A fundamental derivation of two Boris solvers and the Ge-Marsden theorem
Abstract
For a separable Hamiltonian, there are two fundamental, time-symmetric, second-order velocity-Verlet (VV) and position-Verlet (PV) symplectic integrators. Similarly, there are two VV and PV version of exact energy conserving algorithms for solving magnetic field trajectories. For a constant magnetic field, both algorithms can be further modified so that their trajectories are exactly on the gyro-circle. The magnetic PV integrator then becomes the well known Boris solver, while VV yields a second, previously unknown, Boris-type algorithm. Remarkably, the required on-orbit modification is a reparametrization of the time step, reminiscent of the Ge-Marsden theorem.
Keywords
Cite
@article{arxiv.2106.04068,
title = {A fundamental derivation of two Boris solvers and the Ge-Marsden theorem},
author = {Siu A. Chin},
journal= {arXiv preprint arXiv:2106.04068},
year = {2021}
}
Comments
14 pages and 1 figures. Revised Title, Abstract, expanded Introduction and Conclusions