A new method to determine the spin tune is described and tested. In an ideal planar magnetic ring, the spin tune-defined as the number of spin precessions per turn-is given by ν s ¼ γG (γ is the Lorentz factor, G the gyromagnetic anomaly). At 970 MeV=c, the deuteron spins coherently precess at a frequency of ≈120 kHz in the Cooler Synchrotron COSY. The spin tune is deduced from the up-down asymmetry of deuteron-carbon scattering. In a time interval of 2.6 s, the spin tune was determined with a precision of the PRL 115, 094801 (2015) P H Y S I C A L

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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 (≈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 1 standard deviation range of σ=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.

The synchrotron and storage ring COSY accelerates and stores unpolarized and polarized proton or deuteron beams in the momentum range of 0.3 to 3.65 GeV=c [14,15].