Analytical Benchmarks for Precision Particle Tracking in Electric and Magnetic Rings

A set of analytical benchmarks for tracking programs is required for precision storage ring experiments. To determine the accuracy of precision tracking programs in electric and magnetic rings, a variety of analytical estimates of particle and spin dynamics in the rings were developed and compared to the numerical results of tracking simulations. Initial discrepancies in the comparisons indicated the need for improvement of several of the analytical estimates. As an example, we found that the fourth-order Runge-Kutta/Predictor-Corrector method was slow but accurate, and that it passed all the benchmarks it was tested against, often to the sub-part per billion level. Thus, high precision analytical estimates and tracking programs based on fourth-order Runge-Kutta/Predictor-Corrector integration can be used to benchmark faster tracking programs for accuracy.