HIGH LUMINOSITY POLARIZED PROTON COLLISIONS AT RHIC
T. Roser, BNL, Upton, NY 11973, USA
Abstract

the two RHIC rings.

The Brookhaven Relativistic Heavy Ion Collider (RHIC)
provides the unique opportunity to collide polarized proton
beams at a center-of-mass energy of up to 500 GeV andluminosities of up to  32 cm 2 s 1 . Such high luminosity and high energy polarized proton collisions will
open up the possibility of studying spin effects in hard processes. However, the acceleration of polarized beams incircular accelerators is complicated by the numerous depolarizing spin resonances. Using a partial Siberian snake
and a rf dipole that ensure stable adiabatic spin motion during acceleration has made it possible to accelerate polarized
protons to 25 GeV at the Brookhaven AGS. After successful operation of RHIC with gold beams polarized protons
from the AGS have been successfully injected into RHIC
and accelerated using a full Siberian snakes built from four
superconducting helical dipoles. A new high energy proton polarimeter was also successfully commissioned. Operation with two snakes per RHIC ring is planned for next
year.

2 10

1

INTRODUCTION

Polarized proton colliders will open up the completely
unique physics opportunities of studying spin effects in
hard processes at high luminosity, high energy protonproton collisions. It will allow to study the spin structure of the proton, in particular the degree of polarizationof the gluons and antiquarks, and also to verify the many
well documented expectations of spin effects in perturbative QCD and parity violation in W and Z production.
The Brookhaven Relativistic Heavy Ion Collider (RHIC)
is the first hadron accelerator and collider consisting of two
independent rings. It is designed to operate at high collision
luminosity over a wide range of beam energies and withparticle species ranging from polarized protons to heavytoGeV ,ions. A center-of-mass energy range ofas achievable at RHIC[1], is ideal in the sense that it ishigh enough for perturbative QCD to be applicable andlow enough so that the typical momentum fraction of thevalence quarks is about 0.1 or larger which guarantees significant levels of parton polarization.
Initial operation with gold beams has already delivereda peak luminosity of :  25 cm 2 s 1 for the collisionof Gold ions. In terms of collisions of nucleons this corresponds to a luminosity of about 30 cm 2 s 1 demonstrating RHIC’s promise of high luminosity. The first operation
with Gold beams was followed by a highly successful commissioning run of polarized proton acceleration in one of

200 500

3 3 1010

 Work performed under the auspices of the U.S. Department of Energy

2 SPIN DYNAMICS, RESONANCES AND
SIBERIAN SNAKES
Accelerating polarized beams requires the control ofboth the orbital motion and spin motion. Whereas the effect of the spin on the orbit is negligible the effect of theorbit on the spin is usually very strong. The evolution of
the spin direction of a beam of polarized protons in external magnetic fields such as exist in a circular accelerator isgoverned by the Thomas-BMT equation [2],



dP!
=
dt


i
e h !
G B? + (1 + G) B!k  !
Pmwhere the polarization vector P is expressed in the framethat moves and rotates with the particle’s velocity. This
simple precession equation is very similar to the Lorentz
force equation which governs the evolution of the orbital
motion in an external magnetic field:

d!
v
=
dt

 e h i!
m

B?  !
v:

From comparing these two equations it can readily be seen
that, in a pure vertical field, the spin rotates G times fasterthan the orbital motion. Here G:
is the anomalous
magnetic moment of the proton and
E=m. In this casethe factor G then gives the number of full spin precessions
for every full revolution, a number which is also called thespin tune sp . At top RHIC energies this number reaches
about 400. The Thomas-BMT equation also shows that at longitudinal fields B!k can be quite
low energies
effective in manipulating the spin motion, but at high ener!
gies transverse fields B? need to be used to have any effectbeyond the always present vertical holding field.
The acceleration of polarized beams in circular accelerators is complicated by the presence of numerous depolarizing spin resonances. During acceleration, a spin resonanceis crossed whenever the spin precession frequency equals
the frequency with which spin-perturbing magnetic fields
are encountered. There are two main types of spin resonances corresponding to the possible sources of such fields:
imperfection resonances, which are driven by magnet errors and misalignments, and intrinsic resonances, driven by
the focusing fields.
The resonance conditions are usually expressed in termsof the spin tune  sp . For an ideal planar accelerator, where
orbiting particles experience only the vertical guide field,
the spin tune is equal to G , as stated earlier. The resonance condition for imperfection depolarizing resonances= 1 7928
=

(

1)

=

=

523

=

= 12

88

cos(sp ) = cos(G ) cos() :A similar calculation can be done for the effective precession direction or, as it is now often called, the stable spin
direction. The stable spin direction describes those polarization components that are repeated every turn. Note thatboth the stable spin direction and the spin tune are completely determined by the magnetic structure of the accelerator and the beam energy. The magnitude and sign of thebeam polarization, however, depends on the beam polarization at injection and the history of the acceleration process.
The spin tune and stable spin direction calculations apply only to a time-independent static situation or if parameters are changed adiabatically. Far from the resonance thestable spin direction coincides with the main vertical magnetic field. Close to the resonance, the stable spin direction
is perturbed away from the vertical direction by the resonance driving fields. When a polarized beam is accelerated
through an isolated resonance at arbitrary speed, the final
polarization can be calculated analytically [3] and is givenby

Pf =Pi = 2e

jj2
2

1;

where Pi and Pf are the polarizations before and after the
resonance crossing, respectively, and is the change of thespin tune per radian of the orbit angle. When the beam is2
slowly (  jj ) accelerated through the resonance, thespin vector will adiabatically follow the stable spin direction resulting in complete spin flip. However, for a fasteracceleration rate partial depolarization or partial spin flip
will occur.
Over the last ten years new techniques to cross both imperfection and intrinsic resonances adiabatically have beendeveloped. A localized spin rotator or ’partial Siberiansnake’ can make all the imperfection resonance strengths
large and cause complete adiabatic spin flip at every imperfection resonance [4], as shown in Fig. 1. A single
vertical rf dipole magnet can create a strong artificial spinresonance by driving large coherent betatron oscillations,
overpowering the effect of the intrinsic resonances.
At higher energies a ’full Siberian snake’ [5], which isÆ spin rotator of the spin about a horizontal axis, willakeep the stable spin direction unperturbed at all times aslong as the spin rotation from the Siberian snake is muchlarger than the spin rotation due to the resonance driving

180

100
80
60
40

Vertical Polarization=arise when sp G
n, where n is an integer. ImperfecMeVtion resonances are therefore separated by only
energy steps. The condition for intrinsic resonances issp G
kP  y , where k is an integer,  y is thevertical betatron tune and P is the superperiodicity. For
example at the AGS, P
and  y  : .
Close to a spin resonance the spin tune deviates awayfrom its value of G of the ideal flat machine. For a resonance with strength , which is the total spin rotation due
to the resonance driving fields, the new spin tune is givenby the equation

20
0
-20
-40
-60
-80

Snake onSnake off

-100

Figure 1: The measured vertical polarization as a functionof G for a 10% snake is shown with and without a snake.
The solid line is the predicted energy dependence of thepolarization.

fields. Therefore the beam polarization is preserved during acceleration. An alternative way to describe the effectof the Siberian snake comes from the observation that the
spin tune with the snake is a half-integer and energy independent. Therefore, neither imperfection nor intrinsic resonance conditions can ever be met as long as the betatrontune is different from a half-integer.
A local spin rotator can be constructed by using either asolenoid at lower energies or at high energy by a sequenceof interleaved horizontal and vertical dipole magnets producing only a local orbit distortion. Since the orbit distortion is inversely proportional to the momentum of the particle, such a dipole snake is particularly effective for highenergy accelerators, e.g. energies above about GeV .

30

3ACCELERATING POLARIZEDPROTONS IN AGS AND RHIC

Fig. 2 shows the lay-out of the Brookhaven accelerator
complex highlighting the components required for polarized beam acceleration. A new polarized source using the’Optically Pumped Polarized Ion Source’ (OPPIS) technique, assembled at TRIUMF using components of the
KEK OPPIS, was recently installed at BNL[6]. The newsource produced 12 polarized protons per pulse. A single
source pulse is captured into a single bunch and accelerated
in the Booster and AGS for ‘box-car’ injection into RHIC.
This is ample beam intensity to reach the nominal bunch
intensity of  11 polarized protons.
Polarized proton beam experiments at the AGS havepartial snake, that rotates the spindemonstrated that aby 9 degrees, is sufficient to avoid depolarization from imperfection resonances up to the required RHIC transfer energy of about 25 GeV[7]. More recently a novel schemeof overcoming strong intrinsic resonances using a rf dipole
magnet was successfully tested [8]. Full spin flip can beachieved with a strong artificial rf spin resonance excited

10

2 10

5%

RHIC pC Polarimeters

Lmax = 2 ×1032 s −1cm −2

BRAHMS & PP2PP (p)Absolute Polarimeter (H jet)

70% Polarizations = 50 ... 500 GeV

PHENIX (p)STAR (p)Siberian Snakes

Spin Rotators

2 × 1011 Pol. Protons / Bunch
ε = 20 π mm mrad

Partial Siberian Snake
LINAC

BOOSTER

Pol. Proton Source
500 µA, 300 µs

AGS
AGS Internal Polarimeter
Rf Dipoles

200 MeV Polarimeter

Figure 2: The Brookhaven hadron facility complex, which includes the AGS Booster, the AGS, and RHIC. The RHIC
spin project will install two snakes per ring with four spin rotators per detector for achieving helicity-spin experiments.
coherently for the whole beam by driving large coherent
vertical betatron oscillations. The rf dipole was used tocompletely flip the spin at the four strong intrinsic resoy ,y ,y , andy . During thenancesrecent commissioning run beam polarization of about 40%
was maintained at the AGS extraction energy of 25 GeV.
Most of the 30 % polarization loss during acceleration in
the AGS is caused by coupling resonances and weak intrinsic resonances. New betatron tune working points in
the AGS should reduce the effect of these weak resonancesin the future.

0+

12 +

36

36 +

With full snakes in RHIC all depolarizing resonances
should be avoided since the spin tune is a half-integer independent of energy. However, if the spin disturbance fromsmall horizontal fields is adding up sufficiently between
the snakes depolarization can still occur. This is most pronounced when the spin rotation from all the focusing fields
add up coherently which is the case at the strongest intrinsic resonances. A simplistic rule of thumb would thensuggest that as long as the total spin rotation of all the
Siberian snakes is much larger than the total spin rotation
per turn caused by the strongest spin resonance the polarization should be preserved during acceleration. This ruleholds for the AGS partial Siberian snake with regard to theimperfection resonances. It would also predict that for abeam with a normalized 95% emittance of  mm mradat least two snakes are needed for RHIC.

lical magnets minimizes orbit excursions within the extendof the snake or spin rotator which is most important at injection energy. Nevertheless the bore of the helical magnets has to be 10 cm in diameter to accommodate the 3 cm
orbit excursions. The superconducting helical dipoles arebeing constructed at BNL using thin cable placed into helical grooves that have been milled into a thick-walled aluminum cylinder. A schematic picture of the helical dipole
magnet is shown in Fig. 3. For a snake or spin rotator four
full length helical dipole magnets are assembled into a single cryostat with the length of a regular RHIC dipole[10].
Only a single Siberian snake in one of the two RHIC
rings was available for the first polarized proton commissioning in RHIC. This meant that vertically polarized protons needed to be injected without the snake powered, thesnake was then turned on, which rotates the spin into thehorizontal plane, and then finally the beam was accelerated. Even under this more complicated scenario polarized
protons were successfully accelerated to about 30 GeV,20

Of particular interest is the design of the Siberian snakes(two for each ring) and the spin rotators (four for each collider experiment) for RHIC. Each snake or spin rotator consists of four : m long, T helical dipole magnet modules
each having a full 360 degree helical twist [9]. Using he-

24

4

Figure 3: Schematic picture of the superconducting helical
dipole shows the 16 helical current blocks and half of theiron yoke

24.3

29.1

25.1

1

31.5 GeV

4.0

0.8

snake onsnake off

0.6

3.0

−3

Asymmetry(x10 )81+6−νyP ~ 40 % at AGS

2.0

<Sy>

0.4

P ~ 19 %

0.2

0

1.0
−0.2

0.0

−0.4
370

45.0

50.0

55.0

60.0

65.0

70.0

380

390

400
Gγ

410

420

430

Gγ

Figure 4: Measured polarization of the first polarized proton beam in RHIC at injection without Siberian snake(open circle) and accelerated with snake (filled circles).
The graph shows the asymmetry measured with the RHIC
proton-carbon polarimeter. The polarization values given
were obtained from calibration measurements performed
previously in the AGS.

the highest energy accelerated polarized proton beam everachieved. Fig. 4 shows the beam polarization measured in
RHIC during this first commissioning run. More than 20
years after Y. Derbenev and A. Kodratenko made their proposal to use local spin rotators to stabilize polarized beams
in high energy rings it has now been demonstrated that
their concept is working flawlessly even in the presence ofstrong spin resonances at high energy. It also confirms theinitial tests of the Siberian snake concept at low energy thatwere performed at IUCF. Significant polarization was lostat injection when the snake was off and at the first verystrong spin resonance. Spin tracking[11] confirmed that
this latter loss is due to an improper betatron tune setting
and the large uncorrected closed orbit distortions.
Extensive spin tracking also confirms that with two
Siberian snakes and a well corrected closed orbit and awell controlled betatron tune no polarization should be lost
up to the full RHIC energy of 250 GeV. The acceleration
through the energy region of the strongest resonance wassimulated in great detail including a 1 mm rms misalignment of the quadrupoles, and sextupoles as well as the corrector dipoles used to correct the closed orbit. The result isshown in Fig. 5 for a beam with a normalized 95% emittance of  mm mrad. The upper and lower curve show
the result for the full beam and the particles at the edge ofthe beam, respectively. Although there is a significant decrease of the polarization at the energy of the resonance atGy: , the polarization of thefull beam is restored after accelerating completely through20= 5 81+(12) = 422 18

Figure 5: Result of spin tracking through the region of thestrongest resonance in RHIC. The closed orbit was corrected with residuals of less than 0.2 mm.
the resonance region. The simulation also shows that there
is significant polarization loss at the edge of the beam. This
fact highlights the need for a polarimeter that can measurepolarization profiles.
In addition to maintaining polarization the fast, accurate,
and reliable measurement of the beam polarization is ofgreat importance. The analyzing power of only very few reactions has been measured at high energies and the magnitudes are typically rather small. Polarization sensitive interaction with an external electromagnetic field is also muchsmaller than for the much lighter electron for which Compton back scattering is typically used for high energy polarization measurement. Very small angle elastic scattering in
the Coulomb-Nuclear interference region offers the possibility for an analyzing reaction with a high figure-of-meritwhich is not expected to be strongly energy dependent[12].
For polarized beam commissioning in RHIC an ultra thincarbon ribbon was used as an internal target and the recoilcarbon were detected to measure both vertical and radialpolarization component. The detection of the recoil carbon
with silicon detectors using both energy and time-of-flightinformation showed excellent particle identification. It wasdemonstrated that this polarimeter can be used to monitor
polarization of high energy proton beams in a almost nondestructive manner and that the carbon fiber target could bescanned through the circulating beam to measure polarization profiles.

4

COMMISSIONING PLANS ANDSCHEDULE

For the upcoming polarized proton run it is planned to install all four Snakes as well as the proton-carbon polarimeter in the second ring. This should allow for acceleration to
the full RHIC energy of 250 GeV. Collisions are planned

Table 1: Beam and lattice parameters for RHIC proton-proton design and upgrade possibilities.
RHIC Spin design RHIC II Future Upgrade
Emittance(95%), m
20
12
12
Beta function at IR,  ; m1
10.3
Number of bunches, M
120
120
360
11
Bunch population, N;2
2
2
Beam-beam parameter per IR, 
0.00730.012
0.012
Angular beam size at IR,  0 ; rad
112
86
157
RMS beam size at IR,   ; m
112
86
47
Luminosity, L; 32 cm 2 s 1
2.4
4.0
40

[

[10

]
[ ]
[10 ]

[
[ ]

]

]

at 100 GeV on 100 GeV at which energy one of the two
snakes per ring can be turned off to produce longitudinalpolarization at the detectors. The luminosity is expected to
be about  30 cm 2 s 1 .
All spin rotators will be installed for the following
runpossibility to go to full collision energy of
ps with theGeVwith longitudinal polarization at STARand PHENIX. Finally a polarized gas jet will be installed
as an internal target for small angle proton-proton scattering which will allow the absolute calibration of the beampolarization to better than 5 %.

5 10

= 500

5 LUMINOSITY UPGRADES FOR
POLARIZED PROTON OPERATION
The present RHIC spin physics program is based oncolliding polarized proton beams at a center-of-mass energy of up to 500 GeV and a luminosity of up to 
32 cm 2 s 1 . Although the physics potential of thiscapability still needs to be exploited there are upgrades to
RHIC that can significantly extend the physics reach of thisprogram since spin physics relies on high precision measurements.
The proton beam intensity can be increased, or the
beam emittance be decreased until the beam-beam limit
is reached which corresponds to a luminosity of about 32 cm 2 s 1 . The RHIC electron cooler proposed
for heavy ion operation could be used at injection energy toachieve this reduction of the proton beam emittance. Alternatively the bunch intensity could be increased to  11
protons. The machine parameters for the RHIC Spin design
and the luminosity at the beam-beam limit (column “RHIC
II”) are listed in Table 1.
It also seems possible to install in one or two interaction
regions an additional pair of high field focusing triplets thatwould reduce beta-star to about 30 cm increasing the luminosity by an additional factor of 3. Finally, the number ofbunches in each ring could be increased from 120 to 360
increasing the luminosity by another factor of 3. The latter two upgrade options, shown in the last column in Table1, would also require upgrades to the detectors. Taken
together these upgrades would allow for a polarized proton luminosity at 500 GeV of up to  33 cm 2 s 1 , a
20-fold increase over the present luminosity goal.

2

10

4 10

3 10

4 10

6

REFERENCES[1] Design Manual - Polarized Proton Collider at
RHIC, Brookhaven National Laboratory, July 1998,
http://www.cadops.bnl.gov/RHIC/spin/design .
[2] L.H. Thomas, Phil. Mag. 3, 1 (1927); V. Bargmann, L.
Michel, V.L. Telegdi, Phys. Rev. Lett. 2, 435 (1959).
[3] M. Froissart and R. Stora, Nucl. Instr. Meth., 1, 297 (1960).
[4] T. Roser, AIP Conf. Proc. No. 187, ed. K.J. Heller p.1442(AIP, New York, 1988).
[5] Ya.S. Derbenev et al., Part. Accel. 8, 115 (1978).
[6] A.N. Zelinski et al., ’Optically-Pumped Polarized H- ION
Sources for RHIC and HERA Colliders’, Proceedings ofthe 1999 Particle Accelerator Conference, New York, p. 106(1999).
[7] H. Huang et al., Phys. Rev. Lett. 73, 2982 (1994)[8] M. Bai et al., Phys. Rev. Lett. 80, 4673 (1998)[9] V.I.Ptitsin and Yu.M.Shatunov, Helical Spin Rotators andSnakes, Proc. 3. Workshop on Siberian Snakes and Spin
Rotators (A.Luccio and T.Roser Eds.) Upton, NY, Sept. 1213,1994, BNL-52453, p.15;[10] E. Willen et al., ’Construction of helical magnets for RHIC’,
Proceedings of the 1999 Particle Accelerator Conference,
New York, p. 3161 (1999).
[11] A.U. Luccio et al., ’Development of the spin tracking program SPINK’, Proceedings of the 1999 Particle Accelerator
Conference, New York, p. 1578 (1999).
[12] J. Schwinger, Phys. Rev. 73, 407 (1948)