Seeding of the CSR instability in storage rings

1. Seeding of the CSR instability in storage rings John Byrd Lawrence Berkeley National Laboratory

2. Coherence of Synchrotron Radiation Challenges for generating CSR CSR Microbunching Instability CSR from Laser-sliced bunches Seeding the Microbunching instability Fantasies on a theme: High frequency beam transfer function Feedback on the microwave instability Overview

3. Acknowledgements Infrared Beamline:Michael C. Martin, Zhao Hao, Accelerator Physics:John Byrd, Fernando Sannibale, David Robin, Agusta Loftsdottir, Marco Venturini, Laser Slicing:Robert Schoenlein, Sacha Zholents, Max Zolotorev, Zhao Hao Bob Warnock, Sam Heifets, Gennady Stupakov - SLAC, Jim Murphy, Larry Carr- NSLS-BNL, Gode Wustefeld, Peter Kuske, Karsten Holldack- BESSY

4. A CSR Primer Grazie, Caterina

5. coherent Log Flux incoherent Log Frequency Coherence of Synchrotron Radiation Total electric summed over N electrons distributed at time tk. Bunch spectral distribution long bunch (l>sz) short bunch (l<sz) Coherent Incoherent long bunch with bumps (l<sbump)

6. CSR first mentioned by Schwinger in 1945 • First comprehensive report on radiation effects in synchrotron/betatron’s is by Schwinger - 1945 unpublished manuscript. • Questions addressed: • Does a single-particle calculation apply to betatrons where the electron current is distributed along the orbit circumference? • Will coherent radiation from bunched beams in synchrotrons cause unacceptable power loss? (Recall: scaling is ~N2) Manuscript transcribed by M. Furman (1998) LBNL-39088 First mentioned to me by Murphy at PAC 95 In 1949 Schwinger published a paper on radiation in accelerators but left out any reference to coherent effects

7. Radiation Force opening angle~ e- Ef r In free space nominal bunch distribution for s>0 Front Back Total voltage on a bunch wake accelerates bunch front (de)focussing gradient

8. effective source size beam size h vacuum chamber When the effective size of the SR source is equal to the height of the vacuum chamber, SR is suppressed. Impedance of Synchrotron Radiation Vacuum Chamber acts as a High Pass Filter Nodvick, Saxon, Phys. Rev. 96, 1, p. 180 (1954) Shielding by the vacuum chamber limits the SR emission to wavelengths above the waveguide cutoff condition Most rings can not make short enough bunches to generate stable CSR!

9. Microbunching instability • G. Stupakov and S. Heifets (SLAC) apply formalism of classical collective instabilities to determine current threshold for CSR-driven instability using radiation impedance as input • The basic ingredients for linear analysis are • use of Boussard criterion (bunched beam is equivalent to coasting beam with same peak current) • expression for radiation impedance (model of impedance in free space is used with shielding cut-off inserted “by hand”) k = wavenumber of mode w = frequency of mode Dispersion relation for sinusoidal perturbations to linearized Vlasov equation Radiation impedance in free space Can such an instability also account for the time structure of the measured signal? G. Stupakov and S. Heifets, PRST-AB 5 (2002) 054402

10. 10 mA 29 mA Bolometer signal (V) 40 mA Time (msec) Bursts of far-IR CSR observed on a bolometer. Threshold depends on beam energy, bunch length, energy spread, and wavelength. Simulated instability showing bunch shape CSR Instabilities CSR can drive a microbunching instability in the electron bunch, resulting in a periodic bursts of terahertz synchrotron radiation, resulting in a noisy source.

11. d/s z/s Microbunching Model Small perturbations to the bunch density can be amplified by the interaction with the radiation. Instability occurs if growth rate is faster than decoherence from bunch energy spread. Nonlinear effects cause the instability to saturate. Radiation damping damps the increased energy spread and bunch length, resulting in a ‘sawtooth’ instability. • S. Heifets and G. Stupakov, PRST-AB 5, 054402 (2002). • M. Venturini and R. Warnock, PRL 89, 224802 (2002).

12. ALS microbunching results Instability thresholds in general agreement with model Proper scaling with energy and alpha CSR bursts observed at several facilities: SURF-NIST MAX-I NSLS-VUV BESSY MIT Bates And others… Model predictions Burst threshold (mA) Energy (GeV) J. Byrd, et. al. PRL 89, 224801, (2002).

13. Bessy-II Microbunching Bursting threshold Agrees well with predicted microbunching thresholds G. Wuestefeld, Napa CSR Workshop, Oct. 2002

14. Laser Slicing of Beams Laser slicing is a new technique for generating ~100-200 fsec xray pulses in a storage ring. In operation at ALS since 2002, and recently commissioned at Bessy-II, in construction at SLS. • R.W. Schoenlein, et al., Science, Mar 24, (2000) 2237. • A. Zholents, M. Zolotorev, Phys. Rev. Lett. 76, 912, (1996).

15. Holy Bunches 1/24 ring after slicing Holes spread due to time of flight disperson (i.e. momentum compaction) 3/4 ring after slicing Calculated distributions for ALS with nominal and twice nominal momentum compaction.

16. BL 5.3.1 Laser Modulation Region BL 1.4 ALS and Slicing Parameters BL 1.4: ALS IR beamline BL 5.3.1: ‘emergency’ THz Port

17. 1 msec laser rep rate Slicing CSR signals Raw bolometer signal shows a signal synchronous with the laser repetition rate. long slice • Instrumentation bandwidth • Vacuum chamber cutoff Only the high frequency part of the spectrum can be measured short slice • Fine structure due to water absorption. • Larger structure due to interference with the vacuum chamber (‘Waveguide effect’).

18. Slicing as a source? • Laser Modulation: 6 energy spread sigmas • Laser pulse length: 50 fs FWHM • Distance modulator- radiator: 2.5 m • Current per bunch: 10 mA • Horizontal Acceptance 100 mrad (single mode) Paid advertisement • Energy per pulse: 8.5 mJ • Max reprate: 10 - 100 kHz x-ray, visible and THz femtosecond pulses, all synchronous

19. An Unexpected Observation Experimental observation: With a larger momentum compaction lattice (~0.0027 instead of 0.0014) and above the microbunching instability threshold, we observe that: • Most of the CSR bursts associated with the instability become synchronous with the 1 kHz repetition rate of the slicing laser • 2. The average CSR power starts to grow larger than quadratically with the current per bunch.

20. Slicing Synchronized Bursts Slicing laser repetition rate is 1 kHz

21. CSR Power vs. Current per Bunch The CSR power correlated with the laser slicing scales exponentially with the current per bunch above MBI threshold, quadratically below N.B.: these are not CSR spectra. They are just the Fourier Transform of the time domain signals

22. Understanding saturation of instability • Saturation of instability is responsible for • duration of radiation bursts • profiles of power vs. current plots Exponential growth with current • Analytical description of saturation is difficult; several mechanisms are at play. One such mechanism is particle one-mode resonant trapping (particle-wave interaction)

23. Saturation model ALS measurements (Jan 2005) Snapshot at time of saturation Particle density in phase space energy-deviation density flattens p Radiation Peak Power Simple model of saturation exponential growth of mode saturates q Simulation by Marco Venturini

24. BESSY-II K. Holldack Fast burst behavior Using a faster detector (hot electron bolometer) we can observe the structure of the stimulated burst. Burst ~45 µsec ALS Slicing signal Following the initial CSR signal from the slice, a burst grows within a synchrotron period.

25. Unstable modes for ALS conditions Evolution of initial excited modes Radiated power Heifets Model A model has been developed by Sam Heifets which has some of the general features. Evaluates time domain evolution of set of unstable modes.

26. Laser High frequency beam tickling Beam transfer function is a well known technique for measuring beam impedance. For electron bunches, kicker technology limits excitation to only low frequency modes within the bunch (i.e. fs, 2fs, etc.) Slicing provides a technique for exciting high frequency bunch modes and probing high frequency impedance. Typical Long BTF setup via RF phase modulation Modulated bunch Modulator Etalon w/variable spacing Useful for single or multipass systems

27. Really broadband feedback Given the possibility of exciting the beam at wavelengths less than the bunch length, is it conceivable to control the high frequency intrabunch with a feedback system? Can we defeat the microwave instability? • Minor Technical Issues: • Broadband pickup • Operating frequency (slicing works at optical) • Gain medium • Sufficient damping rate (most growth times<1 turn) Optical stochastic cooling schematic

28. CSR microbunching instability driven by bend impedance Fundamental impedance that provides ultimate limit to bunch length (I.e. peak current) in a storage ring Spontaneous instability observed in many rings although much more to learned from experiments Potential well distortion for short bunches (>3-4 psec) Laser slicing can create bunch microstructures which radiate CSR observed at ALS and BESSY-II. possibilities of new range of techniques with high power: pulse stacking, two-color pump/probe laser tailoring allows coherent control of ultrafast T-ray pulses Possible to stimulate CSR instability with laser slicing Analogous to seeded broadband FEL Physics still not completely understood Summary