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].

This paper describes a time-marking system that enables a measurement of the in-plane (horizontal) polarization of a 0.97-GeV=c deuteron beam circulating in the Cooler Synchrotron (COSY) at the Forschungszentrum Jülich. The clock time of each polarimeter event is used to unfold the 120-kHz spin precession and assign events to bins according to the direction of the horizontal polarization. After accumulation for one or more seconds, the down-up scattering asymmetry can be calculated for each direction and matched to a sinusoidal function whose magnitude is proportional to the horizontal polarization. This requires prior knowledge of the spin tune or polarization precession rate. An initial estimate is refined by resorting the events as the spin tune is adjusted across a narrow range and searching for the maximum polarization magnitude. The result is biased toward polarization values that are too large, in part because of statistical fluctuations but also because sinusoidal fits to even random data will produce sizable magnitudes when the phase is left free to vary. An analysis procedure is described that matches the time dependence of the horizontal polarization to templates based on emittance-driven polarization loss while correcting for the positive bias. This information will be used to study ways to extend the horizontal polarization lifetime by correcting spin tune spread using ring sextupole fields and thereby to support the feasibility of searching for an intrinsic electric dipole moment using polarized beams in a storage ring. This paper is a combined effort of the Storage Ring EDM collaboration and the JEDI collaboration.