Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system

TL;DR

This paper introduces a canonical symplectic particle-in-cell method for the Vlasov-Maxwell system, enhancing long-term simulation accuracy and enabling large-scale plasma physics computations.

Contribution

A novel symplectic PIC method based on discretizing the canonical Poisson bracket, with a fast local algorithm for implicit time advancement that scales to very large systems.

Findings

Confirmed Mouhot and Villani's nonlinear Landau damping theory

Accurately simulated nonlinear evolution of wave reflectivity

Enabled large-scale plasma simulations with billions of degrees of freedom

Abstract

Particle-in-Cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretizing its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g., $10^{9}$, degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.