# General description of spin motion in storage rings in presence of oscillating horizontal fields

## TL;DR

This paper provides a comprehensive theoretical framework for understanding how oscillating horizontal magnetic and quasimagnetic fields influence spin dynamics in storage rings, extending previous models to more complex field configurations.

## Contribution

It generalizes existing models to include nonzero horizontal field components that form an ellipse, deriving equations for all polarization components with arbitrary initial polarization.

## Key findings

- Derived general equations for spin evolution with elliptical oscillating fields
- Extended previous models to nonresonant oscillation frequencies
- Analyzed spin behavior influenced by vertical betatron oscillations

## Abstract

The general theoretical description of the influence of oscillating horizontal magnetic and quasimagnetic fields on the spin evolution in storage rings is presented. Previous results are generalized to the case when both of the horizontal components of the oscillating field are nonzero and the vector of this field circumscribes an ellipse. General equations describing a behavior of all components of the polarization vector are derived and the case of an arbitrary initial polarization is considered. The derivation is fulfilled in the case when the oscillation frequency is nonresonant. The general spin evolution in storage rings conditioned by vertical betatron oscillations is calculated as an example.