Æ Plans for Future

Snake Charming at RHIC

DZ Introduction

DZ FY00 Commissioning run with 1 snake

DZ Plans for the future

Waldo MacKay

William W MacKayTalk given by Waldo MacKay at the AGS/RHIC User's Group Meetingin Williamsburg, VA on 5 Oct., 2000 at the DNP2000 meeting.

Particle motion governed by Lorentz force:

d~v

dt'

q

m

h~E + ~v � ~B

i

Spin precession is governed by Thomas BMT equation:

d~S�

dt=

q

m~S��

"(1 +G) ~B? + (1 +G) ~Bk

+

�G +

+ 1

�~E � ~�

c

#;

where S� is the spin vector in the rest frame and the �elds arein the lab system, and the anomalous g-factor is

G =g � 2

2; (1.7928 for protons):

De�nition: Spin tune, �sp, is the number of excess times thespin precesses in one revolution.

For ~E = ~Ek and ~B = ~Bup, �sp = G.

1

BRAHMS & PP2PP (p)

STAR (p)

PHENIX (p)

AGS

LINACBOOSTER

Polarized proton collisions in RHIC

Pol. Proton Source500 µA, 300 µs

GeVs

cmsL

50050

onPolarizati%70

102 2132max

K=

×= −−

Spin Rotators

Partial Siberian Snake

Siberian Snakes

200 MeV Polarimeter AGS Internal PolarimeterRf Dipoles

RHIC pC Polarimeters

Absolute Polarimeter (H jet)

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

First Siberian Snake in RHIC Tunnel

Siberian Snake: 4 superconducting helical dipoles, 4Tesla,2 m long with full 360° twist

ð Acceleration of spin polarized protons beams in RHICð Beam studies in September 2000

Funded by RIKEN, JapanDesigned and constructed at BNL

The Helical Dipole Field

Laplace’s Equation (cylindrical coordinates) for the scalar potential:

∂2Φ

∂r2+

1

r

∂Φ

∂r+

1

r2∂2Φ

∂φ2+∂2Φ

∂z2= 0.

Separation of variables, Φ = R(r)Q(φ)Z(z), gives

d2R

dr2+

1

r

dR

dr−(k2 +

ν2

r2

)R = 0,

d2Q

dφ2+ ν2Q = 0,

d2Z

dz2+ k2Z = 0.

Note:

• Repeat period of helical field: λ = 2π/|k|• ν = 1 since central dipole field repeats after φ = 2π• Assume B0 points vertically upward at z = 0• ~B = −∇Φ gives...

Br = 2B0[I0(kr)−I1(kr)

kr](cos kz sinφ− sin kz cosφ)

Bφ = 2B0I1(kr)

kr(cos kz cosφ+ sin kz sinφ)

Bz = −2B0I1(kr)(cos kz cosφ+ sin kz sinφ)

Look at Bx = Br cosφ − Bφ sinφ, By = Br sinφ + Bφ cosφ andexpand these fields near the longitudinal axis (x, y small); then,

Bx ≈ −B0{

[1 +k2

8(3x2 + y2)] sin kz − k

2

4xy cos kz

}

By ≈ B0{

[1 +k2

8(x2 + 3y2)] cos kz − k

2

4xy sin kz

}

Bz ≈ −B0k{

1 +k2

8(x2 + y2)

}[x cos kz + y sin kz]

0 2 4 6 8 10 12z [m]

-4

-2

0

2

4

B [t

esla

]

BxByBz

AUL6102206

SNAKE OH Fmap γ=25

0 2 4 6 8 10 12z [mm]

-50

-25

0

25

50

x,y

[mm

]

XY

AUL6102204

SNAKE OH Fmap γ=25

0 2 4 6 8 10 12z [m]

-1.0

-0.5

0.0

0.5

1.0

spin

com

pone

nts

AUL6102210

SNAKEOH Fmap

Sx

Sy

Sy

Sz

Sy

γ=25

’orbit.plt’ u 1:2:3

02

46

810

12-4

-2

0

2

4

-10

-5

0

5

10

Rotation Angles for a Helical Snake-5

-4

-3

-2

-1

00 1 2 3 4 5

B1 [T]

B2 [T]

10

20

30

40 50 60 70 80 90100110120130140

150

160

170

190

-10

-20

-30

-40

-50

-60

-70

0 10 20 30 40 50 60 70 80

φ µ

William W MacKayContours for setting the snake rotation. Each snake consists of four identical helical dipoles. The inner pair are wired in series with oppositefields to one power supply and the outer pair are wired in series with opposite fields to a second power supply. The blue contours show rotations of an angle MU about an axis in the horizontal plane. The angle PHI (red contours) specifies the direction of the rotation axis relative to the longitudinal direction.

Proton-Carbon CNI Polarimeter (AGS E950)

l 2-3% energy independent analyzingpower for small-angle elasticscattering in the Coulomb-NuclearInterference (CNI) region

l Slow recoil Carbon detected inbetween bunch crossings

l Fiber target allows for polarizationprofile measurement

Ultra-thin Carbon ribbonapprox. 100 atomic layers thick

Polarized Proton Beam

Forward proton

Recoil Carbon, 100 … 800 keV

Silicon detector

Carbon

Target Out Target In

ADC distribution

TD

C

di

st

ri

bu

ti

on

Æ FY2000 Commissioning Plan

June-July 2000: (independent of RHIC operation)

DZ New pol. source (OPPIS) commissioned and beam transp. through linac:X

65% polarization measured at 200 MeV polarimeter,

200 � and 300 �s beam pulse (4� 1011 polarized protons)

August 2000: (during RHIC Au stores)

DZ Accelerate single bunch (1011 pol. p/bunch) in Booster and AGS to

G = 46:5 ( = 25:94)X

DZ Commission coupled spin resonance crossing using horizontal rf dipole.

August 2000: (during RHIC Au stores)

DZ Inject 6 bunches (*+*+*+) into RHIC blue ring with snake o�.X

DZ Commission pC polarimeter and measure vertical polarization.X

DZ Turn on snake and measure radial polarization.X

DZ Accelerate and measure polarization.X

Polarized proton status and plans

FY2000 run:

l Single Siberian snake and pC polarimeter installed in blue ring

l New polarized proton source: ~ 1012 pol. protons/pulse

l Goal: Accelerate polarized beam in blue ring

FY2001 run:

l All four Snakes and pC polarimeters installed in blue and yellow ring

l Goal: 100 GeV×100 GeV collision with long. pol. at interaction regions Accelerate polarized beam to 250 GeV

FY2002 run:

l All eight spin rotators installed

l Goal: 250 GeV×250 GeV collision with long. pol. at STAR and PHENIXFY2003 run:

l Polarized hydrogen jet target for absolute polarimetry installed

Single Snake in RHIC (E ≤≤ 100 GeV)

At E = 100.53 GeV: Gγ = 192 = 6 × 32→ all IP’s have same polarizationFor snake axis at -52º → longitudinal polarization

STAR

PHENIX

BRAHMSpp2pp

snake

polarimeter

-52º

-40º

For ∆p/p = ±0.001max. deviation from long. polarization:32 ×∆p/p ×360º= ±12º [0.98] (STAR)64 ×∆p/p ×360º= ±24º [0.91] (PHENIX)

Polarized Hydrogen Jet Target

l pC polarimeter is used as fast relative polarization monitorand was calibrated in AGS at 22 GeV to about 15 %.

l Polarized hydrogen jet target allows for absolute beampolarization measurement:

l Jet target thickness of 3×1011 cm-2 achievable(HERMES, PINTEX, NIKHEF)

l Jet polarization measurable to better than 3% using Stern-Gerlach method

l Collaboration started with Wisconsin, IUCF, andAmsterdam

↑↓↓↑↓↓↑↑

↑↓↓↑↓↓↑↑+−−−+−=

TBTBTBTB

TBTBTBTB

NNNN

NNNNPP TargetBeam

Pol. H jet target at Bates from NIKHEF

8

Outside Tunnel Wall

BL-RotatorYR-Rotator

BR-Rotator YL-Rotatorinside of ring

DX DX

STAR

warm straight section warm straight section

Figure 2: Schematic layout of Rotators in STAR region

Outside Tunnel Wall

YL-RotatorBR-Rotator

YR-Rotator BL-Rotatorinside of ring

DX DX

PHENIX

warm straight section warm straight section

Figure 3: Schematic layout of Rotators in PHENIX region

Plans for Future Snake Charming at RHICEqs of Motion and spin precessionAGS/RHIC layout for polarized protons1st Snake in RHICHelical field equationsSnake: fields, orbit, and spin motionTrajectory through snakeContours for snake settingsPhoto of pC CNI polarimeter in Blue ringpC Coulomb Nuclear Interference PolarimeterEarly polarization measurements in RHIC for various conditionsEffect of snake on polarizationFY2000 Commissioning PlanPolarized proton status and plans (future)Longitudinal polarization with a single snakePolarized Hydrogen Jet Target for future polarimeterRotator Layout for STAR and PHENIX