Transient Time Method of Optical Stochastic Cooling

1. Transient Time Method of Optical Stochastic Cooling A. Zholents, M. Zolotorev

2. How it works D L L b N s = N maximum decrement = decrement = kicker S. van der Meer, 1968 number of particles in the sample “bad” mixing “good” mixing g amplifier DL ~1/bandwidth p pick-up L b D. Möhl, “Stochastic Cooling for Beginners”, CERN optimal gain 1 Cooling rate g 1 2

3. OSC obeys the same principles as the microwave stochastic cooling, but explores a superior bandwidth of optical amplifiers, ~ 1014 Hz Fluorescenceandabsorption spectra of Ti:sapphire microwave “slicing” sample length ~10 cm ~100 THz rel. units optical “slicing” sample length ~10 mm Additionally, OSC allows transverse slicing Diffraction limited size of the radiation source resulting in further decrease of Ns:

4. B k q v E Particle interaction with light 1. Transverse force on a particle is practically zero But under certain conditions one can change particle energy

5. E B = B B sin( k z ) 0 w k k B l E w V V Undulator as a kicker Electron trajectory through undulator - S e N Light S N N S N S Magnetic field in the undulator Undulator period Laser wavelength peak field period Undulator parameter:

6. Undulator radiation Coherent length: ~ 10 cycles for undulator with 10 periods A pattern of the field of the undulator radiation Undulator as a pick-up the number of cycles equals to the number of wiggler periods spontaneous radiation -60 -40 -20 20 40 60 Number of photons in a single mode radiated by Ns sample particles: Z is the particle charge Bessel functions

7. Transient Time Method of OSC transverse kick before kick { after kick energy kick . bypass . . . undulator undulator radiation pulse amplifier energy gain/loss dz is particle delay ~1 mm A pick-up and a kicker should be installed in a position with a nonzero dispersion functionfor a simultaneous cooling of energy and transverse coordinates (similar to the Palmer’s method of the momentum cooling). Coupling is used to share dumping between horizontal and vertical coordinates

8. Cooling rates Inverse damping time expressed in the number of passes through cooling section Longitudinal damping Transverse damping

9. Amplification factor Amplitude gain of the amplifier: central wavelength of the amplifier energy spread (relative) classical radius = undulator parameter x

10. Estimation for MIT electron ring Energy = 200 MeV Period = 600 ns Energy spread = 7x 10-4 Bunch length = 1cm Total number of electrons = 2x108 Average current = 50 mA Case 1:one electron bunch, optical wavelength = 2 mm Undulator: 20 periods, period=6 cm, K=4.3, Bpeak=0.77 T Damping time = 1 sec Amplitude gain of the amplifier = 16 Amplifier’s average power = 0.1 mW

11. Estimation for MIT electron ring (2) Case 2:20 electron bunches, optical wavelength = 2 mm Undulator: 20 periods, period=6 cm, K=4.3, Bpeak=0.77 T Damping time = 50 ms Amplitude gain of the amplifier = 330 Amplifier’s average power = 50 mW Case 3:20 electron bunches, optical wavelength = 10 mm Undulator: 20 periods, period=7.5 cm, K=7, Bpeak=1.3 T Damping time = 260 ms Amplitude gain of the amplifier = 300 Amplifier’s average power = 8 mW

12. What can go wrong? Phase distortions in the amplifier Noise added by amplifier Particle mixing in the bypass Diagnostics

13. Noise of the optical amplifier Not a problem! The amplifier is not affected by a thermal noise. Practically, there are no thermal photons with the energy of signal photons because: Noise of the amplifier is due to the spontaneous emission. The equivalent noise of the spontaneous emission at the amplifier front end is one photon per mode. It is like “having extra ~137/2 particles” in a sample *). *) For undulator radiation:

14. absorption fluorescence Amplitude distortions: not a problem, averaging over many thousands turns • Potentially could be phase distortions due to : • Depletion of the population inversion density in the medium • Beam energy spread hn(eV) undulator radiation input signal output signal

15. Particle mixing in the bypass

16. Particle mixing in the bypass (with W. Wan) with sextupoles no sextupoles

17. Particle mixing in the bypass (2) Pattern of undulator radiation in pick-up undulator and kicker undulator Visibility function

18. Particle mixing in the bypass (3) Errors

19. Particle mixing in the bypass (4)

20. 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

21. Thank you