SBSR Nov 2005 page 1 John Byrd Seeding of the CSR instability in storage rings John Byrd Lawrence Berkeley National Laboratory

SBSR Nov 2005 page 2 John Byrd Overview 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

SBSR Nov 2005 page 3 John Byrd Infrared Beamline: Infrared Beamline: Michael C. Martin, Zhao Hao, Accelerator Physics: Accelerator Physics: John Byrd, Fernando Sannibale, David Robin, Agusta Loftsdottir, Marco Venturini, Laser Slicing: 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 Acknowledgements

SBSR Nov 2005 page 4 John Byrd A CSR Primer Grazie, Caterina

SBSR Nov 2005 page 5 John Byrd Coherence of Synchrotron Radiation coherent incoherent Log Flux Log Frequency long bunch ( >  z ) short bunch ( <  z ) Total electric summed over N electrons distributed at time t k. Incoherent Coherent Bunch spectral distribution long bunch with bumps ( <  bump )

SBSR Nov 2005 page 6 John Byrd CSR first mentioned by Schwinger in 1945 First comprehensive report on radiation effects in synchrotron/betatron’s is by Schwinger unpublished manuscript.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 ~N 2 ) In 1949 Schwinger published a paper on radiation in accelerators but left out any reference to coherent effects Manuscript transcribed by M. Furman (1998) LBNL Manuscript transcribed by M. Furman (1998) LBNL First mentioned to me by Murphy at PAC 95

SBSR Nov 2005 page 7 John Byrd Radiation Force In free space  e-e- EE for s>0 Total voltage on a bunch FrontBack nominal bunch distribution wake accelerates bunch front opening angle~ (de)focussing gradient

SBSR Nov 2005 page 8 John Byrd Impedance of Synchrotron Radiation 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 h effective source size beam size vacuum chamber When the effective size of the SR source is equal to the height of the vacuum chamber, SR is suppressed. Vacuum Chamber acts as a High Pass Filter Most rings can not make short enough bunches to generate stable CSR!

SBSR Nov 2005 page 9 John Byrd 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”) G. Stupakov and S. Heifets, PRST-AB 5 (2002) Can such an instability also account for the time structure of the measured signal? Dispersion relation for sinusoidal perturbations to linearized Vlasov equation Radiation impedance in free space k = wavenumber of mode  = frequency of mode

SBSR Nov 2005 page 10 John Byrd Simulated instability showing bunch shape CSR can drive a microbunching instability in the electron bunch, resulting in a periodic bursts of terahertz synchrotron radiation, resulting in a noisy source. 10 mA 29 mA 40 mA Time (msec) Bolometer signal (V) Bursts of far-IR CSR observed on a bolometer. Threshold depends on beam energy, bunch length, energy spread, and wavelength. CSR Instabilities

SBSR Nov 2005 page 11 John Byrd Microbunching Model S. Heifets and G. Stupakov, PRST-AB 5, (2002). M. Venturini and R. Warnock, PRL 89, (2002). 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. z/     Nonlinear effects cause the instability to saturate. Radiation damping damps the increased energy spread and bunch length, resulting in a ‘sawtooth’ instability.

SBSR Nov 2005 page 12 John Byrd ALS microbunching results Instability thresholds in general agreement with model Proper scaling with energy and alpha Model predictions Burst threshold (mA) Energy (GeV) J. Byrd, et. al. PRL 89, , (2002). CSR bursts observed at several facilities: SURF-NIST MAX-I NSLS-VUV BESSY MIT Bates And others…

SBSR Nov 2005 page 13 John Byrd Bessy-II Microbunching G. Wuestefeld, Napa CSR Workshop, Oct Agrees well with predicted microbunching thresholds Bursting threshold

SBSR Nov 2005 page 14 John Byrd Laser Slicing of Beams R.W. Schoenlein, et al., Science, Mar 24, (2000) A. Zholents, M. Zolotorev, Phys. Rev. Lett. 76, 912, (1996). Laser slicing is a new technique for generating ~ fsec xray pulses in a storage ring. In operation at ALS since 2002, and recently commissioned at Bessy-II, in construction at SLS.

SBSR Nov 2005 page 15 John Byrd Holy Bunches Calculated distributions for ALS with nominal and twice nominal momentum compaction. 1/24 ring after slicing 3/4 ring after slicing Holes spread due to time of flight disperson (i.e. momentum compaction)

SBSR Nov 2005 page 16 John Byrd ALS and Slicing Parameters ParameterBL BL 1.4 Modulation-observation point distance [m] Energy [GeV]1.5 Current per bunch [mA]1- 10 Ring length [m]196.7 Dipole bending radius [m]4.957 Momentum compaction Relative energy spread0.001 Relative energy modulation Laser pulse duration FWHM [fs] 75 Laser repetition rate [pps]1000 BL BL 1.4 Laser Modulation Region BL 5.3.1: ‘emergency’ THz Port BL 1.4: ALS IR beamline

SBSR Nov 2005 page 17 John Byrd Raw bolometer signal shows a signal synchronous with the laser repetition rate. Slicing CSR signals 1 msec laser rep rate long slice short slice Instrumentation bandwidth Instrumentation bandwidth Vacuum chamber cutoff Vacuum chamber cutoff Only the high frequency part of the spectrum can be measured Fine structure due to water absorption.Fine structure due to water absorption. Larger structure due to interference with the vacuum chamber (‘Waveguide effect’).Larger structure due to interference with the vacuum chamber (‘Waveguide effect’).

SBSR Nov 2005 page 18 John Byrd 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) Energy per pulse: 8.5  J Energy per pulse: 8.5  J Max reprate: kHz Max reprate: kHz x-ray, visible and THz femtosecond pulses, all synchronous

SBSR Nov 2005 page 19 John Byrd An Unexpected Observation 2.The average CSR power starts to grow larger than quadratically with the current per bunch. 1.Most of the CSR bursts associated with the instability become synchronous with the 1 kHz repetition rate of the slicing laser Experimental observation: With a larger momentum compaction lattice (~ instead of ) and above the microbunching instability threshold, we observe that:

SBSR Nov 2005 page 20 John Byrd Slicing Synchronized Bursts Slicing laser repetition rate is 1 kHz

SBSR Nov 2005 page 21 John Byrd 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

SBSR Nov 2005 page 22 John Byrd Saturation of instability is responsible for –duration of radiation bursts –profiles of power vs. current plots Analytical description of saturation is difficult; several mechanisms are at play. One such mechanism is particle one- mode resonant trapping (particle-wave interaction) Exponential growth with current Exponential growth with current Understanding saturation of instability

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

SBSR Nov 2005 page 24 John Byrd Fast burst behavior Using a faster detector (hot electron bolometer) we can observe the structure of the stimulated burst. ALS Burst BESSY-II K. Holldack Slicing signal ~45 µsec Following the initial CSR signal from the slice, a burst grows within a synchrotron period.

SBSR Nov 2005 page 25 John Byrd Heifets Model Unstable modes for ALS conditions A model has been developed by Sam Heifets which has some of the general features. Evaluates time domain evolution of set of unstable modes. Evolution of initial excited modes Radiated power

SBSR Nov 2005 page 26 John Byrd 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. f s, 2f s, etc.) Slicing provides a technique for exciting high frequency bunch modes and probing high frequency impedance. Typical Long BTF setup via RF phase modulation Laser Modulator Etalon w/variable spacing Modulated bunch Useful for single or multipass systems

SBSR Nov 2005 page 27 John Byrd 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? Optical stochastic cooling schematic Minor Technical Issues: Broadband pickup Operating frequency (slicing works at optical) Gain medium Sufficient damping rate (most growth times<1 turn) Can we defeat the microwave instability?

SBSR Nov 2005 page 28 John Byrd Summary 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