Spin manipulation of 1 : 94 GeV = c polarized protons stored in the COSY cooler synchrotron

024002-1 We recently studied spin flipping of a 1:94 GeV=c vertically polarized proton beam at COSY in Jülich, Germany. We swept an rf-dipole’s frequency through an rf-induced spin resonance to flip the beam’s polarization direction. After determining the resonance’s frequency, we varied the dipole’s strength, frequency range, and frequency ramp time. At the rf-dipole’s maximum strength, and optimum frequency range and ramp time, we measured a spin-flip efficiency of 99:3% 0:1%. This result indicates that an rf dipole may allow efficient spin flipping in high energy proton rings.


I. INTRODUCTION
During the past decade, polarized beam experiments have become an important part of the programs in storage rings such as the IUCF Cooler Ring [1], AmPS at NIKHEF [2], the MIT-Bates Storage Ring [3], COSY [4], LEP at CERN [5], RHIC at BNL [6], and HERA at DESY [7,8].Many polarized scattering experiments require frequent spin-direction reversals (spin flips), while the polarized beam is stored, to reduce their systematic errors.Spin resonances [9,10] induced by either an rf solenoid or an rf dipole can produce such spin flips in a wellcontrolled way [11][12][13][14][15][16][17][18][19][20].At high energy, the spin-flipping efficiency with an rf dipole should be essentially independent of energy due to the Lorentz invariance of a dipole magnet's R Bdl; this is quite important for very high energy polarized proton rings.Therefore, we recently used an rf dipole to study the spin flipping of 1:941 GeV=c polarized protons stored in the COSY ring.
In any flat storage ring or circular accelerator, each proton's spin precesses around the stable spin direction (SSD), which is defined by the ring's magnetic structure.In a ring with no horizontal magnetic fields, the SSD points along the vertical fields of the ring's dipole magnets.The spin tune s , which is the number of spin precessions during one turn around the ring, is proportional to the proton's energy s G; ( where G g ÿ 2=2 1:792 847 is the proton's gyromagnetic anomaly and is its Lorentz energy factor.The vertical polarization can be perturbed by a horizontal rf magnetic field from either an rf solenoid or an rf dipole.This perturbation can induce an rf depolarizing resonance, which can flip the spin of the stored polarized protons [11][12][13][14][15][16][17][18][19][20]; the resonance's frequency is where f c is the protons's circulation frequency and k is an integer.Adiabatically ramping the rf magnet's frequency through f r can flip each proton's spin.The Froissart-Stora equation [9] relates the beam's initial polarization P i to its final polarization P f after crossing the resonance, the ratio f=t is the resonance crossing rate, where f is the ramp's full frequency range during the ramp time t.The resonance strength is given by [21] where e is the proton's charge, p is its momentum, and R B rms dl is the rf-dipole's rms magnetic field integral.

II. EXPERIMENTAL APPARATUS
The apparatus used for this experiment, including the COSY storage ring [22 -25], the EDDA detector [26], the low energy polarimeter, the injector cyclotron, and the polarized ion source [27][28][29] is indicated in Fig. 1, along with the rf dipole.The dipole, which consisted of two 4-turn air-core copper coils in series, was part of an LC resonant circuit; it normally ran at about 6.6 kV rms producing an R B rms dl of about 0:11 0:005 T mm.An earlier version was used to spin flip polarized deuterons [30].The beam emerging from the polarized H ÿ ion source was accelerated by the cyclotron to COSY's 45 MeV injection energy.Then the low energy polarimeter (LEP) monitored the beam's polarization before injection PHYSICAL REVIEW SPECIAL TOPICS -ACCELERATORS AND BEAMS, VOLUME 7, 024002 (2004) 024002-1 1098-4402=04=7(2)=024002(5)$20.00  2004 The American Physical Society 024002-1 into COSY to check the stable operation of the ion source and cyclotron.
We measured the polarization in COSY using the EDDA detector [4,26] as a polarimeter; we reduced its systematic errors by cycling the polarized source between the up and down vertical polarization states.The rf acceleration cavity was turned off and shorted during COSY's flattop; thus, there were no synchrotron sideband effects [13,31,32].The measured flattop polarization, before spin manipulation, was typically about 80% with an error below 1%.

III. EXPERIMENTAL RESULTS
The stored protons' measured circulation frequency in COSY was f c 1:471 17 MHz giving a nominal Lorentz energy factor of 2:2977 and a momentum of 1:9410 GeV=c.With these parameters, Eq. ( 1) gave a spin tune s G of 4.1195; then Eq. ( 2) implied that the k 5 depolarizing resonance should be centered at f r 5 ÿ Gf c 1295:4 kHz: (5) We first determined the resonance frequency by linearly ramping the rf-dipole's frequency by f=2 2 kHz around the calculated f r ; we then continued by making 2 kHz ramps next to each side of the previous frequency range until the beam was either spin flipped or depolarized, as shown in Fig. 2. The 2 kHz data's behavior suggested that the resonance width was comparable to the 2 kHz frequency ramps.
Thus, we next studied f=2 1 kHz frequency ramps with different central frequencies, which are shown in Fig. 2 as open circles; fitting these 1 kHz data gave f r 1306:0 0:5 kHz and an upper limit on the full width at half maximum of w 2:3 0:9 kHz.The FWHM width due to the resonance's , given by w 2f r [11], is only 59 3 Hz.The beam had a measured momentum spread p=p of about 6 10 ÿ4 FWHM.This gives an additional resonance width of about 3 kHz in Eq. ( 5), which is consistent with the upper limit w 2:3 0:9 kHz.The f=2 2 kHz data in Fig. 2 gave f r 1306 1 kHz; its w had too large an error to be useful.The 10.6 kHz difference between the measured and calculated f r is dominated by the measured closed orbit distortions in COSY's ring due to a slight mismatch between the rf accelerating frequency and the dipole field.This changed the beam's circumference and thus its ; thus, the f r in Eq. ( 5) changed.Any contribution due to a higher-order type-3 Siberian snake [33,34] in COSY's vertical-plane electron cooling system should be negligible.
Based on previous studies we chose the frequency range f=2 of 5 kHz, which seemed to safely cover the whole resonance.We then spin flipped the proton beam by ramping the rf-dipole's frequency through this f, with various ramp times t, while measuring the polarizations after each ramp.The measured data are plotted against the ramp time in Fig. 3; this suggests setting t near 7 s.Since the spin-flip efficiency is never exactly 100%, the modified Froissart-Stora formula [16,18] was earlier introduced empirically to describe nonideal single-flip data: The parameter is defined as the upper limit of the achievable spin-flip efficiency when the exponential approaches zero.This limit could be due to many depolarizing mechanisms such as f being too small to completely cover the resonance width; or any weak nearby resonance.This seems a useful parametrization for these many possibilities.
Fitting the Fig. 3 data to Eq. ( 6) gave a spin-flip efficiency of 100:8% 1:2% and a resonance strength of 20:70:210 ÿ6 ; this is consistent with the of 20 1 10 ÿ6 obtained from Eq. ( 4) using the measured R B rms dl 0:11 0:005 T mm.To more precisely determine the spin-flip efficiency, we then measured the polarization after 11 spin flips, while varying the rf-dipole's rms voltage V rms , its ramp time t, and its full frequency range f.This technique enhanced small changes in the spin-flip efficiency's dependence on the rf-dipole's parameters, because the 11th power of even a small single spin-flip depolarization is large.The measured polarization after 11 spin flips P 11 is plotted in Fig. 4 against the rf dipole's f=2, with its t now set at 7.5 s and its R B rms dl set at 0.11 T mm. Figure 4 shows a clear maximum of P 11 centered near f=2 4 kHz.
After setting t, f, and R B rms dl to maximize the spin-flip efficiency, we then determined it more precisely by varying the number of spin flips.We measured the vertical polarization after 0, 1, 11, and 30 spin flips, while keeping t, f, and R Bdl all fixed; these data are plotted against the number of spin flips in Fig. 5.We fit these data using the measured defined by where P n is the measured polarization after n spin flips.The fit gave a measured spin-flip efficiency of 99:3% 0:1%.Note again that, in the limit that the 3.The measured proton polarization at 1:941 GeV=c is plotted against the rf-dipole ramp time t.The rf-dipole's frequency half range f=2 was 5 kHz, and its R B rms dl was 0.11 T mm.The curve is a fit using Eq. ( 6).
PRST-AB 7 V. S. MOROZOV et al. 024002 (2004) 024002-3 024002-3 exponential in Eq. ( 6) goes to zero, comparing Eq. ( 7) for a single flip with Eq. ( 6) yields .We also tried to fit the data in Fig. 4 by taking the 11th power of Eq. ( 6) The curve in Fig. 4 is a fit to Eq. ( 8), where we set equal to the 99:3% 0:1%, obtained from Fig. 5.The fit gave a resonance strength of 19:90:210 ÿ6 , while the initial polarization P i was 80%2%.However, we fit only the data at or above f=2 4 kHz.At small f, when the frequency range is smaller than the resonance width, P 11 must decrease sharply.This is certainly not described by Eq. ( 8), since Eq. ( 8), the Froissart-Stora formula [9], is certainly not valid when f is smaller than the resonance's width.A more general formula is still needed for cases when f is not infinite or when the resonance is not totally isolated.
In summary, by adiabatically ramping an rf-dipole's frequency through an rf-induced spin resonance, we were able to spin flip the polarization of a stored proton beam.After optimizing the spin-flipping parameters, we obtained a 99:3% 0:1% measured spin-flip efficiency for 1:94 GeV=c polarized protons stored in COSY.We now plan to enhance the rf-dipole's strength by enclosing it in a ferrite box and using water-cooled coils to allow running at a higher current and thus a higher R Bdl.This should allow a further increase in the spin-flip efficiency, even with a faster ramp time.8).Also shown is the measured spin-flip efficiency for each f obtained using Eq. ( 7) to take the 11th root of the measured ratio ÿP 11 =P i .The rf-dipole's frequency ramp time t was 10 s; its frequency half range f=2 was 4 kHz, and its R B rms dl was 0.11 T mm.The line is a fit using Eq. ( 7).

FIG. 1 .
FIG. 1. (Color) Layout of the COSY Storage Ring, with its injector cyclotron and polarized ion source.Also shown are the rf dipole, the EDDA detector, and the low energy polarimeter.

2 FIG. 2 .
FIG.2.The measured proton polarization at 1:941 GeV=c is plotted against the central frequency of each ramp; each ramp's f range is shown by a horizontal bar.The rf dipole's R B rms dl was 0.11 T mm; its t was 10 s.The curve is a fit using a firstorder Lorentzian.

4 .
The measured proton polarization at 1:941 GeV=c after 11 spin flips is plotted against the rf-dipole's frequency half range f=2.The rf-dipole's ramp time t was 7.5 s, and its R B rms dl was 0.11 T mm.The curve is a fit to Eq. (

FIG. 5 .
FIG.5.The measured proton polarization at 1:941 GeV=c is plotted against the number of spin flips.The rf-dipole's frequency ramp time t was 10 s; its frequency half range f=2 was 4 kHz, and its R B rms dl was 0.11 T mm.The line is a fit using Eq.(7).