A Methodology for Evaluation of Charged Particle Trajectory Integrators

Simulation codes for the design of advanced charged particle (CP) devices are necessary because of the nonlinear nature of the combined Newton-Lorentz/Maxwell equations.  Numerical techniques for the integration of charged particle trajectories are core features of these codes.  The range of parameters spanned by CP devices requires a variety of techniques to meet accuracy, speed and stability requirements.  This paper examines the accuracy and performance of several leap-frog charged-particle pushers used in both electro-static and electromagnetic simulations.   Accuracy was evaluated by comparison to relativistically correct analytic solutions for a set of six standard field configurations.  The relativistic modified-Boris push and several variants developed to address specific shortcomings were examined.   As with nearly all numerical methods, results depend on the type of problem and the parameter space o interest.   We do not settle on a "best" algorithm, but rather suggest a general methodology for rapidly assessing the performance of individual algorithms for specific performance and problem constraints.