Accelerating Polarized Accelerating Polarized Protons to High EnergyProtons to High Energy

Mei Bai

Collider Accelerator DepartmentBrookhaven National Laboratory

Outline

General introduction of accelerator physics spin dynamics

Accelerating polarized protons to high energy

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

Summary

Synchrotron

The acceleration comes from the electric field with an oscillating frequency synchronized with the particle’s revolution frequency

Alternating gradient A proper combination of focusing and

de-focusing quadrupoles yields a net focusing force in both horizontal and vertical planes

FODO cell: most popular building block for synchrotrons

EB

QF QD QF

L L

Rf cavity

12'1

2

101

10

11

101

10

11

2

101

'

x

x

f

L

f

L

fx

x

Particle motion in a synchrotron

Transverse Betatron oscillation:

Betatron tune: number of betatron oscillations in one orbital revolution

Beta function: the envelope of the particle’s trajectory along the machine

0)(2

2

xsKds

xdx ))(2cos(2)( xxx sQJsx

Spin motion in a circular accelerator

Thomas BMT equation

In a perfect accelerator, spin vector precesses around its guiding field, i.e. vertical

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

horizontal field kicks the spin vector away from its stable direction, i.e. vertical, and can lead toDepolarization resonance when the spin vector gets

kicked at a frequency close to the frequency it precesses

y

x

z

B

S

beam direction

SBGBGm

eS

dt

Sd

])1()1[( //

GQs

Depolarizing spin resonances

For protons, imperfection spin resonances are spaced by 523 MeV

Horizontal magnetic fields

Dipole errors, steeringdipoles, quadrupole misalignments

Focusing field due to betatron oscillation Other multipole fields

Imperfection resonance:

Resonance strength:

Size of vertical closed orbit distortion

Intrinsic resonance:

Resonance strength:

Size of vertical betatron oscillation

yQkPG kG high order resonance

Break the resonance condition: Full Siberian snake

Rotates spin vector by 180o

Cancels the kicks on the spin vector in between the snakes Keeps the spin tune independent

of energy

Challenge in accelerating polarized protons to high energy: preserve beam polarization

)2

ψcos()cos(Gγ)cos(π sQ

Partial snakerotates spin vector by an angle of <180

o

Keeps the spin tune away from integer

Tune jump Jump the betatron tune as quickly as possible Intrinsic resonance only and can cause emittance blow

up

Change the resonance strength Minimize the resonance strength

Harmonic close orbit correction Imperfection resonanceOperationally difficult for high energy

accelerators

Enhance the resonance strength to achieve full spin flip with normal resonance crossing rate

Induce full spin flip using an ac dipoleCan only be applied to strong intrinsic spin

resonancesnot ideal for coupling resonances

Challenge in accelerating polarized protons to high energy: preserve beam polarization

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 acceleration complex at BNL

2

ψsin

2

ψsin

3cosGγ

2

ψcos

2

ψcoscosGγcosπ 2121 sQ

AGS (Alternating Gradient Synchrotron) Energy: 2.3 GeV ~ 23.8 GeV A total of 41 imperfection resonances and 7

intrinsic resonances from injection to extractionOne 5.9% partial snake plus one 10~15%

partial snake

Spin tune with two partial snakes

Courtesy of T. Roser

Spin tune

Ext

ract

ion

36+Qy intrinsic resonance

G

Vertical betatron tuneV

ert

ical

com

pon

en

t of

stab

le s

pin

2

ψsin

2

ψsin

3cosGγ

2

ψcos

2

ψcoscosGγcosπ cwcw sQ

Vertical Tunes8.82 8.84 8.86 8.88 8.90 8.92 8.94 8.96 8.98 9.00

Pol

ariz

atio

n (

%)

-60

-50

-40

-30

-20

-10

0

10

-60

-50

-40

-30

-20

-10

0

100+

36+

Tune scan with the AGS dual snake setup

Prelim

inary

Prelim

inary

• 15% cold snake +5.9% warm snake

Courtesy of H. Huang

Operating working point

Snake resonances

Results of AGS dual snake setup

The dual snake setup in the AGS was successfully commissioned. With the four new trim quadrupoles located at the entrance and exit of the cold and the warm snakes for compensating the optics distortion from the focusing fields from the snakes, 1.5x1011 protons with a beam polarization of 65% were accelerated with the vertical tune close to 9.

H. Huang’s talk: “Polarized Proton Acceleration in the AGS with Two Helical Partial Snakes”, Oct. 2, 17:00, Hall II

Polarized proton acceleration complex at BNL

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 φφ

π

1Q

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

Snake resonance observed in RHIC

¼ snake resonanceCoupled 3/14 snake resonance

Maximum vertical tune |Horizontal tune – 3/14|

Snake resonance observed in RHIC

7/10 snake resonance

polarized protons were accelerated to an energy of G=63, a location of a strong intrinsic spin resonance

How to avoid a snake resonance

Keep the spin tune as close to 0.5 as possible snake current setting

Keep the vertical closed orbit as flat as possible

Flat orbit: Sum of kicks on the spin vector from quads as well as the dipole correctors = 0

How to avoid a snake resonance

Keep the spin tune as close to 0.5 as possible snake current setting

Keep the vertical closed orbit as flat as possible

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

Polarized proton collisions in RHIC

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

Milestones of RHIC pp development

2000

New polarized proton source (OPPIS) commissioned One snake was installed in Blue ring and commissioned CNI polarimeter in Blue installed and commissioned

2002 All snakes for both rings installed and commissioned CNI polarimeter in Yellow installed and commissioned

2003 Spin rotators installed and commissioned

2004

RHIC absolute polarimeter using H Jet target installed and commissioned AGS 5% helical warm snake installed and commissioned

2005

New super-conducting solenoid was installed in the OPPIS source Polarized protons in RHIC were accelerated to 205 GeV with about 30% polarization at top energy AGS strong super-conducting helical snake installed and commissioned

2006

The AGS dual snake configuration was commissioned in the AGS. This configuration (10% cold snake + 5.9% warm snake) yields a polarization of 65% at the AGS extraction with 1.5x1011 protons per bunch Polarized protons were accelerated to 250 GeV with a polarization of 45%

RHIC pp achieved performance

Parameter Unit 2002 2003 2004 20052005 20062006

No. of bunches -- 55 55 56 106106 111111

 bunch intensity 1011 0.7 0.7 0.7 0.90.9 1.31.3

store energy GeV 100 100 100 100 100  100 100 

* m 3 1 1 1 1  1 1 

peak luminosity 1030cm-2s-1 2 6 6 1010 3535

average luminosity

1030cm-2s-1 1 4 4 6 6  2020

Collision points -- 4 4 4 33 22

Time in store % 30 41 38 5656 4646

average polarization, store

% 15 35 46 4747   60~6560~65

Ptitsyn’s talk: “RHIC Performance with Polarized Protons in Run-6”, Oct. 2, 16:45, Hall II

Run6 100 x 100 GeV pp Integrated Luminosity (Final Delivered) for Physics

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

4-M

ar

11

-Ma

r

18

-Ma

r

25

-Ma

r

1-A

pr

8-A

pr

15

-Ap

r

22

-Ap

r

29

-Ap

r

6-M

ay

13

-Ma

y

20

-Ma

y

27

-Ma

y

3-J

un

date

Inte

gra

ted

Lu

min

os

ity

[p

b^

-1]

STAR

PHENIX

min

max

one week shutdown

RHIC pp performance: delivered luminosity

FY05: Provided a total of 12.6pb-1 luminosity with longitudinal polarization at STAR and PHENIX

FY06: faster setup, higher luminosity and higher polarization

0

10

20

30

40

50

60

70

6800 7000 7200 7400 7600 7800 8000

RHIC fill #

aver

age

po

lari

zati

on

Blue Yellow

Blue average polarization: 49.5%

Yellow average polarization:44.5%

RHIC pp performance: average store polarization

FY2005 FY2006

Goal!

RHIC pp performance: polarization transmission efficiency

45%

First look of beam polarization at 250 GeV

Intr

insi

c sp

in r

eso

nance

Qx=

28.7

3,

Qy=

29.7

2,

em

it=

10

achieved

RHIC intrinsic spin resonance strength

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

Outlook of RHIC polarized protons

Luminosity: Goal:

At 100 GeV: 60x1030 cm-2s-1 20x1030 cm-2s-1 (x3) Improve bunch intensity/emittance:

Injector Improvement improve beam transfer efficiency Eliminate beam emittance growth during ramp

Improve luminosity lifetime: 10 Hz feedback loop to fight against the 10 Hz orbit jitter:

work-in-progress minimize non-linear triplet errors to improve the

tolerance to beam-beam effect

At 250 GeV: 150x1030 cm-2s-1 (x2.5 compared w. 100 GeV)

Outlook of RHIC polarized protons

Polarization Goal: 70% 65%

AGS: operating the AGS with both betatron tunes placed in the spin tune gap that dual snakes provide.

Outlook of RHIC polarized protons

Polarization Goal: 70% 65%

AGS: operating the AGS with both betatron tunes placed in the spin tune gap that dual snakes provide

RHIC: Snake current setting is critical to make sure the spin precession tune is very close to 0.5

• Multiple techniques of measuring spin precession tune in RHIC are under development.

Precise tune control• Tune+decoupling feedback system comissioned in FY06

Precise orbit control• Re-alignment of the machine• Improve the quality as well as the robustness of the BPM

system to achieve the rms value of the orbit distortion below 0.3mm

Summary

Over the past 5 years, all the essential hardware and diagnostic apparatus for polarized beam were put in place and successfully commissioned. RHIC has 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, the RHIC 2006 has achieved a faster setup as well as higher luminosity.

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.

Results of AGS dual snake setup

Courtesy of L. Ahrens and K. Brown

Beam intensity

AGS bending magnet field

Vertical betatron tune (8.98)

Horizontal betatron tune

9.0

8.8

8.6

How to avoid a snake resonance

Keep the spin tune as close to 0.5 as possible snake current setting

-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

AGS Horizontal resonance

Courtesy of F. Lin:“Exploration of Horizontal Intrinsic Spin Resonance in the AGS”, April 22, C14.00005

10 0 100

5 105

1 106

1.5 106

2 1062.19 10

6

5.06 103

f x( )

w5

w5 w6

w5 w6f1 x( )

w61

w61 w71

w61 w71

1717 x q q q x u u uTarget position

P

15 10 5 0 5 10 1520

30.5

41

51.5

6262

26.29

P 82 x ( )

w2

w2 w3

w2 w3P1 82 x 1 1 ( )

w21

w21 w31

w21 w31

1515 x q q q x u u uTarget position

P

10% Cold snake 5.9% Warm snake

15% Cold snake 5.9% Warm snake

The tilted stable spin direction also causes about ~5% depolarization at the locations of horizontal tunes