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 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.

16 pages, 7 figures

References in corpus (5)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment
• Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab
• Equation of spin motion in storage rings in a cylindrical coordinate system
• Improved limits on the hadronic and semi-hadronic CP violating parameters and role of a dark force carrier in the electric dipole moment of ${}^{199}$Hg