Computational Methods for a One-Directional Plasma Model with Transport Field

Abstract

The electromagnetic behavior of a collisionless plasma is described by a system of partial differential equations known as the Vlasov-Maxwell sys-tem. From a mathematical standpoint, little is known about this physically accurate three-dimensional model, but a one-dimensional toy model of the equations can be studied much more easily. Knowledge of the dynamics of solutions to this reduced system, which computer simulation can help to deter-mine, would be useful in predicting the behavior of solutions to the unabridged Vlasov-Maxwell system. Hence, we design, construct, and implement a novel algorithm that couples efficient finite-difference methods with a particle-in-cell code. Finally, we draw conclusions regarding their accuracy and efficiency, as well as, the behavior of solutions to the one-dimensional plasma model.