Analytical estimations of the chromaticity and corrections to the spin precession frequency in weak focusing magnetic storage rings

Abstract

Understanding beam and spin dynamics are fundamental in accelerator-based experiments concerning polarized beams. And there has been growing interest in having more precise estimations of the beam and spin dynamics variables, as more high precision particle physics experiments in the intensity frontier appear. This paper provides analytical estimations of some of the important variables such as beam transverse chromaticities and corrections to the spin precession frequency in the simplest type of particle accelerator: a circular magnetic storage ring with weak vertical focusing. We attempt to precisely obtain the next order approximations from the small betatron oscillations or the momentum dispersion, verified by high precision spin tracking simulation. We also discuss a potential way to suppress the corrections to the spin precession frequency, which relevant experiments may find beneficial.