The dipole expansion method for plasma simulation

A procedure for determining the grid charge density and the electrostatic forces due to a system of extended charges for the purpose of plasma simulation is presented. In this scheme a charge (monopole) and a dipole moment, both extended, are assigned to the nearest grid point. The corresponding calculations of the force require the determination of the electric field and its gradient. Comparison with charge sharing schemes indicate that fewer operations per particle are required at the expense of more operations per grid point. We also present a modified version, the subtracted dipole scheme (SUDS). In this version the field calculations do not take significantly longer than in nearest-grid-point calculations. This is particularly important in two- and three-dimensional simulations. We also discuss an optimization of the coding, particularly for the operations that must be done for each particle (computing its contribution to the charge density and updating its position and velocity). For example, this optimization has given a one-dimensional, nearest-grid-point code (lowest order in the multipole expansion scheme) that takes ∼1.8 μsec/particle on the IBM 360/91. We assess the value of the dipole correction by comparing dipole and nearest-grid-point simulations. A comparison between the dipole expansion (SUDS) and charge sharing is also given. 8 refs., 10 figs