Weighting schemes for charges and fields to control self-force in unstructured finite element Particle-in-Cell codes

Abstract

Summary form only given. Particle-in-Cell (PIC) is a powerful technique for simulating physical processes where discrete objects exert forces on each other. In the context of this talk we are examining electrostatic plasmas where the particles represent electrons or ions which are free to move around the system and the electric fields are defined on the mesh. While this talk focuses on electrostatics, the techniques discussed are generalizable to other domains. In traditional structured codes symmetry between the weighting operators which map the particles charge to the mesh and the electric field from the mesh back to the particle results in no self-force. In the unstructured finite element world the traditional approaches result in a self-force which causes a particle to push itself and to violate Newton's laws of motion. This talk focuses on a novel approach in controlling the selfforce of particles in PIC codes. This approach chooses a weighting scheme which closely reproduces the exact potential at grid nodes both near a charged particle and for the long range effects. This potential can then be differenced to compute an electric field at particle locations allowing for a exact cancellation up to the tolerance which the exact solution is reproduced at grid locations. This algorithm can be combined with a particle-particle--particle-mesh (P3M) approach to cancel all local effects and compute the N2 terms directly for a local patch resulting in reduced self-force and superior spatial resolution. This talk will present the details of this algorithm, lower self-force on a single particle, better Coulomb collisions for a few particles, and accurate results for highly under-refined meshes while maintaining the geometric flexibility of unstructured grids.