Coherent phase space structures in a 1D electrostatic plasma using particle-in-cell and Vlasov simulations: A comparative study

Abstract

We present a quantitative comparative study of the formation of coherent phase space structures in one dimension using two widely followed approaches in kinetic simulations of collision-less plasmas, namely, Monte Carlo based Particle-In-Cell (PIC) simulations and phase space grid based Eulerian Vlasov-Poisson simulations. Using a newly developed PIC solver, we demonstrate that, while for linear regimes, there is a ready quantitative agreement between Vlasov-Poisson and PIC solvers, whereas for weakly nonlinear regimes and late time simulations, for comparable field resolutions, Vlasov-Poisson simulation results are found to be relatively noise-free as compared to PIC results with a large number of PIC particles. As an extreme case, we address using high resolution PIC simulations, the formation of giant phase space vortices obtained recently using the Vlasov-Poisson method [P. Trivedi and R. Ganesh, Phys. Plasmas 23, 062112 (2016)] for an infinitesimal amplitude external drive. For identical parameters and numerical resolution, we present a qualitative and quantitative comparison between PIC results of driven giant phase space structures and those of the Vlasov method, for a Maxwellian plasma.