This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Baiod, R.

Courant, E.D.

Derbenev, Ya. S.

Ellison, T.J.P.

Goodwin, J.E.

Krisch, A.D.

Lee, S.Y.

Minty, M.G.

Pancella, P.V.

Phelps, R.A.

Ratner, L.G.

Rinckel, T.

Roser, T.

Ross, M.A.

Sperisen, F.

van Guilder, B.S.

von Przewoski, B.

Vuaridel, B.

English

IUScholarWorks

ACCELERATOR PHYSICS 
SIBERIAN SNAKE AND DEPOLARIZING RESONANCE STUDIES 
AT THE COOLER RING 
R. Baiod, Ya.S. Derbenev, A.D. Krisch, R.A. Phelps, T. Roser, 
B.S. van Guilder, and B. Vuaridela 
Randal l  Lab of Physics,  T h e  Universi ty  of Michigan, Ann Arbor, Michigan 481  09  
T.J.P. Ellison, J.E. ~ o o d w i n ~ ,  S.Y. Leec, M.G. Minty, P.V. pancellad, T. Rinckel, 
M.A. Rosse, F. Sperisen, and B. von Przewoski, E.J. Stephenson 
Ind iana  Universi ty  Cyclotron Facility, Bloomington,  Indiana 47408 
E.D. Courant and L.G. Ratner 
Brookhaven National  Laboratory, Upton,  N e w  York  1 1  9 7 3  
Recent experiments at the IUCF Cooler Ring have shown that Siberian snakes can 
overcome depolarizing resonances and thus preserve the proton spin polarization during 
acceleration. However, we found that the G y = 2 imperfection depolarizing resonance 
appeared to occur about 1.9 MeV below the expected beam energy of 108.4 MeV. Since 
the energy calibration of the Cooler Ring was believed to be accurate to better than 
this apparent 1.9 MeV miscalibration caused some concern. 
An alternate explanation for the observed discrepancy was that the spin tune, us, was 
somehow shifted upward by about 0.0036. This shift would make us = 2.0036 at 108.4 MeV 
and thus move the Gy = 2 resonance to about 106.5 MeV. Recently, Pollock1 suggested 
that the magnets in the electron cooling system of the IUCF Cooler Ring could act as a 
partial type-3 Siberian snake2 which might cause such a spin tune shift. A type-3 snake is 
a device which rotates the spin around the direction perpendicular to the ring plane. In the 
electron cooling region of the Cooler Ring, each proton's spin is rotated by several magnets 
including the main cooling solenoid, two toroids, two compensating solenoids, four vertical 
steerers, and four weaker horizontal steerers. Since spin rotations do n o t  c o m m u t e ,  these 
magnets can rotate a proton's spin and thus shift the spin tune, us. At a fixed energy, 
a shift in us would change the proximity to any nearby depolarizing resonance. This 
proximity can be measured by studying how sharply the radial and vertical polarization 
components depend on the net longitudinal Bad1 of the cooling magnets. 
We recently stored and cooled vertically polarized proton beams at nominal energies of 
104.6, 105.9, 106.9, 107.8, and 110.5 MeV. The stored beam intensity was 15 to 50 nA and 
the cycle period ranged from 4 to 20 seconds. The vertical and radial components of the 
polarization were measured simultaneously using a 4.5 mm thick Carbon skimmer target 
and the cylindrically symmetric CEO 1 detector. The beam polarization was measured 
before injection into the Cooler Ring using a beam line polarimeter;4 it was found to be 
77 f 2% at all incident beam energies. 
At each beam energy we measured5 both the vertical and radial components of the 
beam polarization in the Ring, while varying the net longitudinal field, .[ B-dl by changing 
the currents in the main cooling solenoid and the two compensating solenoids and holding 
fixed the steerer and toroid magnet currents. At each energy, the width of the result- 
ing vertical polarization profile6 was a measure of the actual proximity to the Gy = 2 
imperfection resonance, which should occur at 108.4 MeV. The data are shown in Fig. 1. 
One can better parameterize this proximity by plotting the ratio Pradial/Pvertical 
against J B dl. At each energy Pradial/Pvertical is proportional to the tangent of the 
angle q5 between the vertical and the stable spin direction. Since J B-dl  is small one can 
also show that Pradial/Pvertical is proportional to J B-dl  by using equations 2, 3, and 5 of 
ref. 6, 
Pradial 2 ~ G y  
= -tan q5 . sin (-) = S Bwdl. 
Pvertical 3 J (1) 
27rGy The sin ( ) term occurs because the polarimeter was 120° downstream of the Snake! 
The quantity, S, is given by 
27rGy 
e(1 + G) sin (r) 
S = 3 .  2cp sin (ru,) 7 
where e and p are the proton's electric charge and momentum, while c is the speed of light. 
The new experimental data are plotted against J Bad1 in Fig. 1. The measured values 
of the vertical polarization are plotted on the left, while the measured radial polarization 
values are plotted in the center. The ratio of Pradial to Pvertical is plotted on the right. The 
solid lines in Fig. 1 are straight line fits to the ratio Pradial/Pvertical; the slope of this fit is 
the quantity, S, defined above. The measured slopes at each energy are plotted in Fig. 2 
along with previously published 104.5 and 120.0 MeV data6y7 and a less detailed new data 
set at 110.5 MeV. The curve in Fig. 2 is obtained from equation 2 with the best fit value 
of us = Gy + 0.0036 f 0.0003. This corresponds to a shift in the resonance energy of 
-1.9 -+ 0.2 MeV. 
We directly tested for the existence of a partial type-3 Siberian snake by measuring the 
beam polarization after turning off all the magnetic fields in the cooling system. Turning 
off these magnets should eliminate any possibility of a type-3 snake and thus give an 
absolute energy ~al ibrat ion.~ The ratio Pradial/Pvmtical is plotted against J Bmdl in Fig. 3 
at 105.9 MeV. The dependence of the ratio on J Bad1 was clearly much flatter with the 
cooling magnets off. This change clearly demonstrates that the spin tune, us, and thus 
the resonance energy were significantly shifted by the cooling magnets. The best fit to the 
data in Fig. 3 with the cooling magnets off was vs = 1.9949 f 0.0005; this agrees well 
with the calculated value of Gy = 1.9951 at 105.9 MeV. This agreement directly supports 
the hypothesis1 that the apparent 1.9 MeV energy miscalibration was caused by a partial 
type-3 Siberian snake2 due to the cooling magnets in the Cooler Ring. 
; @ + +  i e * * j  
MeV 
Figure 1. The measured vertical (left) and radial (center) polarization at 104.6, 105.9, 
106.9, 107.8, and 110.5 MeV are plotted against the net longitudinal magnetic field integral 
in the Cooler Ring solenoids. Vertically polarized protons were injected into the ring. The 
narrow dips in the radial and vertical polarizations at 104.6 and 107.8 MeV are probably 
due to synchrotron depolarizing resonances. The ratio Pradial/Pvertical is plotted on the 
right; the curves are straight line fits to the data at each energy. 
110 115 
T [MeV] 
Figure 2. The experimental slopes of the Pradial/Pwrtical curves are plotted against the 
energy. The curve is given by equation 2. 
We plan to make more precise calibrations of the energy and the spin tune by using 
an rf driven solenoid to induce depolarizing resonances at various rf The 
ability to induce a depolarizing resonance will also allow us to study overlapping depolar- 
izing resonances, which are expected to present serious difficulties at TeV energies. In a 
preliminary test we showed that it is indeed possible to induce a depolarizing resonance. 
The measurement was made by connecting a transverse injection kicker dipole to the out- 
put of an rf knockout amplifier, which had been used in betatron tune measurements. The 
resultant oscillating vertical field of about 100 pT-m produced a few hundred p a d  of spin 
precession per orbit in the ring. With the Siberian snake turned on, we then injected 
horizontally polarized beam at 105.9 MeV and varied the kicker driving frequency. The 
measured radial polarization is shown as a function of the frequency in Fig. 4. The plot 
shows an extremely narrow dip in the measured polarization. From the expanded view in 
the inset, the center of this dip occurred near a frequency of 771.0f 0.2 kHz. 
This research was supported by grants from the U.S. Department of Energy and the 
U. S. National Science Foundation. 
/Bedl long. (Tern) 
Figure 3. The measured ratio Pradial/Pvertical is plotted against the net longitudinal J Bdl. 
Vertically polarized 105.9 MeV protons were injected into the ring. The data shown as 
squares at the top were taken with the cooling magnets turned on. The data shown as 
circles at the bottom were taken with the cooling magnets set near zero. 
720 740 760 780 
Kicker Frequency [kHz] 
F i g u r e  4 .  The radial polarization is plotted as a function of the rf kicker driving frequency. 
Horizontally polarized 105.9 MeV protons were injected into the ring. 
"Present Address: D6pt. de Physique Univ. de Genkve, Genkve 4, Switzerland. 
b~resen t  Address: Fermilab, P.O. Box 500, Batavia, IL 60510. 
"On leave of absence from Brookhaven National Laboratory, Upton, New York 11973. 
d~resen t  address: Dept . of Physics, Western Michigan Univ., Kalamazoo, MI 49008. 
ePresent address: Dept. of Physics, Univ. of Wisconsin, Madison, WI 53706 
1. R.E. Pollock, Nucl. Instrum. Methods, Phys. Res., A300, 210 (1991). 
2. T. Roser, Comment at June 1990 Partial Siberian Snake Workshop at Brookhaven. 
3. B. von Przewoski, e t  al., Proc. of the gth International Symposium on High Energy 
Spin Physics, Bonn, September 1990 (to be published). 
4. S.W. Wissink, e t  al., Proceedings of the Seventh International Conference on Polar- 
ization Phenomena in Nuclear Physics, Paris, July, 1990 (to be published). 
5. M.G. Minty, e t  al., to be published in Phys. Rev. D, September 1991, UM HE 91-1. 
6. A.D. Krisch, e t  al., Phys. Rev. Lett. 6 3  (1989) 1137. 
7. J.E. Goodwin, e t  al., Phys. Rev. Lett. 64 (1990) 2779. 
8. Yu. M. Shatunov and A. N. Skrinsky, Part. World 1, 35 (1989). 
9. IUCF experiment CE-20 Proposal, April 1990, A. D. Krisch, e t  al. 


Siberian Snake and Depolarizing Resonance Studies at the Cooler Ring

https://scholarworks.iu.edu/dspace/bitstream/2022/673/1/iucf1990-1991_93-98.pdf

Siberian Snake and Depolarizing Resonance Studies at the Cooler Ring

Abstract

Similar works

Full text

Available Versions

IUScholarWorks