Canonical symplectic particleincell method for longterm largescale simulations of the VlasovMaxwell equations
Abstract
Particleincell (PIC) simulation is the most important numerical tool in plasma physics. However, its longterm accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the VlasovMaxwell system by discretising 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 largescale plasma simulations with many, e.g. 10^{9}, degrees of freedom. The longterm 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.
 Publication:

Nuclear Fusion
 Pub Date:
 January 2016
 DOI:
 10.1088/00295515/56/1/014001
 arXiv:
 arXiv:1503.08334
 Bibcode:
 2016NucFu..56a4001Q
 Keywords:

 Physics  Plasma Physics;
 Physics  Accelerator Physics;
 Physics  Computational Physics
 EPrint:
 Revised submission with more detailed derivation and a new application. 16 pages and 6 figures