Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Yang
He, Ruili Zhang, and Yajuan Sun
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 structure-preserving splitting method discovered by
He et al., which produces five exactly-soluble 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.
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Submitted to: Physics of Plasmas
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