Transcript Beam Dynamics in High Energy Colliders

RHIC 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 charge
a quantum degree freedom associated with the
intrinsic magnetic moment.
q: electrical charge
q
μ s  (1 G) S
m
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
of particle
m: particle mass
spin vector and spin-orbit interaction
 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 orbit interaction
S
S

dS  
 μs  B
dt
N

dJ  
 μ B
dt

I
S
N
μ  IA
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?
P
u
u
Sum of spins of all quarks
1 1
S   ΔΣ
2 2
d
CERN EMC and
SLAC SMC:
 ~ 20%!
Current model:
Proton spin sum-rule
Spin contribution from
all the gluons?
1 1
S   ΔΣ  Δg  L q  L g
2 2
Orbital angular momentum of
quarks and gluons?
Quest to unveil the proton spin structure:
High energy proton proton collisions:
gluon gluon collision and gluon quark collision
gluon spin contribution
g
g
q
g
quark/antiquark spin contribution
RHIC: world’s first polarized proton collider
STAR
RHIC spin physics
 measure gluon spin contribution g
 measure quark and anti quark spin contribution
STAR
• Excellent calorimeter granularity
and muon detection
• electrons, muons, photons and
leading hadrons
• 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
1
n 2 (t )
L(t ) 
f0 N 2
4
 rms (t )
# of bunches

# of particles in one bunch
Transverse beam size
beam polarization
Statistical 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.
Basics of circular accelerator

bending dipole



quadrupole



Constant magnetic field
Keeps particles circulating around the ring
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: particle comes back to the same position after
one orbital revolution
Closed orbit in
a perfect machine:
center of quadrupoles
Courtesy of Lingyun Yang
Closed orbit in
a machine with
dipole errors
Betatron oscillation in a circular accelerator
Betatron tune: number
of oscillations in one
orbital revolution
y ( s )  2 y J cos( 2Q y ( s )   y )
Courtesy of Lingyun Yang
Beta function
Spin motion in circular accelerator:
Thomas BMT Equation




dS  
e
   S   [GB  (1  G) B// ]  S
dt
m
Spin vector in particle’s
rest frame


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,
Q s  Gγ
B
beam
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
y
y
beam
x
beam
z

Bx
Initial
y
x

Bx
1st
beam
z
full betatron
Oscillation period
x

Bx
z
2nd full betatron
Oscillation period
spin depolarizing resonance

Imperfection resonance


Source: dipole errors,
quadrupole misalignments
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
Intrinsic spin resonance
Qx=28.73, Qy=29.72, emit= 10
Spin depolarization resonance in RHIC
• For protons, imperfection spin resonances are spaced
by 523 MeV
• the higher energy, the stronger the depolarizing
resonance
Innovative polarized proton acceleration
techniques: Siberian snake
 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 180
o
Particle trajectory in a snake:
How to preserve polarization using
Siberian snake(s)
 Use one or a group of
snakes to make the spin
tune to be at ½
 Break the coherent buildup of the perturbations
on the spin vector
y
y
beam
beam

Bx
z

Bx
z
Accelerate polarized protons in RHIC
BRAHMS(p)
Absolute Polarimeter (H jet) RHIC pC Polarimeters
Siberian Snakes
Spin flipper
PHENIX (p)
STAR (p)
Spin Rotators
(longitudinal polarization)
Spin Rotators
Solenoid Partial Siberian Snake (longitudinal polarization)
LINAC
Pol. H Source
200 MeV Polarimeter
BOOSTER
AGS
Helical Partial
Siberian Snake
AGS Polarimeters
Strong AGS Snake
Polarized proton in the AGS
E20
5.9%
A20
10~15%
 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
imperfection
Setup time
Energy
GeV
Int
[1011]
Pol
[%]
Fast tune jump
Months
21.7
0.108
42
1994 5%solenoid Fast tune jump
partial snake
2 weeks
23.0
0.05
31
1988 Harmonic
correction
intrinsic
1998 5%solenoid AC dipole @ 3
2 weeks
23.0
0.05
37
partial snake strong intrinsic
resonance
2000
New polarized H- source with high current high polarization
2005 5%helical
AC dipole @ 4
2 weeks
23.8
1.0
50
partial snake strong intrinsic
resonance
2005 5% helical partial snake +10%
2 weeks
23.8
1.5
65
super-conducting helical
partial snake
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
1
Qs  φ1  φ 2
π
1
Qs 
2
Polarized proton acceleration in RHIC
snake depolarization resonance
Store working pt.
mQy  Qs  k
 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
5/8
Ramp working pt.
 Condition
5/6
3/4
7/8
y
6Qy  Qs  k
y
beam
beam
-x

Bx
z
z

Bx
y
y
y
beam
z

Bx
-x
z

Bx
-x
beam
-x
beam
-x

Bx
y
beam
z

Bx
-x
z
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

snake current setting
50
• set the vertical tune to
0.745
40
• measure the beam
polarization with
different snake current
polarization
30
• expect no depolarization
if the corresponding spin
tune is very close to 0.5
20
10
0
300
305
310
315
320
325
330
335
-10
snake Inner Current [Amp]
Blue FY04 flatten orbit
Yellow FY04 zero orbit
Blue FY05 flatten orbit
Yellow FY05 flatten orbit
Yellow FY05 Zero orbit
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
¾ snake resonance
7/10 snake resonance
flattop
*=2m
10 seconds after flattop
beta1
*=2m
Milestones of RHIC pp development
New polarized proton source
2000  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

New super-conducting solenoid for the polarized H- source
2005  205 GeV polarized protons with ~ 30% polarization
 AGS strong super-conducting helical snake

Dual snake configuration for the AGS and reached a polarization
2006 of 65% at the AGS extraction with 1.5x1011 protons per bunch
 250 GeV polarized protons in RHIC with a polarization of 45%

RHIC pp performance
100
[pb ]
70
50
10
40
30
1
20
10
0.1
2001
2002
Courtesy of W. Fischer
2003
2004
Calendar year
2005
2006
0
2007
Beam Polarization [%]
Integrated luminosity
-1
60
RHIC pp performance:
polarization transmission efficiency
Intrinsic spin resonance
Qx=28.73, Qy=29.72, emit= 10
RHIC intrinsic spin resonance strength
Design goal
Achieved
Physics Run
First look of beam polarization at 250 GeV
45% !
Polarization 250 GeV ramp measurement
Resonance around 138 GeV
0.012
Asymmetry
0.01
0.008
0.006
d
0.004
0.002
0
20
40
60
80
100
120
140
160
Beam Energy [GeV]
180
200
220
240
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 beambeam 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.