Synchrotron oscillation effects for spin resonances driven by a localized oscillating rf magnetic field

I derive a generalized tune modulation parameter, to take into account time-of-arrival effects for synchrotron tune modulation of spin resonances driven by a localized rf solenoid or rf dipole, i.e. a time-dependent oscillating magnetic field. I show that the extra effects are negligible for high energy electron storage rings, but they might not be negligible for low or medium energy hadron storage rings. I show that alternative interpretations are possible for some previously published data of bunched stored polarized hadron beams. I suggest benchmark tests for new experimental measurements.