Different forms of first order spin-orbit motion and their utility in spin matching in electron storage rings

TL;DR

This paper derives and compares different first-order spin-orbit motion forms in electron storage rings, demonstrating their utility in spin matching and including fringe field effects for improved accuracy.

Contribution

It introduces a unified derivation of first-order spin-orbit motion forms and applies them to spin matching in electron storage rings, highlighting their practical advantages.

Findings

Different forms of spin-orbit motion are related and can be used interchangeably.

Including fringe fields improves the accuracy of spin matching conditions.

Re-derivation of spin matching conditions demonstrates the utility of certain forms.

Abstract

We derive the first order phase space dependence of spin-orbit motion of a particle in an accelerator by expanding the Thomas-BMT equation. Different forms can be found in the literature and we show how these are related, and care is taken to include fringe fields. The advantages of using certain forms is demonstrated by a detailed re-derivation of the spin matching conditions by V. Ptitsyn for the spin rotators in the Electron Storage Ring (ESR) of the Electron-Ion Collider (EIC) at Brookhaven National Laboratory.