5/20/20084 Th Electron-Ion collider Workshop Hampton University 1 Optical Stochastic Cooling Fuhua Wang MIT-Bates Linear Accelerator Center

5/20/2008 4Th Electron-Ion collider WorkshopHampton University

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Optical Stochastic Cooling

Fuhua Wang

MIT-Bates Linear Accelerator Center


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Outline

• Introduction: history, concept

• Experiment with electron beams:

proposal & research at MIT & MIT/Bates

• OSC for RHIC, Tevatron …

• Summary


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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 87-03, 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.

History A. Zholents,…


4

2

21

4

Heating

Cooling

gg2

g

Heati

ng

/Coolin

g r

ate

1

2 2

2

2decrement

1Max. decrement at 1

sNi i kn n n

ks

srms

s

gx x x

N

x g g

Nx

gN

Stochastic Cooling S. van der Meer, 1968

p

g

pick-up

amplifier

“good” mixing

“bad” mixing

kickerD. Möhl, “Stochastic Cooling for Beginners”, CERN

number of particles in the sampleLb

L ~1/bandwidth=1/B

sb

LN N

L


5

bs NN

optical “slicing”

sample length ~10 m

microwave “slicing”

sample length ~10 cm

dx Diffraction limited size of the radiation source

2

x

dNN

bs

resulting in further decrease of Ns:

OSC also allows transverse slicing

Towards Optical Stochastic Cooling

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

• 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 kickNotice: for =2m, /2 phase shift corresponding 1.7 fs : system

stability ?

N S N S N

Particle emits light pulse of length N

Particle delayedLight pulse delayed and amplified

Particle receives longitudinal kick from amplified light pulse


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Sum of momentum kicks by amplified light from all Ns coherently radiating electrons produces a change of 2 for an individual electron:

2 2 22 1 12 sin / 2sG G N

2

2 2 2 2 2 2 222 1 2 1

1

2 2 2 2 2 2 2 251 52

1( ) 2 e / 2

where =k

sN

k k sns

Gkh G NN

R x R h

Average over all Ns electrons assumed to be normally distributed (Gaussian) in x, , with rms widths <x>, <>, <> to find:

Phase between electron and light at U2:'

51 52 51 52 56=k , ,R Rx R h h R R

Light from U1 is amplified and provides momentum kick at U2:

02 1 sin : optical amplication factor

2u ueE N K

G G g gc p

OSC Formalism


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OSC Formalism, con’t

Cooling rates per orbit: 2 2

2 2

2

2

1

2

T

L

x

x

2

2

/ 2 2 2 256

/ 2 2 2

2 2 2 2 2 2

/ 2

2 / 2

where / / / 2

T s

L s

Gk h R e G N

Gkhe G N

x

Find:


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Experiment with electron beams Significance: • OSC in low energy e-beam ring is ideal for demonstration & test experiment in high-

energy 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.

4 parallel-edge benders and one (split) weak field lens. Choose =65 mrad, L=6mm.

B1 B2 Q1 Q2 B3 B4OpticalAmplifier

0 1 2 m

Q

56

51 52 51

2

2

2 (1 / 2 )

2 / , 2 / 2 / , ~ 230

q

m q q q

R f

R R L R f f f m

L

First order optics:


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Tolerances to conserve coherence are much relaxed for small-angle bypass.

Absolute setting demands:R51, R52, R56 setting within ~±5%• magnet current setting ± 2 %• field lens current setting ± 5 %• magnet longitudinal positioning ± 10 mm• field lens transverse positioning ± 100 mm

Stability (~1 hour) demands:Variation for central orbit length in chicane ≤ 0.1 m = 20°phase • magnet current 10-5

• lens current 3 * 10-3

• magnet longitudinal position 50 m• lens transverse position 250 m

Small-angle bypass: TolerancesC. Tschalär, J. van der Laan


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Bypass optics and ring lattice requirements C. Tschalär

22 222 2 2

56

' '51 52 51 52

2 '2 2 '2

2222 2 56

5

2 '52

5

6

1

2 2

2

/ 2; / 2;

/ / 2; / / 2;

Optimize D and E for maximal cooling rates :

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2

Optimal

A D A Dk A R

B E B E

A R R D R R

B E

RAk A R k

R

R

B B

2 1

Choose bypass (Rij) and ring(Twiss, dispersion) parameters to have a proper range of <2>(,<2>,..) for cooling.


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Bates Experiment ParametersSHR Natural IBS effect

Beam energy (MeV) , RF: f(GHz)/ V (kV) 300, 2.856/14

Electrons/bunch, bunch number, average current 1108 , 12, 0.3mA

Chicane: L(m), bending angle (mrad)/ radius(m) 5.55, 65 / 3.85

Inverse chicane matrix elements: R51, R52, R56 8.610-4, 2.52mm, -12mm

Undulator: L, period, 2m, 20cm, 2m

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

0, 0

20 0

, 2

1 0

1 02

xIBS x x syn x OSC

x

OSCIBS l syn

g g f

fg g

Growth (damping) rates at equilibrium state:


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SHR Lattice for OSC ExperimentOSC 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.

2Initial 1, decreasing

Distribution remained Gaussian.

2Initial 2 , decreasing

Tails developed, Gaussian centeral part.

2 2( ) : radius in normalized - phase space.r x x


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Particle Distribution with OSC: “BOX”

2

2

Initial 1, decreasing

Distribution converted to Gaussian.

Cooling slows down as becomes smaller.

2Initial 2 , decreasing

Tails developed, Gauss

Implication

ian cent

s for ha

eral

dron

part

be s ?

.

am

OSC tracking: 104 particles, 106 turns. Bates SHR, Nb=108.


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OSC Tuning DiagnosticsJ. 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)


2020

Optical amplifier requirements for OSC: Bates & Tevatron F. Kärtner, A. Siddiqui

• 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 conversionUltra-broadband optical amplifiers suitable for OSC at Bates can be built using commercial picosecond lasers, PPLN based OPA at 2 microns

Dispersion free40-70 dB

Amplification

bunch length: 20 ps, 1 nsrepetition rate: 20 MHz, ~2 MHz

Bates: 0.2 pJ

10 µJ, or 20 W2nJ, or 40mWTevatron: 1 pJ


2121

Amplifier layout for Bates OSC

50 ps, 1030 nm Laser20 MHz, 20 W, 1 J Undulator

Radiation

270cm 24cm

Beam radius:

103cm 103cm 270cm

f = 12 cm

Lenses and wedges, 1mm, n=1.5Total optical delay is only 5.5 mm ~ 20 ps

f = 380 cm

BaF2 wedges1mm

0.2 pJ 4 µW

2 nJ 40 mW

2 mmPPLNn=2

f = 380 cm

w = 0.5 mm

F. Kärtner, A. Siddiqui

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 location

OSC for Tevatron: Layout


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Numerical Example for Tevatron OSCC. Tschalär

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-4 -9

0

1045; 21 ; 36; 2.4 10

1.4 10 ; 4.3 10

b bT s n N

m

17 1220 4.8 10 ; 0.83 10 ,LP W A J GG P

2 21; /

Tevatron: protons

Undulators: 10 periods of 2.7m = 27 m long B=8 Tesla; K=1.1; =0.38; =2; k=•106/m

Amplifier:

OSC Chicane: choose

256

451 52

/ 0.22 ; 0.93 ; 3.7

for 18 ; 2 ; .11: 4.7 10 ; 8.4

m A mm R mm

m m R R mm

Cooling time : 2/ 1 1/ 2 / 2 hoursT T e G

Current luminosity lifetime ~ 10 hours


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Small-Angle Magnetic Bypass Chicane (conceptual design)

Dipole 4.4T, 25.6m

Undulator 8T, 27m

Dipole 8.0T

Dipole 8.2 T, 8m

Quadrupole 2m , g 400T/m, aperture 2cm.

Bending angle and drift space set to have:

Path delay : L=10mm=30 ps

x=55.7cm

Eased magnet tolerances

Optical line

32.5 mrad

19.7 mrad

72m

Original Long Straight

OSC Insertion

89.4m


2727

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 LaboratoryMIT-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.

High-Power Optical Amplifier for Tevatron: Development Plan

J. Gopinath et al., MIT-LL, A. Siddiqui et al.,MIT-RLE


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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.

Documents

5/20/20084 Th Electron-Ion collider Workshop Hampton University 1 Optical Stochastic Cooling Fuhua Wang MIT-Bates Linear Accelerator Center