Discontinuous Galerkin particle-in-cell simulation of longitudinal plasma wave damping and comparison to the Landau approximation and the exact solution of the dispersion relation

We present results showing the measured Landau damping rate using a high-order discontinuous Galerkin particle-in-cell (DG-PIC) [G. B. Jacobs and J. S. Hesthaven, J. Comput. Phys. 214, 96 (2006)] method. We show that typical damping rates measured in particle-in-cell (PIC) simulations can differ significantly from the linearized Landau damping coefficient and propose a simple numerical method to solve the plasma dispersion function exactly for moderate to high damping rates. Simulation results show a high degree of agreement between the high-order PIC results and this calculated theoretical damping rate.