Addenda to General Spin Precession and Betatron Oscillation in Storage Ring

TL;DR

This paper extends the theoretical framework for spin precession of particles in storage rings, incorporating higher-order effects, electric and magnetic fields, and addressing inconsistencies in previous models.

Contribution

It provides a generalized expression for spin precession that includes higher-order effects and the presence of electric and magnetic fields, improving upon prior models.

Findings

Derived higher-order spin precession equations.

Identified inconsistencies in existing focusing field models.

Emphasized importance of considering both E and B fields in 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 in higher order than the previous work and in the presence of ${\bf E}$ field as well as ${\bf B}$ field. These addenda are essential since some experiments consider the focusing field in the second order of the beam extent and in the presence of both ${\bf B}$ and ${\bf E}$ fields . It is shown that some focusing fields with constant magnitude of the velocity considered in many literatures lead to the violation of self consistency.