Non-exponential decoherence of radio-frequency resonance rotation of spin in storage rings

Abstract: Precision experiments, such as the search for electric dipole moments of charged particles using radiofrequency spin rotators in storage rings, demand for maintaining the exact spin resonance condition for several thousand seconds. Synchrotron oscillations in the stored beam modulate the spin tune of off-central particles, moving it off the perfect resonance condition set for central particles on the reference orbit. Here we report an analytic description of how synchrotron oscillations lead to non-exponential decoherence of the radiofrequency resonance driven up-down spin rotations. This non-exponential decoherence is shown to be accompanied by a nontrivial walk of the spin phase. We also comment on sensitivity of the decoherence rate to the harmonics of the radiofreqency spin rotator and a possibility to check predictions of decoherence-free magic energies.