Analytical Estimations of the Chromaticity and Corrections to the Spin Precession Frequency in Weak Focusing Magnetic Storage Rings

TL;DR

This paper provides analytical estimations of beam transverse chromaticities and spin precession frequency bias in weak focusing storage rings, verified by simulations, with potential methods to suppress frequency bias for high-precision experiments.

Contribution

It introduces next-order analytical approximations for beam and spin variables in weak focusing rings, enhancing precision in accelerator physics modeling.

Findings

Analytical estimations match high-precision simulations.

Identifies potential methods to suppress spin precession bias.

Improves understanding of beam and spin dynamics in storage rings.

Abstract

Understanding beam and spin dynamics are fundamental in accelerator physics, 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. The present paper provides analytical estimations of some of the important variables such as beam transverse chromaticities and the spin precession frequency bias 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 spin precession frequency bias which relevant experiments may find beneficial.