Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

TL;DR

This paper introduces explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems that conserve key physical properties and are suitable for long-term, large-scale simulations on supercomputers.

Contribution

The paper develops a novel class of explicit, high-order, structure-preserving algorithms based on non-canonical symplectic geometry for particle-field systems governed by Vlasov-Maxwell equations.

Findings

Algorithms conserve a discrete non-canonical symplectic structure.

Algorithms are gauge invariant and charge conserving.

Validated through nonlinear Landau damping and electron Bernstein wave simulations.

Abstract

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially-discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a splitting method discovered by He et al., which produces five exactly-soluable sub-systems, and high-order structure- preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.