. Each refinement can be seen as a finer grid in a multiple-grid system. The standard bilinear weighting method in two-dimensional ( r– z) cylindrical coordinates using a multiple-grid system is detailed and an inadequacy in the method is presented. A new algorithm of particle to node weighting in a multiple-grid system is then described and compared to the standard bilinear weighting method in two-dimensional ( r– z) cylindrical coordinates. This description pays particular attention to the nodes near the interface between grids of differing cell-size. The volume weighting method used in this study is geometrically similar to the standard bilinear PIC method in Cartesian coordinates, but weights in proportion to the volumes of revolution of the areas about the z-axis, rather than the areas themselves. As the volume weighting method has the axisymmetric geometry built in, it is a natural system to use in this particular case. A full particle-in-cell (PIC) simulation of metal plasma-immersion ion implantation and deposition (MePIIID) of a flat stage using three grids of cell size: 0.5 × 0.5, 1 × 1 and 2 × 2 mm; is performed and results are compared to those obtained from a single-grid simulation with the same parameters. The multiple grid method compares very well to the single-grid simulation.