Self-force subtraction in particle in cell simulations

Abstract

A method is presented to remove the numerical self-force that appears in particle-in-cell (PIC) simulations in computational domains discretized with general meshes and boundary conditions. The self-force is a non-physical force that a particle exerts on itself as a result of the discretization of charge density on a computational grid, and the interpolation of electric fields back to particle positions. With a uniform grid and periodic boundary conditions, Hockney and Eastwood (1988) demonstrated that this spurious force can be suppressed to machine accuracy if consistent interpolations of particle charges to grid points, and electric field back to particle positions are used. In non uniform unstructured meshes with multiply connected domains, or more general boundary conditions however, the self-force is unavoidable in the standard PIC approach, which can be a concern in some simulations. In this paper a straightforward and efficient method is presented to suppress the self-force for unstructured meshes and open boundary conditions in electrostatic codes as used, for example, to simulate spacecraft-environment interaction. The method consists of precomputing an array of self-forces associated with unit charges at each mesh vertex of the computational grid, which can then be used to interpolate the self-force at any particle position. The computed self-force can then be subtracted from the force computed in the standard PIC approach thus enabling particle trajectory integrations that are free from this unphysical force. The method is illustrated with simulation results using an unstructured tetrahedral mesh in spherical geometry.