Contour Dynamics for One-Dimensional Vlasov-Poisson Plasma with the Periodic Boundary

Abstract

We revisit the contour dynamics (CD) simulation method which is applicable to large deformation of distribution function in the Vlasov-Poisson plasma with the periodic boundary, where contours of distribution function are traced without using spatial grids. Novelty of this study lies in application of CD to the one-dimensional Vlasov-Poisson plasma with the periodic boundary condition. A major difficulty in application of the periodic boundary is how to deal with contours when they cross the boundaries. It has been overcome by virtue of a periodic Green's function, which effectively introduces the periodic boundary condition without cutting nor reallocating the contours. The simulation results are confirmed by comparing with an analytical solution for the piece-wise constant distribution function in the linear regime and a linear analysis of the Landau damping. Also, particle trapping by Langmuir wave is successfully reproduced in the nonlinear regime.