Wide spin resonance with an rf-bunched proton beam

0.17 MB·English

by  V. S. Morozov

Wide spin resonance with an rf-bunched proton beam
V.S. Morozov,1,∗ A.W. Chao,1,† A.D. Krisch,1 M.A. Leonova,1 J. Liu,1
R.S. Raymond,1 D.W. Sivers,1 V.K. Wong,1 and A.M. Kondratenko2
1Spin Physics Center, University of Michigan, Ann Arbor, MI 48109-1040, USA
2GOO Zaryad, Russkaya St. 41, Novosibirsk, 630058 Russia
(Dated: Submitted to PRL 22oct09; submitted to PRST-AB22dec09)
We recently used an rf solenoid to study the widths of rf spin resonances with both unbunched
and bunched beams of 2.1 GeV/c polarized protons stored in the COSY synchrotron. A map,
with unbunched beam at different fixed rf-solenoid frequencies, showed a very shallow possible
0 depolarization dipat theresonance. Nextwemadefrequencysweepsof 400Hz,centeredat similar
1 frequencies, which greatly enhanced the dip. But, with a bunched proton beam, both the fixed-
0 frequencyandfrequency-sweeptechniquesproducedsimilarmaps,andbothbunched mapsshowed
2 full beam depolarization over a wide region. Moreover, both were more than twice as wide as the
unbunched dip. This widening of the proton resonance due to bunching is exactly opposite to
n
therecently observed narrowing of deuteron resonances dueto bunching.
a
J
PACSnumbers: 29.27.Bd,29.27.Hj,41.75.Ak
9

] The ability to preserve and precisely control a beam’s fromthe polarizedH− ionsourcewasacceleratedby the
h
p polarizationduring accelerationandstorageis neededto cyclotronto 45MeV and then strip-injected into COSY.
- study the spin dependence of nuclear and particle inter- Before this injection, the LEP measured the H− beam’s
c
actions[1–5]. Rfmagnetscaninducerfspinresonancesin polarization to monitor its stability.
c
a storage rings, which allow one to manipulate the beam’s The 24.5 keV electron Cooler reduced the beam’s mo-
. polarization;theyalsoallowdetailedspinresonancestud- mentum spread ∆p/p by cooling it, both longitudinally
s
c iesandbeamdiagnostics. Runninganrfmagnetatdiffer- andtransversely,for15sattheprotons’45MeVinjection
i ent fixedfrequencies ormaking small-rangesweeps ofits energy. Theprotonswerethenacceleratedto2.1GeV/c,
s
y frequencynearaspinresonancecanproducearesonance where the rf acceleration cavity was either off during
h map. Suchmapscanpreciselydeterminetheresonance’s COSY’sflat-topgivinganunbunched beam,oron giv-
p properties,suchasitsstrength,width,centralfrequency, ing a bunched beam.
[
and frequency spread, as well as the beam’s properties, Aspinresonancewasinducedusinganrfsolenoidmag-

1 suchasits energyandits momentum spread. Itwasear- net [35]; it was a 25-turn air-core water-cooled copper
v lier discussed that bunching beams of muons [6, 7], elec- coil, of length 57.5 cm and average diameter 21 cm. Its
6 tronsandpositrons[8–10],ordeuterons[11]couldnarrow inductance was 41±3 µH. It was part of an RLC reso-
5
aresonance’swidthandthusincreasethemeasurements’ nantcircuit,whichoperatednear902.6kHz, typicallyat
4
precision. We recently used2.1GeV/cpolarizedprotons anrfvoltageof5.7kVrms. Thelongitudinalrfmagnetic
1
stored in the COSY synchrotron for a detailed experi- field at its center was about 1.17 mT rms, giving an rf
.
1 mental study of both unbunched and bunched proton RBdl of 0.67 ± 0.03 T·mm rms.
0
beam resonances. The cylindrical EDDA polarimeter [27, 28] then mea-
0
In flat circular rings, each beam particle’s spin nor- sured the beam’s polarization in COSY. We reduced its
1
mally precesses around the vertical fields of the ring’s systematicerrorsbycyclingthepolarizedsourcebetween
:
v dipole magnets. The spin tune ν = G γ is the num- the up and down vertical polarization states. The mea-
s
i
X ber of spin precessions during one turn around the ring; suredflattoppolarization,beforespinmanipulation,was
G=(g−2)/2istheparticle’sgyromagneticanomalyand typically about 75%.
r
a γ isitsLorentzenergyfactor. Ahorizontalmagneticfield IntheCOSYring,theprotons’averagecirculationfre-
canperturbtheparticle’sstableverticalpolarizationcre- quency f was 1.49185 MHz at 2.1 GeV/c, where their
c
ating a spin resonance [12–14]. Rf magnets can induce Lorentz energy factor was γ =2.4514. For these param-
rf spin resonances [15–22]. A proton’s rf-induced spin eters, the spin tune ν = Gγ was 4.395. Thus, Eq. (1)
s
resonance’s frequency is gave that the k = 5 spin resonance’s central frequency
should be near
f =f (k±G γ), (1)
r c p
f =(5−Gγ)f =902.6 kHz. (2)
r c
where f is the proton’s circulation frequency, k is an
c
integer, and G =1.792847. We first obtained the rf-induced spin resonance’s
p ε
The apparatus for this experiment, including the strength experimentally [19–22]. The polarization
COSY storage ring [23–26], the EDDA detector [27, 28], was measured after ramping the rf solenoid’s frequency
the electron Cooler [29], the low energy polarimeter throughtheresonancewithvariousramptimes∆t,while
(LEP) [30], the injector cyclotron, and the polarized ion the ramp’s frequency range ∆f and voltage were both
source[31–33]wereshowninFig.4ofref[34]. Thebeam fixed. We then fit these data to the modified [36]
2
FIG. 1: Polarization ratio P/Pi, measured at 2.1 GeV/c FIG. 2: Vertical polarization ratio P/Pi, measured at
withanunbunched protonbeam,plottedvstherfsolenoid’s 2.1 GeV/c with a bunched proton beam, plotted vs the rf
central frequency f, where P and Pi are the final and ini- solenoid’scentralfrequencyf. Therf-solenoidparametersare
tial verticεal polarizations, respectively. The spin resonance in Fig. 1 caption; the beam’s synchrotron frequency fs was
strength atfullrf-solenoidvoltagewas31.3×10−6. Therf 56Hz. Thecurvesarefitstoempirical3rd-orderLorentzians.
solenoid’srampε-upandramp-downtimestR were200ms;its
on-timeatfull wastON =2s. Thefrequencysweepdata’s
range was 400 Hz; its sweep time was 2 s. COSY’s proton
holdingitsfrequencyfixed;wethenrampeditsfrequency
momentum spread is usually less than 10−3. The curves are ε
by 400 Hz in 2 s; we next ramped down to zero while
fitstoempirical2nd-orderLorentzians. Theerrorsarepurely
again holding the frequency fixed. We made many such
statistical.
sweeps adjacent to one another to cover the entire reso-
nance range. The resulting data are plotted against the
ε
Froissart-Stora equation [12] with as a fit parameter sweeps’centralfrequenciesinFig.1alongwiththefixed-
ε
to obtain =(31.3 ± 0.1)×10−6. frequency data. Each point’s frequency-sweep range is
A resonance map was then obtained with the beam indicated by a horizontal bar.
unbunched. For different fixed rf-solenoid frequencies As seen from Fig. 1, the frequency-sweep technique
f near 902.6 kHz, we linearly ramped the rf solenoid’s greatly enhanced the unbunched map’s depolariza-
ε
strength from zero to full during t = 200 ms; we tion dip allowing a precise determination of the res-
ε R
then held fixed during t = 2 s; next we linearly onance’s location and width. Fitting the frequency-
ON
ramped it to zero during t = 200 ms. The resulting sweep data in Fig. 1 to a 2nd-order Lorentzian yielded
R
measured polarization ratios P/Pi are plotted in Fig. 1. fr of 901.7±0.2 kHz and w of 1.7±0.2 kHz FWHM
Note thatanypossible depolarizationdipisveryshallow with χ2/(N − 3) of 0.8. Note that the errors in
and the measured final polarization is almost consistent fr and w are dominated by the frequency-sweep’s
with its initial value. This is probably due to the proton ±200 Hz size. Averaging the fixed-frequency and
beam’s large momentum spread ∆p/p [37]. We fit these frequency-sweep results gave fr =901.7±0.2 kHz and
fixed-frequency unbunched P/P data to an empirical w =1.7±0.2 kHz FWHM for unbunched beam.
i
2nd-order Lorentzian function obtaining χ2/(N −3) of We nextusedthe proceduredescribedaboveto obtain
0.9. The fit gave a central resonance frequency fr of fixed-frequencyandfrequency-sweepmapsofabunched
901.8±0.8 kHzandawidthwof2±2 kHzFWHM.The proton beam with a synchrotron frequency f of 56 Hz.
s
large uncertainties in this fixed-frequency fit are due to These data are shown in Fig. 2 using the same scale
the possible dip being very shallow. and notation as in Fig. 1. We fit both Fig. 2 resonance
To enhance the depth of the unbunched resonance maps to empirical 3rd-order Lorentzians. For the fixed-
andthusimprovetheprecisionofitsfrequencyandwidth frequencymap,thefitgavef of906.17±0.02 kHzandw
r
measurements, we made 400 Hz rf-solenoid frequency of3.61±0.04 kHzFWHMwithχ2/(N−3)=5. Forthe
sweeps near the resonance. We again ramped the rf frequency-sweep map, the fit gave f of 906.3±0.2 kHz
ε r
solenoid’s strength from zero to full in 200 ms while and w of 3.5±0.2 kHz FWHM with χ2/(N −3) = 7.
3
The errors in f and w of the frequency-sweep map are due to the proton beam’s large momentum spread. We
r
again dominated by the frequency sweep’s size. Note next made a frequency-sweep map using 400 Hz sweeps
that, for bunched beam, both the f and w results centered at different frequencies near the resonance;this
r
from the fixed-frequency map and the frequency-sweep greatly enhanced the unbunched dip. Then we used
map are consistent. Averaging the fixed-frequency and the same technique to obtain both fixed-frequency and
frequency-sweepresultsgavef =906.17±0.02 kHzand frequency-sweepresonancemapswithabunched proton
r
w =3.61±0.04 kHz FWHM for bunched beam. beam; these bunched maps were consistent with each
Comparing Figs. 1 and 2 shows that bunching the other in both shape and magnitude. We found that the
beam increased the resonance’s width by more than a bunched mapsweremorethantwiceaswide asthe un-
factor of 2. Moreover, both bunched maps show full bunched map. Moreover, the bunched maps showed
depolarization over a wide frequency region around the full depolarization over a wide frequency range near the
resonance. Also notethat, unlike the unbunched maps, resonance. This proton resonance widening due to
the two bunched maps are consistent with each other bunching is exactly opposite to the recently observed
in both shape and magnitude. Finally note that the ob- deuteron resonance narrowing [11] due to bunching.
servedwidening oftheproton resonanceduetobunch-
ing is exactly opposite to the earlier observed [11] nar- We thank COSY’s staff for a successful run. We
rowing of a deuteron resonance due to bunching. thank E.D. Courant, Ya.S. Derbenev, D. Eversheim,
In summary, we recently used an rf solenoid to study A. Garishvili, R. Gebel, F. Hinterberger, A. Lehrach,
the widths of rf spin resonances with both unbunched B. Lorentz, R. Maier, Yu.F. Orlov, D. Prasuhn,
and bunched beams of 2.1 GeV/c polarized protons H. Rohdjeß, T. Roser, H. Sato, A. Schnase, W. Scobel,
stored in the COSY synchrotron. We first ran the rf E.J. Stephenson, H. Stockhorst, K. Ulbrich, D. Welsch
solenoidat different fixed frequencies near the resonance and K. Yonehara for help and advice. The work was
with the unbunched beam. We found only a very shal- supported by grants from the German BMBF Science
low possible depolarization dip; this shallowness may be Ministry and its JCHP-FFE program at COSY.
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