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

TL;DR

This paper applies the contour dynamics method to simulate one-dimensional Vlasov-Poisson plasma with periodic boundaries, effectively handling boundary crossings and validating results against analytical solutions and nonlinear phenomena.

Contribution

It introduces the application of contour dynamics to periodic boundary conditions in 1D Vlasov-Poisson plasma, overcoming boundary crossing challenges with a periodic Green's function.

Findings

Successful reproduction of Landau damping in linear regime

Validation against analytical solutions

Reproduction of particle trapping in nonlinear regime

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.