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arXiv · 1509.02863

Comment on "Symplectic integration of magnetic systems": a proof that the Boris algorithm is not variational

C. L. Ellison·J. W. Burby·H. Qin
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Abstract

The Boris algorithm for integrating charged particle trajectories in electric and magnetic fields is popular due to its simple implementation, rapid iteration, and observed long-term numerical fidelity. The underlying cause of this long-term fidelity has become a matter of controversy, with one article claiming the method to be symplectic [S. D. Webb, J. Comput. Phys. 270 (2014) 570], and others claiming the method to be volume preserving but not symplectic [e.g. H. Qin et al., Phys. Plasmas 20 (2013) 084503]. To resolve the discrepancy, this letter leverages a discrete Helmholtz condition to demonstrate that no variational formulation of the Boris algorithm exists, indicating that the long-term fidelity should be attributed to the volume-preserving properties of the algorithm.

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C. L. Ellison, J. W. Burby, H. Qin. 2015-09-09. Comment on "Symplectic integration of magnetic systems": a proof that the Boris algorithm is not variational. https://doi.org/10.1016/j.jcp.2015.09.007

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