  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.
