RHIC Spin and ColliderRHIC Spin and Collider

Mei Bai

Outline

Introduction: why polarized protons spin “crisis” accelerate polarized protons to high energy

RHIC: the first polarized proton collider brief history of RHIC spin program achieved performance of RHIC pp

Conclusion plan for RHIC improvements

What is Spin? From Google…

revolve quickly and repeatedly around one's own axis, "The dervishes whirl around and around without getting dizzy"

twist and turn so as to give an intended interpretation, "The President's spokesmen had to spin the story to make it less embarrassing"

a distinctive interpretation (especially as used by politicians to sway public opinion), "the campaign put a favorable spin on the story"

What is Spin?Classical definition

the body rotation around its own axis

Particle spin: an intrinsic property, like mass and chargea quantum degree freedom associated with the intrinsic magnetic moment.

Smq

G)(1s μ

G: anomalous gyromagnetic factor, describes the particle internal structure. For particles:

point-like: G=0 electron: G=0.00115965219 muon: G=0.001165923 proton: G=1.7928474

m: particle mass

q: electrical charge of particle

Spin: single particle pure spin state align along a quantization axis

Spin vector S: a collection of particles the average of each particle spin expectation value along a given direction

spin vector and spin-orbit interaction

BμdtSd

s

S

N

Spin orbit interaction

SN

I IAμ

S

BμdtJd

Discovery of Spin: 1925

“This is a good idea. Your idea may be wrong, but since both of you are so young without any reputation, you would not lose anything by making a stupid mistake.” --- Prof. Ehrenfest 

G.E. Uhlenbeck and S. Goudsmit, Naturwissenschaften 47 (1925) 953. A subsequent publication by the same authors, Nature 117 (1926) 264,

Spin Crisis: what makes up the proton spin?

ΔΣ21

21

S

P

u

d

u

Sum of spins of all quarks

CERN EMC and SLAC SMC: ~ 20%!

Current model: Proton spin sum-

rule

gq LLg21

21

S ΔΔΣ

Orbital angular momentum ofquarks and gluons?

Spin contribution from all the gluons?

gg

q

gluon spin contribution

quark/antiquark spin contribution

g

High energy proton proton collisions: gluon gluon collision and gluon quark collision

Quest to unveil the proton spin structure:

STAR

RHIC: world’s first polarized proton collider

RHIC spin physics

STAR

• Excellent calorimeter granularity and muon detection • electrons, muons, photons and leading hadrons

measure gluon spin contribution g measure quark and anti quark spin contribution

• Large acceptance with Time Projection Chamber and calorimeters• Jets and photons and electrons

Design parameters for RHIC pp

Parameter Unit p-p

relativistic , injection … 25.9

 relativistic , store … 266.5

no of bunches, nb … 112

ions per bunch, Nb 1011 2.0

emittance eN x,y 95% mm-mrad 20

average luminosity 1030 cm-2s-1 150

polarization,store % 70

Figure of merit of polarized proton collider

Luminosity: number of particles per unit area per unit time. The

higher the luminosity, the higher the collision rates

beam polarizationStatistical average of all the spin vectors.

zero polarization: spin vectors point to all directions. 100% polarization: beam is fully polarized if all spin vectors

point to the same directions.

)(

)(

4

1)(

2

2

0 t

tnNftL

rms

Transverse beam size

# of particles in one bunch

# of bunches

Basics of circular accelerator

bending dipole Constant magnetic field Keeps particles circulating around the ring

quadrupole Magnetic field proportional to the distance from the

center of the magnet. Keeps particles focused

radio frequency cavities Electric field for acceleration and keeping beam

bunched longitudinally

Closed orbit in a circular accelerator

Closed orbit in a machine with dipole errors

Closed orbit ina perfect machine:center of quadrupoles

Courtesy of Lingyun Yang

Closed orbit: particle comes back to the same position after one orbital revolution

Betatron oscillation in a circular accelerator

))(2cos(2)( yyy sQJsy Beta function

Betatron tune: number of oscillations in one orbital revolution

Courtesy of Lingyun Yang

Spin motion in circular accelerator: Thomas BMT Equation

In a perfect accelerator, spin vector precesses around the bending dipole field direction: vertical

Spin tune Qs: number of precessions in one orbital revolution. In general,

SBGBGm

eS

dt

Sd

])1([ //

Spin vector in particle’s rest frame

B

beam

GγQs

polarized proton acceleration challenges: preserve beam polarization Depolarization(polarization loss) mechanism

Come from the horizontal magnetic field which kicks the spin vector away from its vertical direction

Spin depolarizing resonance : coherent build-up of perturbations on the spin vector when the spin vector gets kicked at the same frequency as its precession frequency

xB

x

y

z

beam

Initial

xB

x

y

z

beam

1st full betatron Oscillation period

xB

x

y

z

beam

2nd full betatron Oscillation period

spin depolarizing resonance

Imperfection resonance Source: dipole errors,

quadrupole mis-alignments

Resonance location:

G = k k is an integer

Intrinsic resonance Source: horizontal

focusing field from betatron oscillation

Resonance location:

G = kP±Qy,P is the periodicity of the

accelerator, Qy is the vertical

betatron tune

Intr

insi

c sp

in r

eso

nance

Qx=

28.7

3,

Qy=

29.7

2,

em

it=

10

Spin depolarization resonance in RHIC

• For protons, imperfection spin resonances are spaced by 523 MeV

• the higher energy, the stronger the depolarizing resonance

First invented by Derbenev and Kondratenko from Novosibirsk in 1970s

A group of dipole magnets with alternating horizontal and vertical dipole fields

rotates spin vector by 180o

Innovative polarized proton acceleration techniques: Siberian snake

Particle trajectory in a snake:

Use one or a group of snakes to make the spin tune to be at ½

How to preserve polarization using Siberian snake(s)

xB

y

z

beam

xB

y

z

beam

Break the coherent build-up of the perturbations on the spin vector

Accelerate polarized protons in RHIC

PHENIX (p)

AGS

LINACBOOSTER

Pol. H- Source

Solenoid Partial Siberian Snake

200 MeV Polarimeter

Helical Partial Siberian Snake

Spin Rotators(longitudinal polarization)

Siberian Snakes

Spin Rotators(longitudinal polarization)

Strong AGS Snake

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

STAR (p)

BRAHMS(p)

AGS Polarimeters

Spin flipper

Polarized proton in the AGS

AGS (Alternating Gradient Synchrotron) Energy: 2.3 GeV ~ 23.8 GeV

A total of 41 imperfection resonances and 7 intrinsic resonances from injection to extraction

AGS polarized proton development

1988 Harmonic

correction

Fast tune jump Months 21.7 0.108 42

imperfection intrinsic Setup time Energy

GeV

Int

[1011]

Pol

[%]

1994 5%solenoid

partial snake

Fast tune jump 2 weeks 23.0 0.05 31

1998 5%solenoid

partial snake

AC dipole @ 3 strong intrinsic resonance

2 weeks 23.0 0.05 37

2005 5%helical

partial snake

AC dipole @ 4 strong intrinsic resonance

2 weeks 23.8 1.0 50

2000 New polarized H- source with high current high polarization

2005 5% helical partial snake +10% super-conducting helical partial snake

2 weeks 23.8 1.5 65

Polarized proton acceleration setup in RHIC

Energy: 23.8 GeV ~ 250 GeV (maximum store energy) A total of 146 imperfection resonances and about

10 strong intrinsic resonances from injection to 100 GeV.Two full Siberian snakes

2

1 Qs

21s φφπ

1Q

Polarized proton acceleration in RHIC

snake depolarization resonance

Condition

even order resonance When m is an even

number Disappears in the two

snake case like RHIC if the closed orbit is perfect

odd order resonance When m is an odd number Driven by the intrinsic

spin resonances

Ram

p w

orki

ng p

t.

Sto

re w

orki

ng p

t.

3/4

5/6

7/8

5/8

kQmQ sy

z

beam

xB

y

-xxB

-x

y

z

beam

z

beam

xB

y

-x

z

beam

xB

y

-x

z

beam

xB

y

-x

z

beam

xB

y

-x

kQQ sy 6

Snake resonance observed in RHIC

7/10 snake resonance

How to avoid a snake resonance

Keep the spin tune as close to ½ as possible

-10

0

10

20

30

40

50

300 305 310 315 320 325 330 335

snake Inner Current [Amp]

po

lari

zati

on

Blue FY04 flatten orbit Yellow FY04 zero orbit Yellow FY05 Zero orbit

Blue FY05 flatten orbit Yellow FY05 flatten orbit

• set the vertical tune to 0.745

• measure the beam polarization with different snake current

• expect no depolarization if the corresponding spin tune is very close to 0.5

snake current setting

How to avoid a snake resonance Keep the vertical closed orbit as flat as possible

rms: 0.45mm

How to avoid a snake resonance

Keep the spin tune as close to ½ as possible snake current setting

Keep the vertical closed orbit as flat as possible orbit control

Keep the betatron tunes away from snake resonance locations Precise tune control

Betatron tune along the ramp

flattop*=2m

10 seconds after flattop beta1*=2m

¾ snake resonance

7/10 snake resonance

Milestones of RHIC pp development

2000

New polarized proton source One snake installed in Blue ring of RHIC New fast polarimeter in Blue

2002 All 4 snakes for both rings and CNI polarimeter in Yellow

2003 Spin rotators

2004 RHIC absolute polarimeter using H Jet target AGS 5% helical warm snake

2005

New super-conducting solenoid for the polarized H- source 205 GeV polarized protons with ~ 30% polarization AGS strong super-conducting helical snake

2006

Dual snake configuration for the AGS and reached a polarization of 65% at the AGS extraction with 1.5x1011 protons per bunch 250 GeV polarized protons in RHIC with a polarization of 45%

0.1

1

10

100

2001 2002 2003 2004 2005 2006 2007

Calendar year

Inte

grat

ed lu

min

osit

y

[

pb-1

]

0

10

20

30

40

50

60

70

Bea

m P

ola

riza

tio

n [

%]

RHIC pp performance

Courtesy of W. Fischer

RHIC pp performance: polarization transmission efficiency

Intr

insi

c sp

in r

eso

nance

Qx=

28.7

3,

Qy=

29.7

2,

em

it=

10

AchievedPhysics Run

RHIC intrinsic spin resonance strength

Design goal

45% !

First look of beam polarization at 250 GeV

0

0.002

0.004

0.006

0.008

0.01

0.012

20 40 60 80 100 120 140 160 180 200 220 240

Beam Energy [GeV]

Asy

mm

etry

d

Resonance around 138 GeV

Polarization 250 GeV ramp measurement

Plan for RHIC polarized protons

Improve luminosity performance

Increase the average luminosity at 100 GeV from 6.0x1030 cm-2s-1 to 20x1030 cm-2s-1 (x3) Luminosity limit beam-beam effect Accelerator developments to mitigate the beam-

beam effect increase bunch intensity eliminate emittance grow

At 250 GeV: 150x1030 cm-2s-1

Reach polarization of 70% or higher

AGS: operating the AGS with both betatron tunes

in the spin tune gap to avoid additional polarization loss due to horizontal betatron oscillation as observed in RHIC 2006 Run

RHIC: preserve beam polarization to 250 GeV

Improve the tune control technique Improve the orbit control system to control the

orbit distortion within 0.3mm or less.

Conclusion

Over the past 5 years, all the essential hardware and diagnostic apparatus for

polarized beam were put in place and successfully commissioned.

successfully accelerated polarized protons to 100 GeV with no polarization loss.

The performance of RHIC pp in Run 2006 was greatly improved due to the great success of the AGS dual snake setup as well as the improvement of RHIC systems.

The 500 GeV development demonstrated a beam polarization of 45% at 250 GeV and also identified the location of depolarizing resonances.

With the success in the AGS and improvements in RHIC, we expect RHIC to achieve the design goal in the near future.

Great physics is ahead of us, stay tuned in …

Acknowledgement

L. Ahrens, I.G. Alekseev, J. Alessi, J. Beebe-Wang,M. Blaskiewicz, A. Bravar, J.M. Brennan, D. Bruno,G. Bunce, J. Butler, P. Cameron, R. Connolly, J. Delong,T. D’Ottavio, A. Drees, W. Fischer, G. Ganetis, C. Gardner, J. Glenn, T. Hayes, H-C. Hseuh. H. Huang, P. Ingrassia,U. Iriso-Ariz, O. Jinnouchi, J. Laster, R. Lee, A. Luccio,Y. Luo, W.W. MacKay, Y. Makdisi, G. Marr, A. Marusic,G. McIntyre, R. Michnoff, C. Montag, J. Morris, A. Nicoletti, P. Oddo, B. Oerter, J. Piacentino, F. Pilat, V. Ptitsyn,T. Roser, T. Satogata, K. Smith, D.N. Svirida, S. Tepikian,R. Tomas, D. Trbojevic, N. Tsoupas, J. Tuozzolo, K. Vetter, M. Milinski. A. Zaltsman, A. Zelinski, K. Zeno, S.Y. Zhang.

Acknowledgement

Special Thanks to my mentors

Prof. S. Y. Lee, Indiana University

Dr. Thomas Roser, C-A Department

Dr. Mike Syphers, Fermi Lab.