Title: Phase locking the spin precession in a storage ring,
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.