Thomas RoserXIIth International Workshop on Polarized Sources, Targets & Polarimetry

September 12, 2007

Polarized Proton Acceleration inAGS and RHIC

Spin dynamics and depolarizing resonances

Partial and Full Siberian Snakes

Polarization development in the AGS

Polarization development in RHIC

Spin flipper and spin tune meter

RHIC

NSRLLINAC

Booster

AGS

Tandems

STAR6:00 o’clock

PHENIX8:00 o’clock

(PHOBOS)10:00 o’clock

Jet Target12:00 o’clock

RF4:00 o’clock

e-cooling(BRAHMS)2:00 o’clock

RHIC – a High Luminosity (Polarized) Hadron Collider

Operated modes (beam energies):

Au–Au 4.6, 10, 28, 31, 65, 100 GeV/n

d–Au* 100 GeV/n

Cu–Cu 11, 31, 100 GeV/n

p–p 11, 31, 100, 205, 250 GeV

Possible future modes:

Au – Au 2.5 GeV/n (AGS, SPS c.m. energy)

p – Au* 100 GeV/n (*asymmetric rigidity)

Achieved peak luminosities (100 GeV, nucl.-pair):

Au–Au 1201030 cm-2 s -1

p–p 351030 cm-2 s -1

Other large hadron colliders (scaled to 100 GeV):

Tevatron (p – pbar) 291030 cm-2 s -1

LHC (p – p, design) 1401030 cm-2 s -1

EBIS

RHIC Spin Physics

Spinning Proton Spinning Proton

Spinning Quarks or Gluons

Quark, Gluon, Photon,Electron or Neutrino fromW or Z Decay

• Spin structure functions of gluon and anti-quarks• Parity violation in parton-parton scattering• Requires high beam polarization and high luminosity

Delivered Luminosity and Polarization

Spin Dynamics in Rings

Precession Equation in Laboratory Frame:(Thomas [1927], Bargmann, Michel, Telegdi [1959])

dS/dt = - (e/m) [(1+GB + (1+G) BII ] S

Lorentz Force equation:

dv/dt = - (e/m) [ B ] v

• For pure vertical field:Spin rotates Gtimes faster than motion, sp = G

• For spin manipulation:At low energy, use longitudinal fieldsAt high energy, use transverse fields

Spin tune and Depolarizing Resonances

Depolarizing resonance condition:

Number of spin rotations per turn = Number of spin kicks per turnSpin resonance strength = spin rotation per turn / 2

Imperfection resonance (magnet errors and misalignments):

sp = n

Intrinsic resonance (Vertical focusing fields):

sp = Pn± Qy

P: Superperiodicity [AGS: 12]Qy : Betatron tune [AGS: 8.75]

Weak resonances: some depolarizationStrong resonances: partial or complete spin flip

Illustration by W.W. MacKay

Spin Resonance Crossing

Froissart-Stora: : crossing speed]

Non-adiabatic (2/1) Adiabatic (2/1)

Pf /Pi = 1 Pf /Pi = 1

1- e 2 2

2

i

f -

PP

KG

GK

GK

KG

G=K

Spin Resonance Crossing

Non-adiabatic (2/1) Adiabatic (2/1)

Pf /Pi = 1 Pf /Pi = 1

Imperfection Resonances:

Correction Dipoles (small) Partial Snake (large)

Intrinsic Resonances:

Pulsed Quadrupoles (large) RF Dipole (large)

Lattice modifications (small) Strong Partial Snake (large)

Asymmetry flips sign at every G = N and intrinsic res.

~1 ms bin width

Raw

asy

mm

etry

= A

N

Pbe

am 0.015

0.01

-0.015

-0.005

-0.01

0.005

0

Ebeam

25 30 35 40 45

12 14 16 18 20 22 24

36 -

36 +

AGS polarization with (weak) partial snake and rf dipole

Siberian Snakes (Local Spin Rotators)

cos(180 sp) = cos(/2) · cos(180 G)

0 sp n

No imperfection resonancesPartial Siberian snake (AGS)

= 180 sp = ½No imperfection resonances andNo Intrinsic resonancesFull Siberian Snake(Ya.S. Derbenev and A.M. Kondratenko)

Two Siberian Snakes in RHIC

(Naïve) Limits for Siberian Snakes

Spin rotation of Siberian snake () > Spin rotation of driving fields ()“Spin rotation of Siberian snake drives strong imperfection resonance”

Imperfection resonances EnergyIntrinsic resonances Energy

Partial Siberian snake (AGS, = 9° ) < /360°

One full snake < 1/2Two full snakes (RHIC) < 1N full snakes (LHC? N 16) < N/2

Ultimate energy limit: Imperfection resonance strength for corrected orbit ~ 0.05RHIC (250 GeV) 200 m residual error LHC (7 TeV) ~20 m residual error ?

RHIC – First Polarized Hadron Collider

BRAHMS

STAR

PHENIX

AGS

LINACBOOSTER

Pol. H- Source

Spin Rotators(longitudinal polarization)

Siberian Snakes

200 MeV Polarimeter Internal Polarimeter

pC PolarimetersAbsolute Polarimeter (H jet)

pC Polarimeter

10-25% Helical Partial Siberian Snake

5.9% Helical Partial Siberian Snake

PHOBOS

Spin Rotators(longitudinal polarization)

Spin flipper

Siberian Snakes

Without Siberian snakes: sp = G = 1.79 E/m ~1000 depolarizing resonancesWith Siberian snakes (local 180 spin rotators): sp = ½ no first order resonancesTwo partial Siberian snakes (11 and 27 spin rotators) in AGS

Siberian Snakes

AGS Siberian Snakes: variable twist helical dipoles, 1.5 T (RT) and 3 T (SC), 2.6 mRHIC Siberian Snakes: 4 SC helical dipoles, 4 T, each 2.4 m long and full 360 twist

Major funding by RIKEN, JapanRT helical dipole constructed at Tokano Ind., JapanSC helical dipoles constructed at BNL

2.6 m 2.6 m

Strong Partial Siberian Snake for AGS

A strong partial Siberian snake generates large spin tune gap for G = n. With strong enough snake, gap is large enough to cover both imperfection and intrinsic spin resonances.

Note: With a strong snake, the stable spin direction will deviate from vertical direction (18 degree for 20% snake).

Gsp cos2/coscos1 1

Intrinsic resonance

Imperfection resonance

Two partial snakes in the AGS

Spin tune

Ext

ract

ion

36+Qy intrinsic resonance

G

Vert

ical

com

pon

en

t of

stab

le s

pin

Vertical betatron tune

warm snake

cold snake

Betatron Tune and Spin Tune

Courtesy of H. Huang

Ramp Measurement

AGS Polarization

Dual Partial Snake (Run 6)AC Dipole plus Partial Snake (Run 5)

Dual Partial Snake in AGS avoided depolarization from all vertical depolarizing resonances and largely eliminated intensity dependence

Plan to study low energy polarization loss and also increase acceleration rate at low energy goal to reach 70% polarization at AGS extraction energy.

Spin Resonances in RHIC w/o Snakes

Intrinsic resonance strength for 10 mm mrad particle

Imperfection resonance strength for corrected orbit with 150 m residual error

Beam Polarization Near a Strong Intrinsic Resonance

1

1

n3 .32 Gg .3( )

n3 .32 Gg .6( )

n3ns .32 Gg .3( )

n3ns .32 Gg .6( )

55 Gg4 2 0 2 4

1

0.5

0

0.5

1

Without snakes: spin flip, width ~ ± 5With snakes: opening/closing of “spin cone”, nodes at ± 2

Resonance strength = 0.3, 0.6

G

With Snakes:Resonance crossing during acceleration is adiabatic with no polarization loss.

Snake Resonances

single snakeor two snakes with orbit errors

two snakes (m: odd)New tune working point

1

1

n3 Q Gg0( )

0.50 Q0 0.1 0.2 0.3 0.4

1

0.5

0

0.5

1

1/6

3/14

3/10

1/10

Old tune working point

0.60.70.80.9

Stable polarizationon resonance, = 0.3

• Higher order resonance condition sp + mQy = k (m, k = integer) driven by interaction of intrinsic resonance G + Qy = k with large spin rotations of dipoles and snakes.

• No non-linear drive term necessary – combination of rotations is already non-linear.• “Snake resonance strength” depends on intrinsic resonance strength and therefore energy• For sp=1/2+sp Qy = (2k-1)/2m-sp/m• First analytical solution of isolated resonance with snakes by S.R. Mane, NIM A 498

(2003) 1

1/4

3/8

1/61/10

1/8

1/12 3/10

0.60.70.80.9

Stable polarizationon resonance, = 0.3

Luminosity and Polarization Lifetimes in RHIC at 100 GeV

19:00 21:00 23:00 01:00 03:00

20

40

60

0

50

0

0

10

20

% P

olar

izat

ion

Lu

min

osit

y 10

30 c

m-2 s

-1P

roto

ns

x 10

11 Start of collisions

Start of acceleration ramp

60 % polarization

100

150

30

Collimation complete

Polarized Proton Acceleration to 250 GeV

250 GeVinjection

45 % polarization on first acceleration to 250 GeV!

Ramp Measurement to 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

Loss at strong intrinsic resonance (136 GeV)

Spin Flipper (plan)

Use spin resonance driven by AC dipole(s) to induce spin flip Single AC dipole (oscillation) drives two resonances that interfere

at sp = 0.5, only partial spin flip Two AC dipoles with vertical spin precession in between creates rotating

drive fieldAC dipole AC dipole

-45 -4590

One AC dipole Two AC dipoles

Spin Tune Measurement (plan)

Use AC dipoles to excite coherent spin precession (drive tune spin tune, d >> sp)

Measure radial polarization component as Fourier component of turn-by-turn asymmetry measurement.

Ratio of vertical over radial component (or “cone opening”) measures difference of drive tune and spin tune

sp - d = d Pv/PrVERTICALVERTICAL

RADIALRADIAL

Beam

Summary

65 -70 % polarization reached in AGS at 24 GeV

60 - 65 % polarization reached in RHIC at 100 GeV

45 % polarization reached in RHIC at 250 GeV