Unified Current Mapping Framework for Mixed Finite Element Particle in Cell Methods

There has been significant recent effort to improve analysis of plasma physics particle in cell methods that use finite element methods for transient electromagnetic analysis. The challenge with any of these formulations is the mapping the charges and currents on the grid consistently so that charge is conserved as the particle distribution evolves in time. This work analyzes this challenge by determining the spatial and temporal requirements needed to satisfy the governing equations, and presents a unified approach for source representation on both primal and dual grids are presented. It is shown that the proposed approach leads to charge conserving scheme when combined with an appropriate time integration methods.