D. W. Sivers

Unexpected enhancements and reductions of rf spin resonance strengths

1098-4402= We recently analyzed all available data on spin-flipping stored beams of polarized protons, electrons, and deuterons. Fitting the modified Froissart-Stora equation to the measured polarization data after crossing an rf-induced spin resonance, we found 10–20-fold deviations from the depolarizing resonance strength equations used for many years. The polarization was typically manipulated by linearly sweeping the frequency of an rf dipole or rf solenoid through an rf-induced spin resonance; spin-flip efficiencies of up to 99:9% were obtained. The Lorentz invariance of an rf dipole’s transverse R Bdl and the weak energy dependence of its spin resonance strength E together imply that even a small rf dipole should allow efficient spin flipping in 100 GeVor even TeV storage rings; thus, it is important to understand these large deviations. Therefore, we recently studied the resonance strength deviations experimentally by varying the size and vertical betatron tune of a 2:1 GeV=c polarized proton beam stored in COSY. We found no dependence of E on beam size, but we did find almost 100-fold enhancements when the rf spin resonance was near an intrinsic spin resonance.

HIGHER ORDER SPIN RESONANCES IN 2 . 1 GeV / c POLARIZED PROTON BEAM

Spin resonances can depolarize or spin flip a polarized beam. We studied 1st and higher order spin resonances with stored 2.1  GeV/c vertically polarized protons. The 1st order vertical (ν(y)) resonance caused almost full spin flip, while some higher order ν(y) resonances caused partial depolarization. The 1st order horizontal (ν(x)) resonance caused almost full depolarization, while some higher order ν(x) resonances again caused partial depolarization. Moreover, a 2nd order ν(x) resonance is about as strong as some 3rd order ν(x) resonances, while some 3rd order ν(y) resonances are much stronger than a 2nd order ν(y) resonance. One thought that ν(y) spin resonances are far stronger than ν(x), and that lower order resonances are stronger than higher order; the data do not support this.

Siberian snake experiments at the IUCF Cooler Ring

Recent polarized proton beam experiments in the IUCF Cooler Ring found an evidence for a second-order snake depolarizing resonance, when the vertical betatron tune was inadvertently set near a quarter-integer. We have also studied the possibility of spin-flipping the beam polarization in the presence of a full Siberian snake using an RF solenoid. By varying the rf solenoids ramp time and frequency range, we reached a spin-flip efficiency of about 97%.

Spin-flipping with an rf-dipole and a full Siberian snake

We recently used a vertical-field rf-dipole magnet to study the spin-flipping of a 120 MeV horizontally polarized proton beam stored in the presence of a nearly-full Siberian snake in the IUCF Cooler Ring. The spin was flipped by ramping the rf-dipole’s frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin-flips to measure a maximum spin-flip efficiency of 86.5±0.5% in April 2000, and 92.5±0.5% in June 2000. The spin-flip efficiency was apparently limited by the maximum achievable current in the rf-dipole. This result indicates that spin-flipping a stored polarized proton beam should be possible in high energy rings such as RHIC (and perhaps HERA in the future), where Siberian snakes are utilized and the dipole rf-flipper-magnets should be quite practical. During the June 2000 run, a new faster technique of locating the rf depolarizing resonance frequency was developed.

SPIN-COSY: Spin-Manipulating Polarized Deuterons and Protons

We studied spin manipulation of 1.85 GeV/c polarized deuteron beam stored in COSY obtaining a spin‐flip efficiency of 97±1%. We first discovered experimentally and then explained theoretically interesting behavior of the deuteron tensor polarization. We, for the first time, studied systematically spin resonance strengths induced by rf dipoles and solenoids. We found huge disagreements between the strengths measured in controlled Froissart‐Stora sweeps and the theoretical values calculated using the well‐known formulae. These data instigated re‐examination of these formulae. We tested Chao’s proposed new matrix formalism for describing the spin dynamics due to a single spin resonance, which may be the first fundamental improvement of the Froissart‐Stora equation in that it allows analytic calculation of the beam polarization’s behavior inside a resonance. Our measurements of the deuteron’s polarization near and inside the resonance agreed precisely with the Chao formalism’s predicted oscillations. We teste...

Experimental Verification of Predicted Oscillations near a Spin Resonance

The Chao matrix formalism allows analytic calculations of a beam’s polarization behavior inside a spin resonance. We recently tested its prediction of polarization oscillations occurring in a stored beam of polarized particles near a spin resonance. Using a 1.85 GeV/c polarized deuteron beam stored in COSY, we swept a new rf solenoid’s frequency rather rapidly through 400 Hz during 100 ms, while varying the distance between the sweep’s end frequency and the central frequency of an rf‐induced spin resonance. Our measurements of the deuteron’s polarization for sweeps ending near and inside the resonance agree with the Chao formalism’s predicted oscillations.

Chao Formalism & Kondratenko Crossing Tests

We recently started testing Chao’s proposed new matrix formalism for describing the spin dynamics due to a single spin resonance; this seems to be the first generalization of the Froissart‐Stora equation since it was published in 1960. The Chao matrix formalism allows one to calculate analytically the polarization’s behavior inside a resonance, which is not possible using the Froissart‐Stora equation. We recently tested some Chao formalism predictions using a 1.85 GeV/c polarized deuteron beam stored in COSY. We swept an rf dipole’s frequency through 200 Hz while varying the distance from the sweep’s end frequency to an rf‐induced spin resonance’s central frequency. While the Froissart‐Stora formula can make no prediction in this case, the data seem to support the Chao formalism.We also started investigating the new Kondratenko method to preserve beam polarization during a spin resonance crossing; the method uses 3 rapid changes of the crossing rate near the resonance. With a proper choice of crossing par...

Unexpected Enhancements and Reductions of RF Resonance Strengths

We recently analyzed all available data on spin-flipping stored beams of polarized protons, electrons, and deuterons. Fitting the modified Froissart-Stora equation to the measured polarization data after crossing an rf-induced spin resonance, we found 10 ‐20-fold deviations from the depolarizing resonance strength equations used for many years. The polarization was typically manipulated by linearly sweeping the frequency of an rf dipole or rf solenoid through an rf-induced spin resonance; spin-flip efficiencies of up to 99:9% were obtained. The Lorentz invariance of an rf dipole’s transverse R Bdl and the weak energy dependence of its spin resonance strength E together imply that even a small rf dipole should allow efficient spin flipping in 100 GeV or even TeV storage rings; thus, it is important to understand these large deviations. Therefore, we recently studied the resonance strength deviations experimentally by varying the size and vertical betatron tune of a 2:1 GeV=c polarized proton beam stored in COSY. We found no dependence of E on beam size, but we did find almost 100-fold enhancements when the rf spin resonance was near an intrinsic spin resonance.

99.9% Spin‐Flip Efficiency in the Presence of a Strong Siberian Snake

We recently studied the spin-flipping efficiency of an rf-dipole magnet using a 120-MeV horizontally polarized proton beam stored in the Indiana University Cyclotron Facility Cooler Ring, which contained a nearly full Siberian snake. We flipped the spin by ramping the rf dipoles frequency through an rf-induced depolarizing resonance. By adiabatically turning on the rf dipole, we minimized the beam loss. After optimizing the frequency ramp parameters, we used 100 multiple spin flips to measure a spin-flip efficiency of 99.63+/-0.05%. This result indicates that spin flipping should be possible in very-high-energy polarized storage rings, where Siberian snakes are certainly needed and only dipole rf-flipper magnets are practical.

Spin Flipping and Polarization Lifetimes of a 270 MeV Deuteron Beam

We recently studied the spin flipping of a 270 MeV vertically polarized deuteron beam stored in the IUCF Cooler Ring. We swept an rf solenoid’s frequency through an rf‐induced spin resonance and observed the effect on the beam’s vector and tensor polarizations. After optimizing the resonance crossing rate and setting the solenoid’s voltage to its maximum value, we obtained a spin‐flip efficiency of about 94 ± 1% for the vector polarization; we also observed a partial spin‐flip of the tensor polarization. We then used the rf‐induced resonance to measure the vector and tensor polarizations’ lifetimes at different distances from the resonance; the polarization lifetime ratio τvector/τtensor was about 1.9 ± 0.4.