General Spin Precession and Betatron Oscillation in Storage Ring

TL;DR

This paper derives generalized formulas for spin precession and betatron oscillations in storage rings, accounting for electric and magnetic dipole moments and including radial and vertical oscillations, with applications to muon storage rings.

Contribution

It provides new, comprehensive formulas for spin precession and betatron oscillations in storage rings, extending previous models to include electric dipole moments and radial oscillations.

Findings

Generalized spin precession formula for particles with dipole moments.

Extended betatron oscillation formula including radial and vertical oscillations.

Useful equations for muon storage ring experiments.

Abstract

We give the geralized expression of spin precession of extended bunch particles having both anomalous magnetic and electric dipole moments in storage ring. The transversal betatron oscillation formula of the bunch is also given. The latter is the generalization of the Farley's pitch correction \cite{Farley}, including radial oscillation as well as vertical one. Some useful formulae for muon storage ring are discussed in appendix.