A Grid-Free Particle Method for Electrostatic Plasma Simulations

This grant provided support for a postdoc at the University of Michigan to assist in developing a grid-free particle method for electrostatic plasma simulations. The aim of the work is to substantially improve the accuracy and efficiency of these simulations. The proposed method is an alternative to traditional mesh-based methods such as particle-in-cell (PlC). In the new approach, the standard Eulerian formulation of the Vlasov-Poisson equation is replaced by a Lagrangian formulation in which the charge flow map is the key unknown quantity. Discretizing the Lagrangian formulation leads to a grid-free particle method. The investigators made progress in formulating and testing this approach. Numerical results are presented for the cold one-stream and two-stream instabilities. The method is especially well suited for tracking charge transport and resolving fine structures in phase space.