Optical Stochastic Cooling
Fuhua Wang
MIT-Bates Linear Accelerator Center
5/20/2008
4Th Electron-Ion collider Workshop
Hampton University
1
Outline
• Introduction: history, concept
• Experiment with electron beams:
proposal & research at MIT & MIT/Bates
• OSC for RHIC, Tevatron …
• Summary
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History
A. Zholents,…
1968 - Stochastic Cooling proposed by S. van der Meer. It was proved to be a remarkably
successful over next several decades. (For a detailed historic account see CERN report 8703, 1987, by D. Möhl.)
1993 - Optical Stochastic Cooling (OSC) proposed by Mikhalichenko and Zolotorev
1994 - Transient time method of OSC proposed by Zolotorev and Zholents
1998 - Proposal for proof-of-principle experiment in the Duke Electron Storage Ring
(potential application for Tevatron was in mind)
2000 - OSC of muons by Wan, Zholents, Zolotorev
2001 - Proposal for proof-of-principle experiment in the storage ring of the Indiana
University
2001 - Quantum theory of OSC, by Charman and also by Heifets, Zolotorev
2004 - Babzien, Ben-Zvi, Pavlishin, Pogorelsky, Yakimenko, Zholents, Zolotorev, Optical
Stochastic Cooling for RHIC Using Optical Parametric Amplification
2007 - Proposals for Optical amplifier development and OSC experiment at MIT-Bates.
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Stochastic Cooling
S. van der Meer, 1968
D. Möhl, “Stochastic Cooling for Beginners”, CERN
L ~1/bandwidth=1/B
kicker
“bad”
mixing
g
amplifier
“good”
mixing
Lb
p
L
number of particles in the sample
Ns  N
Lb
pick-up
i
n 1
x
g
x 
Ns
i
n
decrement 
Ns
k
x
 n
k
  x2 
2
xrms
2g  g 2

Ns
1
Max. decrement 
at g  1
Ns
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Towards Optical Stochastic Cooling
microwave “slicing”
Ns  N
sample length
~10 cm

b
optical “slicing”
sample length
~10 mm
OSC also allows transverse slicing

x   d 

resulting in further decrease of Ns: N s  N
Diffraction limited size
of the radiation source
  d

 b  x



2
OSC explores a superior bandwidth of optical amplifiers, BOSC~ 1014 Hz
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Transit-time method of OSC
M. Zolotorev & A. Zholents, 1994
N
S
N
S
Particle emits light pulse
of length N
N
Particle delayed
Light pulse delayed and amplified
Particle receives longitudinal
kick from amplified light pulse
• Particles in the second undulator see light emitted by themselves and neighboring
particles within “coherent slice” Nu
• Bypass delay ℓ for particles on central orbit set such that it is on the zero crossing
of the electric field in the 2nd undulator
• “Off axis” particles receive a momentum kick
Notice: for =2mm, /2 phase shift corresponding 1.7 fs : system stability ?
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OSC Formalism
Phase between electron and light at U2:
  R51 x  R52  hd ,
 =k ,
h  R51  R52 '  R56
Light from U1 is amplified and provides momentum kick at U2:
eE0 N u u K
d 2  d1  G sin 
Gg
g : optical amplication factor
2c p
Sum of momentum kicks by amplified light from all Ns coherently radiating electrons
produces a change of d2 for an individual electron:
d 22  d12  2Gd1 sin   G 2 N s / 2
Average over all Ns electrons assumed to be normally distributed (Gaussian) in
x, , d with rms widths <x>, <>, <d> to find:
1
Ns
Ns
 (d
n 1
2
2k
 d12k )  d 2  2   d1  2    d  2  2Gkh  d  2 e
 2
2
 G2 Ns / 2
where  2 =k 2  R512  x  2  R52 2    2  h 2  d  2 
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OSC Formalism, con’t
Cooling rates per orbit:
Find:
1    x 2    2 
T   

2
2 
2  x 
  
  d 2
L  
 d 2
T  Gk  h  R56  e
 L  2Gkhe
 2 / 2
 2 / 2
 G 2 N s 2 /  2  d  2 
 G 2 N s /  2  d 2 
where  2   2 /  x  2  2 /    2   d  2 / 2
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Experiment with electron beams
Significance:
•
•
•
•
OSC in low energy e-beam ring is ideal for demonstration & test experiment in highenergy hadron beam collider rings.
OSC cooling can be observed in seconds: short experiment time scale.
Optical amplifier is available.
Low cost beam bypass, undulators and ring interface, low experiment cost.
OSC experiment at MIT-Bates SHR ring : 2007(BNL CAD review)Motivation:
• Proof-of-principle & OSC system study for high-energy colliders.
• Concept developments: Cooling mechanism, OSC and ring lattice
interface.
• Technical system: optical amplifier, diagnostics & control.
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Collaboration List
W. Barletta, K. Dow, W. Franklin, J. Hays-Wehle, E. Ihloff, J. van der Laan, J. Kelsey, R.
Milner, R. Redwine, S. Steadman, C. Tschalär, E. Tsentalovich, D. Wang and F. Wang,
MIT Laboratory for Nuclear Science, Cambridge, MA 02139 & MIT-Bates Accelerator Center,
Middleton, MA 01949
F. Kärtner, J. Moses, O.D. Mücke and A. Siddiqui
MIT Research Laboratory of Electronics, Cambridge, MA 02139
T.Y. Fan, Lincoln Laboratory, Lexington, MA 02420
M. Babzien, M. Blaskiewicz, M. Brennan, W. Fischer, V. Litvinenko, T. Roser and V.
Yakimenko, Brookhaven National Laboratory, Upton, NY 11973
S.Y. Lee
Indiana University Cyclotron Facility, Bloomington, IN 47405
W. Wan, A. Zholents and M. Zolotorev
Lawrence Berkeley National Laboratory, Berkeley, CA 94720
V. Lebedev,V. Shiltsev
Fermilab, Batavia, IL 60510
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Small-angle bypass: Concept
Based on Optical parametric amplifier: total signal delay ~20ps only! Then we can
choose small-angle chicane with path length increase of 20 ps ~ 6 mm.
Q
B1

0
B2
1
Optical
Amplifier
Q1
Q2
B3
B4
2m
4 parallel-edge benders and one (split) weak field lens. Choose =65 mrad, L=6mm.
First order optics:
R56  2  2 (1  / 2 f q )
R51  2 R52 / L,
R51  2m / f q  2  / f q ,
f q ~ 230m
L   2
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Small-angle bypass: Tolerances
C. Tschalär, J. van der Laan
Tolerances to conserve coherence are much relaxed for small-angle bypass.
Absolute setting demands:
R51, R52, R56 setting within ~±5%
• magnet current setting
• field lens current setting
• magnet longitudinal positioning
• field lens transverse positioning
±2 %
±5 %
± 10 mm
± 100 mm
Stability (~1 hour) demands:
Variation for central orbit length in chicane ≤ 0.1 mm = 20°phase
• magnet current
10-5
• lens current
3 * 10-3
• magnet longitudinal position
50 mm
• lens transverse position
250 mm
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Bypass optics and ring lattice requirements
C. Tschalär
2
2


A

D
A

D




2 2
2
2
  k 

   2 A  R56  d 
B

E
B

E


A   R51   ' R52  / 2;
D   R51   ' R52  / 2;
B   2 /    '2   / 2;
E   2 /    '2   / 2;
Optimize D and E for maximal cooling rates :
2
R52  2 '

R51

2
 2 A2
2 2
2 R56
  k 
   2 A  R56  d   k

2B
 B

2
2
Optimal  2  1
Choose bypass (Rij) and ring(Twiss, dispersion) parameters
to have a proper range of <2>(,<d2>,..) for cooling.
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Bates Experiment Parameters
SHR
Natural
Beam energy (MeV) , RF: f(GHz)/ V (kV)
300, 2.856/14
Electrons/bunch, bunch number, average current
1108 , 12, 0.3mA
Chicane: L(m), bending angle (mrad)/ radius(m)
5.55, 65 / 3.85
Inverse chicane matrix elements: R51, R52, R56
8.610-4, 2.52mm, -12mm
Undulator: L, period, 
2m, 20cm, 2mm
Lattice parameters at second undulator
=3m, =6m , =2
SR damping time x (sec.)
4.83
Beam emittance, x (nm), 10% coupling
47
96
Energy spread, rms bunch length
8.5e-5, 5.1 mm
1.67e-4, 9.8mm
Growth (damping) rates
at equilibrium state:
5/20/2008
IBS effect


g IBS  x  g x , syn  x 0  1  f 0 x OSC  0
 x

 d 02
 f
g IBS d  gl , syn  2  1  0 d OSC  0
2
d

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SHR Lattice for OSC Experiment
OSC Insertion
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SHR OSC Simulation: x and <2>
<2> decreases with x.
Optimal cooling achieved by adjusting G.
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Particle Distribution with OSC: Gaussian
C. Tschalär
OSC tracking: 104 particles, 106 turns. Bates SHR, Nb=108.
Initial  2  1, decreasing
Initial  2  2 , decreasing
Distribution remained Gaussian.
Tails developed, Gaussian centeral part.
r  x 2  ( ) 2 : radius in normalized x- phase space.
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Particle Distribution with OSC: “BOX”
OSC tracking: 104 particles, 106 turns. Bates SHR, Nb=108.
Initial  2  1, decreasing
Distribution converted to Gaussian.
Initial  2  2 , decreasing
Tails developed, Gaussian centeral part.
Cooling slows down as  2 becomes smaller.
Implications for hadron beams ?
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OSC Tuning Diagnostics
J. Hays-Wehle, W. Franklin
•Interference signal maximal when light amplitudes same (low gain alignment)
•E2 is maximal for f=0 (f=/2 for OSC) use in feedback system
•Perform phase feedback in high gain operation ? (work on analysis and bench test, J Hays-Wehle)
•Correlate with beam size measurements (sync. Light monitors, streak camera)
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Optical amplifier requirements for OSC:
Bates & Tevatron F. Kärtner, A. Siddiqui
Tevatron: 1 pJ
Bates: 0.2 pJ
bunch length: 20 ps, 1 ns
repetition rate: 20 MHz, ~2 MHz
10 µJ, or 20 W
2nJ, or 40mW
Dispersion free
40-70 dB
Amplification
• High broadband amplification: G~104 (107), 10% bandwidth (undulator)
• Dispersion free: group delay variation less than 0.1 optical cycles
• Short overall delay to enable short chicane bypass to maintain
interferometric stability and reduce cost
 Broadband Optical Parametric Amplification (OPA) with low conversion
Ultra-broadband optical amplifiers suitable for OSC at Bates can be built
using commercial picosecond lasers, PPLN based OPA at 2 microns
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Amplifier layout for Bates OSC
F. Kärtner, A. Siddiqui
50 ps, 1030 nm Laser
20 MHz, 20 W, 1 mJ
Undulator
Radiation
Beam radius:
w = 0.5 mm
0.2 pJ
4 µW
f = 12 cm
f = 380 cm
270cm
2 nJ
40 mW
BaF2 wedges
1mm
2 mm
PPLN
n=2
f = 380 cm
24cm
103cm
103cm
Lenses and wedges, 1mm, n=1.5
Total optical delay is only 5.5 mm ~ 20 ps
270cm
PPLN: Periodically Poled Lithium Niobate
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OSC for RHIC
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Integrated luminosity gain (slow down emittance growth) estimates for proton
beams: 60% to 100%. MIT/Bates proposal review 2/12/2007 W. Fischer
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OSC for Tevatron: Layout
OSC location
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Numerical Example for Tevatron OSC
C. Tschalär
Tevatron: protons
  1045; T  21m s; nb  36; N b  2.4 1011
d
0
 1.4 10-4 ;   4.3 10 -9 m
Undulators: 10 periods of 2.7m = 27 m long
B=8 Tesla; K=1.1; =0.38; =2m; k=•106/m
Amplifier:
P  20W  AL  4.8 1017 J ;  G  0.83 1012 ,
OSC Chicane: choose
G P
  1;  2 /    2 
  2 /   0.22m; A  0.93mm; R56  3.7mm
 for   18m;   2m;    .11:
Cooling time : 
 T /  T d
R51  4.7 104 ; R52  8.4mm
e 1  1/ 2 2 / G  2 hours
Current luminosity lifetime ~ 10 hours
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Small-Angle Magnetic Bypass Chicane
(conceptual design)
Original Long
Straight
32.5 mrad
72m
OSC
Insertion
19.7 mrad
Optical line
89.4m
Dipole 4.4T, 25.6m
Bending angle and drift space set to have:
Dipole 8.0T
Path delay : L=10mm=30 ps
Undulator 8T, 27m
x=55.7cm
Dipole 8.2 T, 8m
Quadrupole 2m , g 400T/m, aperture
2cm.
5/20/2008
Eased magnet tolerances
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High-Power Optical Amplifier for Tevatron:
Development Plan
J. Gopinath et al., MIT-LL, A. Siddiqui et al.,MIT-RLE
OSC at the Tevatron needs >20 W output power and linear gain => 1 kW
pump power with 2% conversion. OPA needs “perfect” beam (M2<1.2)
•High-Power pump Laser:
Cryogenically cooled Yb:YAG lasers (Demo: 500-W, 2007)
T. Y. Fan, MIT Lincoln Laboratory
MIT-LL ATILL Program (5kW laser)
•High-power OPA design and demonstration:
• Trade study to evaluate NLO crystal candidates for average-power
performance and designs for high-power OPA
• Measure key engineering parameters needed for high-power OPA
(thermal conductivity, optical absorption, dn/dT)
• Demonstration of 20-W OPA with phase control
Successful OSC at the Tevatron needs forward looking
development now if it needs to be available in 2 years.
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Summary
• OSC concept, based mostly on current technology, is a viable
solution to high-energy hadron beam cooling.
• Important development tasks include: high average output
power optical amplifier (including pump laser), OSC interface
with collider rings and cooling diagnostics & control.
• Experiment with electron beam can advance OSC concepts and
technical systems in a short time period and with minimal
funding support. It is an essential step prior to a full-scale
implementation of OSC systems in high-energy hadron beam
colliders.
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