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Polarization of CEPC
M. Bai
Collider Accelerator Department
Brookhaven National Laboratory, Upton, NY 11973
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Outline
• Challenges of high energy polarized electrons
– Depolarizing mechanism
– Achieved polarization in circular accelerators
• VEPP, ELSA, LEP and HERA
• A preliminary look at CEPC polarization
• What can be done to reach high energy
polarized electrons?
– Think out of the box
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Spin motion in a circular accelerator
Thomas BMT Equation: (1927, 1959)
Spin vector in
particle’s rest frame
L. H. Thomas, Phil. Mag. 3, 1 (1927); V.
Bargmann, L. Michel, V. L. Telegdi, Phys,
Rev. Lett. 2, 435 (1959)
G
Magnetic field along
the direction of the
particle’s velocity
 :
Magnetic field
perpendicular to the
particle’s velocity
is the anomoulous g- factor, for
proton,
G=1.7928474
Lorenz factor
Spin tune Qs: number of precessions in one orbital revolution:
Dec. 16-17, 2013
Q = Gg
s Energy Circular Colliders, IHEP,
International workshop on Future High
Beijing
Depolarizing mechanism in a synchrotron

horizontal field kicks the spin vector away from its
vertical direction, and can lead to polarization loss




dipole errors, misaligned qadrupoles, imperfect orbits
betatron oscillations
other multipole magnetic fields
other sources
y
y
beam
x
beam
z

Bx
x
Initial
y

Bx
1st
beam
z
full betatron
Oscillation period
x

Bx
z
2nd full betatron
Oscillation period
Depolarizing Resonance

Intrinsic resonance:
•
•
Focusing field due to the intrinsic
betatron oscillation
Location:

Imperfection resonance:
• Source: dipole errors,
quadrupole misalignments
• Resonance location:
G = kP±Qy
G = k, k is an integer
P: super periodicity of the
accelerator,
Qy: vertical betatron tune
• Resonance strength:
• Proportional to the size of the
betatron oscillation
• Resonance strength:
• Proportional to the size of the
vertical closed orbit distortion
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Depolarizing Resonances@ SPERA
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Sokolov-Ternov Radiative Polarization Limit
• Synchrotron radiation has a weak dependence on the spin
direction of the particle
cCg E 4 é
55
wc ù
Pqm =
1- (
+ n̂ × b̂)
ú
2 ê
2pr ë
E û
8 3
• Spin flip transition rate
cCg E 2 é 2
8
wc ù
2
W = wc
n̂ × b̂
ê1- (n̂ × ŝ) +
ú
2p Rr ë 9
E û
5 3
• Beam polarization for the case of a uniform magnetic field
W+ -W8
-t/t p
P=
Þ P = P¥ (1- e ) =
» 0.924
W+ +W5 3
with
Dec. 16-17, 2013
5 3
g5
P¥ =
» 0.924; t =
c c re 3
8
r
5 3
8
-1
p
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
In a planar circular accelerator
• The magnetic field is distributed piece-wisely instead of
uniformly
P¥ =
8
r -3 n̂ × b̂
5 3 r -3 [1- 2 (b̂ × n̂)2 ]
9
2ù
5 3
2
-1
5
-3 é
tp =
c c reg r ê1- b × n ú
ë 9
û
8
(
)
• Clearly, a single snake or other configurations which lays the
stable spin direction in the horizontal plane, can cancel the
S-T radiative polarization build-up
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Now, let’s add in spin diffusion
• An emission of a photon yields a sudden change of the
particle’s energy, as well as its spin phase
P¥ =
r -3 b̂ ×[ n̂ - g
8
5 3
2
2
11 ¶n̂
2
r [1- (b̂ × n̂) + g
]
9
18 ¶g
-3
5 3
t =
c c reg 5
8
-1
p
Dec. 16-17, 2013
¶n̂
]
¶g
2ù
é 2
2
11 ¶n̂ ú
-3
ê
r 1- b × n + g
18 ¶g úû
êë 9
(
)
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Synchrotron Sideband
• Spin tune is modulated due to synchrotron oscillation
g = g 0 + Dg cosy with y = n sq + f0
n = Gg = n 0 +GDg cosy with n 0 = Gg 0
• Hence, the spin-orbit coupling factor averaged over all
synchrotron phase becomes
2
G
2
J m2 ( Dn / n s )
¶n̂
=g
= n 02e K2 å
2
2
¶g
é
2
ù
m
êë (n 0 - K ) - n s úû
(
C. Biscari, J. Buon, B. Montague, CERN/LEP-TH/83-8
)
Enhancement factor due to synchrotron motion
• For a spin tune spread distribution of
f ( Dn ) =
2Dn
s Dn
e
2
-Dn / s 2Dn
• Spin-orbit coupling factor becomes
G
2
= n 02e K2 e
-s D2n /2n s2
åé
êë((n
m
fc = (n 0 - K ) e
4
-s D2n /2n s2
I m2 (s D2n / 2n s2 )
2ù
K
m
n
n
)
0
s)
sú
û
åé
êë((n
m
2
2
=
n 02e K2
(n 0 - K )
I m2 (s D2n / 2n s2 )
0
- K ) - mn s )
C. Biscari, J. Buon, B. Montague, CERN/LEP-TH/83-8
2
- n ùú
û
2
s
2
4
fc
LEP Enhancement Factor
• Synchrotron tune ~0.07, momentum spread ~ 0.0007
• At beam energy 51.5GeV, ~50% vertical polarization
was achieved with careful spin matching to minimize
the resonance strength
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
100
50
90
45
80
40
70
35
60
30
polarization
50
25
beam energy
40
20
30
15
20
10
10
5
0
0
www.desy.de/~mpybar/psdump/amspap2.ps.gz
Beam Energy [GeV]
Polarization [%]
Achieved Electron Polarization
Current CEPC Design SPECs
Qin, et al, Preliminary Accelerator Design of a Circular Higgs Factory in China, TUPBA03, NAPAC13
Preliminary Estimate
• S-T polarization build-up time for beam energy at 120 GeV
t p » 20 min
~120.72GeV
• Enhancement factor due to synchrotron motion
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Preliminary Estimate of Equilibrium Polarization
Beam Energy ~ 120.68 GeV
Equilibrium polarization
Momentum spread 0.0007
Momentum spread 0.0013
Synchrotron tune
For both cases, a resonance strength of 0.001 is assumed
Preliminary Estimate of Equilibrium Polarization
Beam Energy ~ 90.245 GeV
Equilibrium polarization
Momentum spread 0.0007
Momentum spread 0.001
Synchrotron tune
For both cases, a resonance strength of 0.001 is assumed
For Polarized CEPC/TLEP
• Careful lattice design from day one to make sure a good spin
matching to minimize the depolarizing resonance strength
• Careful choices of beam parameters including longitudinal to
avoid depolarization
– betatron tunes and synchrotron tune
– small momentum spread
• Excellent spin matching and very precise beam control, i.e.
closed orbit, betatron tune, are required to minimize the
depolarizing resonance strength
– In general, the depolarizing resonance gets stronger at
higher energies. This means the tolerance to closed orbit
distortion as well as other beam parameters is much tighter
than LEP
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Preliminary Estimate of Equilibrium Polarization
• However, one may still have to make compromise between
luminosity and polarization due to the beam-beam induced
tune spread, which pushes particles to the spin resonances.
Such an effect has been seen at LEP, HERA.
• In addition, one still has to build spin rotator
• In summary, it seems very daunting to have polarized beams at
~50% or higher polarization at the energy of CEPC or TLEP
Criterion for Keeping Polarization
¶n̂
r b̂ ×[ n̂ - g ]
¶g
-3
P¥ =
8
5 3
2
9
r -3 [1- (b̂ × n̂)2 +
5 3
t =
c c reg 5
8
-1
p
2
11 ¶n̂
g
]
18 ¶g
2ù
é 2
2
11 ¶n̂ ú
-3
ê
r 1- b × n + g
18 ¶g úû
êë 9
(
)
• Keep the stable spin direction along the main B field direction
– To allow ST polarization built-up
• Reduce spin chromaticity
– Improve equilibrium polarization
– Minimize synchrotron side band
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Can Siberian Snake Help?
• In a storage ring like RHIC, a pair of Siberian snakes located
diametrically to yield a spin tune of ½, energy independent.
This is good 
• However, the same advantage of completely cancels out
Sokolov-Ternov effect, which is bad 
• So, one could conceive the scenario of accelerate prepolarized electrons to the top energy. But,
– What about positron? One way to solve this, is to have a
polarizer ring for both e+ and e- beam at lower energy to
establish polarization
– Even with dual snake, it may still not efficient enough to
suppress the spin-orbit coupling factor[J. Buon, LAL-RT-84-05].
But, what about three pairs? Detailed analysis including
simulation needs to be done.
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
With Siberian Snakes
• Low energy polarizer ring
– Reasonable polarization time
– > 50% polarization
– Both injector and main ring are equipped
with snakes. Main ring needs spin rotators
snake
• Polarization wigglers for the injector
– No need of low energy polarizer ring
– Both injector and main ring are equipped with snakes, plus the
spin rotator for main ring
– However, challenge is whether one can achieve >50% polarization
within reasonable time
Dec. 16-17, 2013
International workshop on Future High Energy Circular Colliders, IHEP,
Beijing
Conclusion
• It is very challenge to establish polarized electron-positron
beam with > 50% polarization at CEPC/TLEP
• Several critical R&D items
– Lattice design with spin matching
– Local spin rotator for high energy electron/positron beam
– Explore the feasibility of applying dual snake or odd pairs
of snake to overcome the strong depolarizing mechanism
due to quantum excitation
• Wigglers or other beam manipulations to generate S-T
polarization
– In addition to existing algorithms for spin-coupling factor
calculations, SLIM, SODOM, etc, a robust numerical
simulation code for high energy polarized electronpositron collider