# Phase locking the spin precession in a storage ring

## TL;DR

This paper demonstrates a feedback control method to precisely lock and manipulate the spin precession phase and rate in a storage ring, enabling advanced experiments like electric dipole moment searches.

## Contribution

It introduces a real-time feedback technique to control spin precession phase and rate in a storage ring using polarization measurements and RF solenoid synchronization.

## Key findings

- Achieved phase control within 0.21 radians.
- Demonstrated frequency adjustments as small as 3.7 mHz.
- Controlled spin precession to facilitate electric dipole moment experiments.

## Abstract

This letter reports the successful use of feedback from a spin polarization measurement to the revolution frequency of a 0.97 GeV/$c$ bunched and polarized deuteron beam in the Cooler Synchrotron (COSY) storage ring in order to control both the precession rate ($\approx 121$ kHz) and the phase of the horizontal polarization component. Real time synchronization with a radio frequency (rf) solenoid made possible the rotation of the polarization out of the horizontal plane, yielding a demonstration of the feedback method to manipulate the polarization. In particular, the rotation rate shows a sinusoidal function of the horizontal polarization phase (relative to the rf solenoid), which was controlled to within a one standard deviation range of $\sigma = 0.21$ rad. The minimum possible adjustment was 3.7 mHz out of a revolution frequency of 753 kHz, which changes the precession rate by 26 mrad/s. Such a capability meets a requirement for the use of storage rings to look for an intrinsic electric dipole moment of charged particles.