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					            Optical Stochastic Cooling

                          Fuhua Wang
               MIT-Bates Linear Accelerator Center




5/20/2008         4Th Electron-Ion collider Workshop   1
                         Hampton University
                     Outline

• Introduction: history, concept
• Experiment with electron beams:
  proposal & research at MIT & MIT/Bates
• OSC for RHIC, Tevatron …
• Summary



5/20/2008     4Th Electron-Ion collider Workshop   2
                     Hampton University
                                     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 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.

    5/20/2008                   4Th Electron-Ion collider Workshop                     3
                                       Hampton University
                      Stochastic Cooling                         S. van der Meer, 1968
                          D. Möhl, “Stochastic Cooling for Beginners”, CERN
              kicker                                                      L ~1/bandwidth=1/B

“bad”                                      “good”
mixing        g       amplifier            mixing
                            p                                                    Lb
                                                                L
                                                         Ns  N    number of particles in the sample
                                                                Lb
         pick-up
                            Ns
                   g
     xi
      n 1    x i
                  n
                   Ns
                            k
                               k
                              xn

                            x2      2g  g 2
     decrement              2
                                     
                            xrms         Ns
                      1
     Max. decrement     at g  1
                      Ns
  5/20/2008                          4Th Electron-Ion collider Workshop                         4
                                            Hampton University
             Towards Optical Stochastic Cooling
                                                                  optical “slicing”
microwave “slicing”                  Ns  N
                                                 b
                      sample length                 sample length
                      ~10 cm                        ~10 mm


OSC also allows transverse slicing
                                        
                              x  d                            Diffraction limited size
                                                                 of the radiation source
                                                                                 2
                                                                    d     
             resulting in further decrease of Ns: N s  N                   
                                                                   b  x
                                                                      
                                                                             
                                                                             

OSC explores a superior bandwidth of optical amplifiers, BOSC~ 1014 Hz


 5/20/2008                   4Th Electron-Ion collider Workshop                          5
                                    Hampton University
                         Transit-time method of OSC
     M. Zolotorev & A. Zholents, 1994


    N      S    N    S       N




                                              Particle delayed
Particle emits light pulse          Light pulse delayed and amplified        Particle receives longitudinal
of length N                                                                 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 ?
        5/20/2008                       4Th Electron-Ion collider Workshop                        6
                                               Hampton University
                                       OSC Formalism
Phase between electron and light at U2:
 =k ,     R51 x  R52  hd ,  h  R51  R52 '  R56
Light from U1 is amplified and provides momentum kick at U2:
                                  eE N  K
   d 2  d1  G sin       Gg 0 u u       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:
       Ns                                                                          2
  1
  Ns
        (d
       n 1
              2
              2k    d12k )  d 2  2   d1  2    d  2  2Gkh  d  2 e    2
                                                                                           G2 Ns / 2

  where  2 =k 2  R512  x  2  R52 2    2  h 2  d  2 

   5/20/2008                          4Th Electron-Ion collider Workshop                            7
                                             Hampton University
                           OSC Formalism, con’t

Cooling rates per orbit:            1    x 2    2 
                             T                    2 
                                    2  x   2
                                                    
                                      d 2
                             L  
                                      d 2
 Find:

           T  Gk  h  R56  e        2 / 2
                                                    G 2 N s 2 /  2  d  2 

            L  2Gkhe     2 / 2
                                        G 2 N s /  2  d 2 
           where  2   2 /  x  2  2 /    2   d  2 / 2



    5/20/2008                   4Th Electron-Ion collider Workshop                8
                                       Hampton University
                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.


    5/20/2008                 4Th Electron-Ion collider Workshop                   9
                                     Hampton University
                             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


   5/20/2008                    4Th Electron-Ion collider Workshop                   10
                                       Hampton University
                          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                  B2   Q1
                                                 Optical
                                                                         Q2   B3               B4
                                                 Amplifier

 0                   1                      2m


     4 parallel-edge benders and one (split) weak field lens. Choose =65 mrad, L=6mm.
                               R56  2  2 (1  / 2 f q )
     First order optics:
                               R51  2 R52 / L,       R51  2m / f q  2  / f q ,   f q ~ 230m
                               L   2

      5/20/2008                     4Th Electron-Ion collider Workshop                       11
                                           Hampton University
                   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                           ±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 mm = 20°phase
• magnet current                                         10-5
• lens current                                           3 * 10-3
• magnet longitudinal position                           50 mm
• lens transverse position                               250 mm


  5/20/2008                4Th Electron-Ion collider Workshop           12
                                  Hampton University
            Bypass optics and ring lattice requirements
                                           C. Tschalär
                                                                         2
                    A  D 2     A  D   2A  R 2 d 2 
                                          2

        2  k 2                                56    
                  
                     BE           BE                     
                                                            
       A   R51   ' R52  / 2;      D   R51   ' R52  / 2;
       B   2 /    '2   / 2;      E   2 /    '2   / 2;
                                                                        R52  2 '
       Optimize D and E for maximal cooling rates :                         
                                                                        R51   
               2 A2                  2 2
                                                  2
                                               2 R56
         k 
            2    2
                        2 A  R56  d   k       
               B                               2B
       Optimal  2  1

  Choose bypass (Rij) and ring(Twiss, dispersion) parameters
  to have a proper range of <2>(,<d2>,..) for cooling.
5/20/2008                       4Th Electron-Ion collider Workshop                   13
                                       Hampton University
                    Bates Experiment Parameters
SHR                                                            Natural                IBS effect
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

                                                                       
                                         g IBS  x  g x , syn  x 0  1  f 0 x OSC  0
   Growth (damping) rates                                       x      
   at equilibrium state:                                        d 02    f
                                         g IBS d  gl , syn  2  1  0 d OSC  0
                                                               d              2

5/20/2008                      4Th Electron-Ion collider Workshop                                  14
                                      Hampton University
            SHR Lattice for OSC Experiment
                              OSC Insertion




5/20/2008       4Th Electron-Ion collider Workshop   15
                       Hampton University
            SHR OSC Simulation: x and <2>




                                   <2> decreases with x.
                                   Optimal cooling achieved by adjusting G.


5/20/2008          4Th Electron-Ion collider Workshop                16
                          Hampton University
            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  x2  ( )2 : radius in normalized x- phase space.

5/20/2008                    4Th Electron-Ion collider Workshop                         17
                                    Hampton University
            Particle Distribution with OSC: “BOX”

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




Initial  2  1, decreasing                       Initial  2  2 , decreasing
Distribution converted to Gaussian.                Tails developed, Gaussian centeral part.
Cooling slows down as  2 becomes smaller.        Implications for hadron beams ?


5/20/2008                    4Th Electron-Ion collider Workshop                         18
                                    Hampton University
                           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)


  5/20/2008                      4Th Electron-Ion collider Workshop                        19
                                        Hampton University
               Optical amplifier requirements for OSC:
               Bates & Tevatron F. Kärtner, A. Siddiqui

                    bunch length: 20 ps, 1 ns                 10 µJ, or 20 W
Tevatron: 1 pJ      repetition rate: 20 MHz, ~2 MHz           2nJ, or 40mW
 Bates: 0.2 pJ             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

  5/20/2008              4Th Electron-Ion collider Workshop             20
                                Hampton 20University
                         Amplifier layout for Bates OSC
                                   F. Kärtner, A. Siddiqui
                              50 ps, 1030 nm Laser
                                                                                              2 nJ
                               20 MHz, 20 W, 1 mJ
Undulator                                                                                    40 mW
Radiation                                                          BaF2 wedges
Beam radius:
 w = 0.5 mm                              f = 12 cm                 1mm




0.2 pJ                                    2 mm
4 µW                                      PPLN
                 f = 380 cm                                             f = 380 cm
                                           n=2

     270cm             103cm          24cm          103cm                            270cm
                        Lenses and wedges, 1mm, n=1.5
                    Total optical delay is only 5.5 mm ~ 20 ps

         PPLN: Periodically Poled Lithium Niobate

     5/20/2008                     4Th Electron-Ion collider Workshop                         21
                                          Hampton 21University
            OSC for RHIC




5/20/2008   4Th Electron-Ion collider Workshop   22
                   Hampton University
Integrated luminosity gain (slow down emittance growth) estimates for proton
beams: 60% to 100%. MIT/Bates proposal review 2/12/2007 W. Fischer
 5/20/2008               4Th Electron-Ion collider Workshop             23
                                Hampton University
            OSC for Tevatron: Layout




                                        OSC location




5/20/2008         4Th Electron-Ion collider Workshop   24
                         Hampton University
            Numerical Example for Tevatron OSC
                                     C. Tschalär
  Tevatron: protons        1045; T  21m s; nb  36; Nb  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 ,         G P

    OSC Chicane: choose               1;  2 /    2 
                   2 /   0.22m; A  0.93mm; R56  3.7mm
                  for   18m;   2m;    .11:      R51  4.7 104 ; R52  8.4mm

   Cooling time :     T /  T d             e 1  1/ 2 2 / G  2 hours
                                      Current luminosity lifetime ~ 10 hours


5/20/2008                 4Th Electron-Ion collider Workshop                           25
                                 Hampton University
                      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
                                                        Eased magnet tolerances
   Quadrupole 2m , g 400T/m, aperture
   2cm.
  5/20/2008                          4Th Electron-Ion collider Workshop                       26
                                            Hampton University
               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.
5/20/2008                    4Th Electron-Ion collider Workshop                  27
                                    Hampton 27University
                           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.

 5/20/2008           4Th Electron-Ion collider Workshop      28
                            Hampton University

				
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