polarization reversal of stored proton beams in the indiana cooler

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Polarization reversal of stored proton beams in the Indiana Cooler B. von Przewoski, W. A. Dezarn, J. Doskow, J. G. Hardie, H. O. Meyer, R. E. Pollock, T. Rinckel, F. Sperisen, W. Haeberli, B. Lorentz, F. Rathmann, T. Wise, and P. V. Pancella Citation: Review of Scientific Instruments 67, 165 (1996); doi: 10.1063/1.1146565 View online: http://dx.doi.org/10.1063/1.1146565 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/67/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Polarized Internal Target Experiments (PINTEX) at the Indiana Cooler AIP Conf. Proc. 675, 949 (2003); 10.1063/1.1607275 Beam diagnostics in the Indiana University Cooler Injector Synchrotron AIP Conf. Proc. 390, 544 (1997); 10.1063/1.52308 Spin flipping a stored vertically polarized proton beam with an RF solenoid AIP Conf. Proc. 343, 118 (1995); 10.1063/1.48887 Spin flipping a stored polarized proton beam at the IUCF cooler ring AIP Conf. Proc. 338, 361 (1995); 10.1063/1.48557 Polarized H or D target for experiments on the Indiana cooler: Development of the atomic beam source AIP Conf. Proc. 293, 10 (1993); 10.1063/1.45164 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 150.214.146.47 On: Tue, 25 Nov 2014 11:01:33

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Page 1: Polarization reversal of stored proton beams in the Indiana Cooler

Polarization reversal of stored proton beams in the Indiana CoolerB. von Przewoski, W. A. Dezarn, J. Doskow, J. G. Hardie, H. O. Meyer, R. E. Pollock, T. Rinckel, F. Sperisen,W. Haeberli, B. Lorentz, F. Rathmann, T. Wise, and P. V. Pancella Citation: Review of Scientific Instruments 67, 165 (1996); doi: 10.1063/1.1146565 View online: http://dx.doi.org/10.1063/1.1146565 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/67/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Polarized Internal Target Experiments (PINTEX) at the Indiana Cooler AIP Conf. Proc. 675, 949 (2003); 10.1063/1.1607275 Beam diagnostics in the Indiana University Cooler Injector Synchrotron AIP Conf. Proc. 390, 544 (1997); 10.1063/1.52308 Spin flipping a stored vertically polarized proton beam with an RF solenoid AIP Conf. Proc. 343, 118 (1995); 10.1063/1.48887 Spin flipping a stored polarized proton beam at the IUCF cooler ring AIP Conf. Proc. 338, 361 (1995); 10.1063/1.48557 Polarized H or D target for experiments on the Indiana cooler: Development of the atomic beam source AIP Conf. Proc. 293, 10 (1993); 10.1063/1.45164

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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Page 2: Polarization reversal of stored proton beams in the Indiana Cooler

Polarization reversal of stored proton beams in the Indiana CoolerB. von Przewoski, W. A. Dezarn, J. Doskow, J. G. Hardie, H. O. Meyer, R. E. Pollock,T. Rinckel, and F. SperisenIndiana University Cyclotron Facility, Bloomington, Indiana 47405

W. Haeberli, B. Lorentz, F. Rathmann, and T. WiseUniversity of Wisconsin–Madison, Madison, Wisconsin 53706

P. V. PancellaWestern Michigan University, Kalamazoo, Michigan 49008

~Received 29 June 1995; accepted for publication 20 September 1995!

A spin flipper of reliable and robust long-term operation was developed and has been usedsuccessfully at the Indiana University Cooler Storage Ring. To reverse the polarization of the storedbeam, the frequency of a rf solenoid is swept adiabatically across a depolarizing resonancefrequency. Depolarizing sidebands to the resonance are eliminated by shorting out the ring’sbunching rf cavity prior to the frequency sweep. With the spin flipper it is no longer necessary todump the stored beam and to refill the ring with protons of opposite spin state. Rather, beamaccumulation continues without reversing the spin at injection, and instead the polarization of thestored beam is flipped periodically. Thus the luminosity is significantly increased when the flipperis used. ©1996 American Institute of Physics.@S0034-6748~95!04212-8#

I. INTRODUCTION

The use of polarized proton beams to study the spindependence in nuclear or high-energy reactions is now com-mon practice. Elimination of systematic errors requires peri-odic reversal of the beam polarization, or the interchange ofleft and right detectors, as discussed, e.g., in Ref. 1. In recentyears, polarized beams have commonly been produced bypolarized-ion sources, in which case the beam polarizationcan be reversed by exposing the beam of polarized atoms tosuitable rf transitions prior to ionization and injection intothe accelerator.

In conventional experiments, the polarized beam is inci-dent upon a target external to the accelerator. Recently, how-ever, interest has developed in using a polarized circulatingbeam in storage rings in combination with internal targets tostudy spin dependences in nuclear and particle physics. Thetargets in this case may be polarized or unpolarized gas tar-gets or suitable fiber targets.2 In a storage ring, however, thepolarization of the stored beam is given by the polarizationdirection during injection. Reversal of the polarization thenrequires one to dump the beam and to stop the experimentuntil the ring is again filled with protons of opposite spin.

Considerably improved efficiency results, if tools can bedeveloped to flip the spin of the stored beam without discard-ing the stored particles. This paper reports successful opera-tion of a spin flipper of high flip efficiency in the ‘‘Cooler’’proton storage ring at Indiana University. While successfultests of a spin flipper have previously been reported3 theemphasis here is on improvements that lead to very reliableand robust operation during long data-taking runs.

II. PRINCIPLE OF OPERATION

When a depolarizing resonance is crossed, the polariza-tion direction of the stored beam is either conserved or re-versed, depending on whether the crossing occurs rapidly orslowly.4 In a storage ring, a depolarizing resonance occurs

when the spin tune is such that nonvertical magnetic fieldcomponents are encountered in phase on subsequent revolu-tions. In other words, small rotations of the polarization vec-tor of the stored beam add up in many turns around the ring.

It has been shown that a depolarizing resonance can beintroduced by a rf solenoid whose magnetic field oscillatesalong the beam axis.5 A depolarizing resonance is introducedif the frequency of the oscillating longitudinal field,f sol, isgiven by

f sol5 f circ~vspin6N!, ~1!

where f circ is the circulation frequency of the stored beam,andvspin is the spin tune. The integerNmay be chosen suchthat f sol lies in the frequency range of the solenoid. If thefield in the ring is purely vertical, the spin tune equalsGgwhereG51.783 is the anomalous magnetic moment of theproton andg is the usual relativistic factor.

For the measurements reported here the solenoid is partof a LC circuit whereC, a high voltage capacitor, is adjust-able such that~for a given frequency! the circuit is driven inresonance and thus the amplitude of the magnetic field ismaximized. The frequency range of the solenoid,f sol, is 1–3MHz. The resonance has aQ value of 256 and the maximumamplitude of the oscillating longitudinal magnetic field inte-gral is 0.0017 T m. Spin flip is achieved, if the solenoidfrequency is ramped adiabatically across the resonance fre-quency which is given by Eq.~1!. The LC-resonant circuitwas tuned to the frequency in the middle of the band acrosswhich the frequency was swept.

In the presence of a bunching rf cavity the momenta ofthe particles in the ring are modulated due to synchrotronoscillations about the momentum of the ideal particle. Depo-larizing sidebands to the resonance frequency occur at6 f syncwheref sync is the synchrotron frequency of the storedparticle6

165Rev. Sci. Instrum. 67 (1), January 1996 0034-6748/96/67(1)/165/5/$6.00 © 1996 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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f sync5 f circA heVh

2pb2E. ~2!

Hereh is the harmonic number,V the cavity voltage, andEthe energy of the beam. The dispersion in revolution fre-quency,h, is given byh51/gtr

221/g 2, whereg is the usualrelativistic parameter, andgtr is the transition energy in unitsof the rest energy of the stored particles. For the Cooler wehavegtr54.85.

In order to be used for nuclear physics experiments adevice is desired that operates reproducibly and reliably, andthat does not require time-consuming preparatory measure-ments. Initial tests of the rf solenoid as a spin-flipping devicehave been performed at a beam energy of 139 MeV.3 In thesetests, a crossing of the sidebands was avoided by restrictingthe frequency ramp to a narrow range on either side of theresonance. With increasing beam energy this mode of opera-tion becomes more and more difficult, because the synchro-tron frequency scales with the inverse square root of themomentum of the stored beam. In principle, the sidebandscan be moved away from the main resonance by increasingthe cavity voltage and harmonic number. However, as thebeam energy increases, this eventually requires cavity volt-ages beyond the specification of a given device~2 kV maxi-mum in our case!. The test at 139 MeV was performed witha cavity voltage of 1200 V andh59. In addition, main reso-nance and synchrotron sidebands have a finite width. For thetest at 139 MeV a careful optimization procedure was nec-essary to place the end points of the frequency range betweenthe tails of main resonance and the two sidebands. In thismode, the flipper has been demonstrated to work with a highefficiency. However, a mode of operation that is not limitedto low energies, and that lets the experimenter chose thecavity voltage and harmonic number, is desirable.

In order to eliminate the requirement to locate the endpoints of the solenoid frequency ramp precisely between thesynchrotron sidebands, we attempted to ramp the solenoidfrequency through both sidebands and the main resonance.For this, and all following measurements the solenoid fre-quency was ramped linearly fromf sol52.2743 MHz tof sol52.2943 MHz and back tof sol52.2743 MHz for twosubsequent polarization reversals. The duration of one fre-quency ramp was 500 ms. At the end points of the frequencyramp the voltage across the solenoid was 5 kV peak to peak.Since the tuning capacitor was fixed, the voltage across thesolenoid followed the resonance curve for each frequencyramp. It reached a maximum value of 12 kV peak to peak onresonance.

III. MEASUREMENTS

All beam polarization measurements reported in this pa-per have been obtained using the CE35 storage cell target.7

CE35 is an experiment whose goal is to measure spin corre-lation coefficients inpp elastic scattering with an internalpolarized hydrogen target at 200 MeV.7 The target gas waseither polarized hydrogen atoms from an atomic beamsource8 or unpolarized hydrogen bled into the target cellthrough a Teflon™ tube.

The spin-flip efficiencyj shall be the ratio of the mag-nitude of the beam polarization after a frequency ramp di-vided by the magnitude of the beam polarization before thefrequency ramp. Because the loss of polarization in a singleflip is small, j was measured by flipping the polarizationmany times before measuring the remaining polarization.

The data in Fig. 1~a! ~open circles! show clearly thatpassing through the sidebands results in a low overall spin-flip efficiency. Since the sidebands are depolarizing reso-nances themselves, one passage corresponds tothree rever-sals of the beam polarization, each individual reversal with aspin-flip efficiency less than one.

Shorting the rf cavity removes the time structure of thestored beam and should therefore result in a resonance with-out the sidebands. With the sidebands removed it should thenbe possible to flip the polarization with higher efficiency byramping the frequency across the main resonance alone. In asecond measurement we therefore shorted out the cavityprior to the frequency ramp. After the frequency ramp wascomplete the rf cavity was turned back on and the beam wasrebunched. We allowed 5 s for debunching and 5 s for re-bunching after the flip. By observing the time structure of anelectrostatic pickup signal we verified that 5 s is sufficientfor the beam to loose its time structure completely. As can beseen from Fig. 1~a! ~solid dots! the spin-flip efficiencyj isgreatly increased. From the data one obtains a value of

FIG. 1. ~a! Polarization flipping by crossing an induced depolarizing reso-nance. Shown is the fraction of polarization of a 200 MeV beam remainingafter multiple flips. The solid symbols were obtained when, during flipping,the beam was debunched by shorting out the ring rf cavity. The efficiency is0.98460.004. The open symbols illustrate the same measurement with abunched beam, corresponding to an efficiency of 0.8360.03. The efficien-cies were obtained from fits to the data, shown as solid lines.~b! The samemeasurement as in~a! but during another experiment at 200 MeV. As for thesolid symbols in~a! the ring cavity was shorted. The efficiency is 0.97160.003. As in~a! the efficiency was obtained from a least-square fit to thedata.

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j50.98460.004 for the remaining fraction of the initial po-larization after one flip.

After having established that the flipper can be used as areliable and easily tunable device, if the bunching rf cavity isshorted, the spin flipper was used routinely by the CE35collaboration. During a week of running the reproducibilityand the long-term performance of the flipper was studied.Again we measured the remaining beam polarization as afunction of the number of spin flips@Fig. 1~b!#. The fre-quency range and the duration of the sweep were set exactlyas for the data shown in Fig. 1~a!. However, this time wemeasured a slightly lower efficiency ofj50.97160.004. It isnot known where the small, but significant drop in efficiencycomes from. Possibly, the center frequency was not as wellmatched to the resonance frequency as in the previous run.This could well be the case since in the absence of bunchingrf the beam energy is determined by the velocity of the cool-ing electrons; the energy during the flip could thus differslightly from the energy defined by the rf cavity.

IV. CONSEQUENCES FOR COOLER EXPERIMENTS

Using the flipper enabled us to establish a new mode forexperiments with stored, polarized beams. Previously, thebeam had been injected in one of two spin states, then—ifrequired by the experiment—accelerated. After data takingby the experiment, the beam was dumped to empty the ringbefore accepting the freshly injected beam in the oppositespin state. Now, with the flipper, the ring is always filled withthe beam in the same spin state. The new mode of runningconsists of injection, use of the beam, spin flip of the storedbeam, use of the beam, another spin flip, use of the beam,and finally injection of the beam in the same spin statewith-out dumping the beam prior to injection. Figure 2~b! illus-trates the polarization reversal during a full cycle, i.e., be-tween refills of the ring. The data are binned in 6 s intervals.Shown is the beam polarization as measured with the CE35detector.9 Also shown is the beam polarization for runs with‘‘unpolarized’’ beam. Unpolarized beam was obtained byswitching off the rf transitions in the polarized ion source.This method yields beam with a small, remnant polarization~;4%!. Note, that the reversal of this remaining beam polar-ization during each frequency ramp is clearly visible.

The proton–proton elastic scattering rate as a function oftime is shown in Fig. 2~a!. This rate is proportional to theluminosityL. During the spin flips~arrows!, which last 10.5s including the debunching and rebunching, some of thebeam is lost. The beam loss becomes larger with increasingintensity as can be seen from the fact that the intensity lossduring the first flip is larger than that during the second flip.

If the beam were dumped at the end of each cycle, thetrigger rate would be the same for every cycle. If the beam isnot dumped at the end of a cycle—typically every few hun-dred seconds—the luminosity increases in subsequent cycles.This increase is illustrated in Fig. 3~a! where the trigger ratein the CE35 detector is plotted as a function of cycle time fora sequence of four cycles. For polarization experiments,however, one has to consider the figure of meritLP2, whereL is the luminosity andP is the beam polarization. the datapoints in Fig. 3~b! represent the measured beam polar-

ization for each cycle as a function of cycle number. The datapoints were obtained using the cross ratio method10 for everycycle. LetN1

( l ,r ) be the number of counts in spin state oneand N2

( l ,r ) be the number of counts in spin state two in aleft/right symmetric detector system. The asymmetrye isthen given by

e5PA5r21

r11, ~3!

whereP is the polarization,A the analyzing power of thereaction, and the cross ratior 25(N1

l N2r )/(N1

r N2l !. The

method assumes the same magnitude of polarization for spinstate one and spin state two. If the polarizations are not thesame, the method yields the geometric mean of the polariza-tions in the two spin states. The cross ratio was calculatedusing software time gates before and after the two spin flipsto obtainN1

( l ,r ) and another software time gate between thetwo spin flips to obtainN2

( l ,r ). Thus, the data points representthe average polarization during each cycle. It can be easilyseen from Figs. 3~a! and 3~b! that the gain in luminosity isgreater than the loss inP2, resulting in a net gain in thefigure of merit.

In Fig. 3~b! we also show the expected, calculated beampolarization as a function of time. In the calculation we as-sume that the spin-flip efficiency isj50.97, as measured, forall flips. The increase in beam current during injection as afunction of time is parametrized in the following way: The

FIG. 2. ~a! Proton–proton elastic scattering rate in the detector as a functionof cycle time. The rate is proportional to the luminosityL. The arrows markthe times when the spin was flipped.~b! Beam polarization as a function ofcycle time. The upper curve corresponds to polarized beam injected into thecooler. The lower curve corresponds to the polarization measured for unpo-larized beam which was obtained by turning off the rf transitions in the ionsource. The reversal of the small residual polarization of the ‘‘unpolarized’’beam delivered by the ion source is clearly visible. Also shown are the timegatest1– t4 ~see the text!.

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ring is assumed to be filled following anI o„12exp~2t/t f!…functional dependence. The two parametersI o andtf empiri-cally describe the performance of the ring such that the ex-perimentally observed time dependence of the beam currentis reproduced. As the stored beam current approachesI o dur-ing injection the same number of stored protons is lost as isinjected per unit time. Since the available phase space is thesame for protons that remained stored from previous cyclesand newly injected protons, we assume that the protons thatdo not remain in the ring consist of equal parts of protonsthat remain from previous cycles~and thus may have a lowerpolarization! and of protons that have been added during thecurrent injection, thus having the polarization that the ionsource delivers. The filling curve of the beam current wasmeasured and a saturation beam current ofI o5300mA andtf55.5 min was deduced. The polarization delivered fromthe ion source was 74%. The measured polarization agreeswithin error bars with the expected polarization as can beseen from Fig. 3~b!.

For an idealized polarized-ion source, both spin stateshave equally high polarization, but in reality the polarizationof one of the spin states delivered by the source is usuallyhigher. The new mode enabled us to pick the spin state withthe higher polarization~by 5%! for injection. Since the spin-flip efficiency is known, it is also possible to calculate thedifference in magnitude of the polarizations. In fact, it can beshown that this is possible without any assumptions aboutdetector efficiencies, solid angles, and integrated luminosi-ties.

During CE35 we also had the opportunity to study thelong-term performance of the spin flipper. Figure 4~a! showsthe spin-flip efficiency as a function of run number during aCE35 production run in October 1994. The statistical errorfor efficiencies for single flips is too large to determine effi-ciency fluctuations on the short time scale between flips, thusthe spin-flip efficiency was only evaluated per run and notper single flip. A typical run consisted of approximately 12cycles and thus 24 flips. However, the sign of the left/rightasymmetry before and after each individual flip was moni-tored throughout the entire run. It was verified that none ofthe 518 frequency ramps failed to change the sign of thestored beam polarization. In calculating the spin-flip effi-ciency per run the following algorithm was used: the periodof data taking between subsequent injections was dividedinto four time gates as shown in Fig. 2~a!. The first time gatebefore the first flip, the second and third gate of equal lengthin between the first and second flip, and the fourth time gateafter the second flip. Using the cross ratio method to elimi-nate instrumental asymmetries one extracts the spin-flip effi-ciency per run as follows: Let us calle i ,k the asymmetriesdetermined from the data in time gatest i ,tk . The polariza-tion within time gatei shall be denotedPi . ThenP25jP1andP45j2P1 . The asymmetries calculated from count ratesbefore and after the flip measure the geometric mean of thepolarizations before and after the flip. Thuse1,2 5 P1Aj ande3,45 P1jAj. The ratio betweene3,4 ande1,2 is then the spinflip efficiency j. The spin-flip efficiency evaluated in this

FIG. 3. ~a! Trigger rate in the CE35 detector as a function of time for foursubsequent cycles. The beam left at the end of a cycle remains in the ring.The dashed line indicates the filling of the ring during which the rate is notmeasured.~b! Beam polarization as a function of time. The circles corre-spond to the measured beam polarization averaged over one cycle. The linerepresents the expected polarization as a function of time due to filling of thering ~dashed! and flipping the spin of the stored beam~arrows!; see the textfor details.

FIG. 4. ~a! Spin-flip efficiencyj as a function of run number to illustratelong-term stability. Real time elapsed between run 1 and run 50 was ap-proximately one week. The dashed line is atj50.971 which is the valuefound by measuring the effect of multiple flips@see Fig. 1~b!# at the begin-ning of the experiment.~b! Check for polarization loss due to effects otherthan spin flipping as a function of run number. The definition of the quantityd, which is sensitive to changes in polarization between flips, is given in thetext. The weighted average,d51.00160.011, is consistent with 1~solidline!, i.e., with no polarization loss other than from spin flipping.

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manner and then averaged over all runs isj50.96160.009with a x 2 per degree of freedom of 1.25. Within statisticsthis is the same value as found at the beginning of the ex-periment by measuring the polarization before and after mul-tiple flips ~j50.97160.004!.

Within the accuracy of our measurement, the flipping ofthe polarization is the only mechanism for polarization loss.In order to verify this, the same method of using cross ratioswas employed, but using different time gate combinations.Calculating the asymmetries for gate combinationst1 ,t3 andt2 ,t4 instead of t1 ,t2 and t3 ,t4 a deviation d5~e3,4/e1/2!~e1,3/e2,4! from unity can be calculated. If the polarizationdecreases due to any other mechanisms,d would deviatefrom unity. Figure 4~b! showsd as a function of run number.The weighted mean over all runs isd51.00160.011 with ax2 per degree of freedom of 1.59. This indicates that thepolarization is indeed constant except for the loss due to thespin flips.

V. DISCUSSION

In conventional fixed-target experiments it is desired toreverse the polarization rapidly~every few seconds!. It canbe shown that rapid polarization reversal eliminates certainclasses of systematic errors, e.g., those associated with slowdrifts of the beam position.11 In a storage ring, slow drifts ofthe beam position are less of a danger. If the beam position inone location deviates from the closed orbit, the beam is sim-ply no longer stored. More important, polarization-dependentbeam shifts are excluded, since there is only one closed orbit.Thus, in a storage ring, one spin flip between injections, ortwo if one desires to inject in one spin state consistently, issufficient to greatly reduce systematic errors. However, cer-tain high precision experiments, such as parity violation ex-periments, still require a detailed study of possible system-atic effects and may require polarization reversals on a fastertime scale. The experiment benefits from using the spin flip-per of a known and constant efficiencyj, because then thedifference in magnitude between the two spin states is

known. In order to calculate this difference for a givenj,neither the integrated luminosities in the two spin states northe detector efficiencies have to be known.

In summary the spin flipper has been demonstrated to bea reliable device. Its spin-flip efficiency is reproducibly inexcess of 97%. If it is used to reverse the polarization of thestored beam, an increase in the average luminosity and theoverall figure of merit is achieved, since it is no longer nec-essary to empty the ring prior to injection.

ACKNOWLEDGMENTS

This work is supported by the US National ScienceFoundation~NSF! under Grants No. PHY-8714406 and No.PHY-9019983, and by the US Department of Energy~DOE!under Grant No. DE-FG02-88E440438. One of us~F.R.! wassupported by an Alexander von Humboldt grant.

1R. C. Hanna, Proceedings of the Second International Symposium onPolarization Phenomena in Nuclear Physics, Birkhaeuser, 1966~Basel!,edited by P. Huber and H. Schopper, p. 280.

2H. O. Meyer,Proceedings of the 19th INS Symposium on Cooler Ringsand their Applications, Tokyo, edited by T. Katayama and A. Noda~WorldScientific, Singapore, 1991!, p. 148.

3D. D. Caussynet al., Phys. Rev. Lett.73, 2857~1994!.4M. Froissart and R. Stora, Nucl. Instrum. Methods7, 297 ~1960!.5V. A. Anferov et al., Phys. Rev. A46, R7383~1992!.6B. W. Montague, in Proceedings of the First Course of the InternationalSchool of Particle Accelerators of the Ettore Majorana Centre for Scien-tific Culture, Erice, 10–22 November 1976, edited by M. H. Blewett, CernReport No. 77-13, p. 63.

7W. A. Dezarnet al., contributed to the 8th Symposium on PolarizationPhenomena in Nuclear Physics, Bloominton, IN, September 1994~unpub-lished!, p. 62.

8T. Wise, A. D. Roberts, and W. Haeberli, Nucl. Instrum. Methods A336,410 ~1993!.

9W. A. Dezarnet al., IUCF Scientific and Technical Report, 1992–1993~unpublished!, p. 161.

10W. Haeberli, R. Henneck, C. Jaquemart, J. Lang, R. Mu¨ller, M. Simmo-nius, W. Reichart, and C. Weddingen, Nucl. Instrum. Methods163, 403~1979!.

11G. Ohlsen, Proceedings of the Fourth Symposium on Polarization Phe-nomena in Nuclear Physics, Birkhaeuser 1975~Zurich!, edited by W.Gruebler and V. Ko¨nig ~unpublished!, p. 287.

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