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A set of analytical benchmarks for tracking programs is required forprecision storage ring experiments. To determine the accuracy of precisiontracking programs in electric and magnetic rings, a variety of analyticalestimates of particle and spin dynamics in the rings were developed andcompared to the numerical results of tracking simulations. Initialdiscrepancies in the comparisons indicated the need for improvement of severalof the analytical estimates. As an example, we found that the fourth-orderRunge-Kutta/Predictor-Corrector method was slow but accurate, and that itpassed all the benchmarks it was tested against, often to the sub-part perbillion level. Thus, high precision analytical estimates and tracking programsbased on fourth-order Runge-Kutta/Predictor-Corrector integration can be usedto benchmark faster tracking programs for accuracy.

Analytical Benchmarks for Precision Particle Tracking in Electric and Magnetic Rings