Comparison of Charged Particle Tracking Methods for Non-Uniform Magnetic Fields

摘要

Five particle tracking methods are compared for their ability to determine trajectory and conserve energy. The trajectory integrators include: the Boris particle tracking method (a widely used method for charged particles), the classical fourth order Runge-Kutta (a ubiquitous high order integrator), Stormer-Verlet as a partitioned Runge-Kutta (a second order symplectic integrator), fourth order Gauss Runge-Kutta (a fourth order symplectic integrator), and Wirz's modified Boris method (a new particle tracker constructed to handle large magnetic gradients). In general, it is the goal of this study to compare the symplectic integrators with the classical methods, as well as benchmark the Wirz's algorithm against these proven particle trackers. The symplectic integrators control their overall energy error, but at the cost of being implicit, where as the classical "Newtonian" methods are explicit but slowly accumulate errors in energy over time. Wirz's modified Boris is shown to strike the balance between the two classes with explicit implementation and conservation of total energy.