Analytical Benchmarks for Precision Particle Tracking in Electric and Magnetic Rings

Abstract

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.

9 pages, 10 figures

References in corpus (4)

• Muon (g-2) Technical Design Report
• A Storage Ring Experiment to Detect a Proton Electric Dipole Moment
• Spin coherence time analytical estimations
• Confirmation of some formulas related to spin coherence time

Cited by in corpus (8)

• Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles
• Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab
• Storage Ring Probes of Dark Matter and Dark Energy
• Comprehensive Symmetric-Hybrid ring design for pEDM experiment at below $10^{-29}e\cdot$cm
• General classical and quantum-mechanical description of magnetic resonance: An application to electric-dipole-moment experiments
• A new computational framework for particle and spin simulations based on the stochastic Galerkin method
• Reduction of coherent betatron oscillations in a muon g-2 storage ring experiment using RF fields
• Thomas-BMT equation generalized to electric dipole moments and field gradients