Spin motion at and near orbital resonance in storage rings with Siberian Snakes I: at orbital resonance

D P Barber,M Vogt

doi:10.1088/1367-2630/8/11/296

Abstract

In this paper, and in a sequel, we invoke the invariant spin field to provide an in-depth study of spin motion at and near low order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarization at and near so-called snake resonances in proton storage rings.

Highlights

In earlier papers we and collaborators have emphasised the utility of the invariant spin field (ISF) and the amplitude dependent spin tune (ADST) for analysing spin motion in circular particle accelerators and storage rings [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Under certain conditions, the ISF is unique up to a global sign and in that case it allows estimates to be made of the maximum equilibrium beam polarisation and the maximum time averaged beam polarisation in proton storage rings
In this paper we have presented and contrasted four scenarios for spin motion on and off orbital resonance within the confines of our simple model, and by this means we have developed a clean, elegant account of the special features of spin motion at a snake resonance

Summary

Introduction

In earlier papers we and collaborators have emphasised the utility of the invariant spin field (ISF) and the amplitude dependent spin tune (ADST) for analysing spin motion in circular particle accelerators and storage rings [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. In our opinion, snake resonances have presented problems [17, 18], the numerical and theoretical investigations made so far have provided no completely coherent picture of spin motion at and near snake–resonance tunes, either with or without acceleration These papers provide a new contribution towards such a picture, at least within our adopted simple model. The spin motion can become very erratic close to the spin–orbit resonance condition νs(J) = k0 + k1Q1 + k2Q2 + k3Q3 where the Q’s are orbital tunes and the k’s are integers Near these resonances the ISF can spread out so that Plim is very small. We are primarily interested in [Q2] at and near 1/6 but the other cases serve to familiarise the reader with the “normal” cases

Off orbital resonance

Summary and conclusion