Analytic expressions for the potentials and fields of flat and cylindrical plates, including the fringe fields, are given. The present analysis extends and simplifies the current expression for the fields of flat plates and develops expressions for the fringe fields of cylindrical plates in terms of polar coordinates. The development of a FORTRAN program to output the field strength at a given location within the Proton Electric Dipole Moment (Proton EDM) ring is then described. Fourth-order Runge-Kutta integration is used to investigate the effect of fringe fields on particle and spin dynamics with precision tracking in the proposed Proton EDM experiment.

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.