Unexpected enhancements and reductions of RF resonance strengths

We analyzed all available data on spin-flipping stored beams of protons, deuterons and electrons. We first calculated the rf-induced spin resonance strength ratio ε_FS/*ε_Bdl; the ε_FS was obtained by fitting the measured polarization data to the modified Froissart-Stora equation, while *ε_Bdl was calculated using the ∫Bdl of the rf dipole or rf solenoid. We found that ε_FS/*ε_Bdl was often 7 times lower than predicted for deuterons, and 12 to 170 times higher than predicted for protons. We studied these discrepancies with vertically polarized beams of 2.1 GeV/c protons and 1.85 GeV/c deuterons stored in the COSY ring in Jülich, Germany. These studies involved flipping their polarization direction, by sweeping the frequency of a water-cooled ferrite rf dipole, of typically ∫Bdl_rms = 0.60 ± 0.3 Tmm, through an rf-induced spin resonance. We studied the dependence of ε_FS/* _Bdl on the beam size, the momentum spread and the distance from the nearest 1^st-order intrinsic spin resonance for both protons and deuterons, and on the frequency sweep range Δf for deuterons. We observed no measurable dependence of ε_FS/*_Bdl on the beam's size or momentum spread for either protons or deuterons. When we varied the vertical betatron tune ν_y near a 1^st-order intrinsic spin resonance, we observed a strong enhancement of ε_FS/*ε_Bdl with a hyperbolic dependence on the distance from the 1^st-order intrinsic spin resonance for both protons and deuterons. This explained much of the proton discrepancy, but did not explain the deuteron's very small ε_FS/ *ε_Bdl. All early deuteron data had small Δf values of 100-200 Hz; however, when Δf was increased from 100 to 3000 Hz, in four steps, there was no dependence of ε_FS/ *ε_Bdl on Δf Thus, this anomalously small ε_FS/*ε_Bdl ratio may be due to some unexpected behavior of relativistic spin-1 deuterons in an rf dipole.