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Explicit high-order non-canonical symplectic particle-in-cell algorithms forclassical particle-field systems governed by the Vlasov-Maxwell equations aredeveloped. The algorithm conserves a discrete non-canonical symplecticstructure derived from the Lagrangian of the particle-field system, which isnaturally discrete in particles. The electromagnetic field isspatially-discretized using the method of discrete exterior calculus withhigh-order interpolating differential forms for a cubic grid. The resultingtime-domain Lagrangian assumes a non-canonical symplectic structure. It is alsogauge invariant and conserves charge. The system is then solved using asplitting method discovered by He et al., which produces five exactly-soluablesub-systems, and high-order structure- preserving algorithms follow bycombinations. The explicit, high-order, and conservative nature of thealgorithms is especially suitable for long-term simulations of particle-fieldsystems with extremely large number of degrees of freedom on massively parallelsupercomputers. The algorithms have been tested and verified by the two physicsproblems, i.e., the nonlinear Landau damping and the electron Bernstein wave.

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