Seeding of the CSR instability in storage rings

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Seeding of the CSR instability in storage rings

• John Byrd
• Lawrence Berkeley National Laboratory

2
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

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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
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A CSR Primer
Grazie, Caterina
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Coherence of Synchrotron Radiation
Total electric summed over N electrons
distributed at time tk.
Bunch spectral distribution
long bunch (lgtsz)
short bunch (lltsz)
Coherent
Incoherent
long bunch with bumps (lltsbump)
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CSR first mentioned by Schwinger in 1945

• First comprehensive report on radiation effects
  in synchrotron/betatrons 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  unpublished manuscript.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
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Radiation Force
opening angle
e-
Ef
r
In free space
nominal bunch distribution
for sgt0
Front
Back
Total voltage on a bunch
wake accelerates bunch front
(de)focussing gradient
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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!
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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
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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.
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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).
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ALS microbunching results
Instability thresholds in general agreement with
model Proper scaling with energy and alpha
CSR bursts observed at several facilities SURF-NI
ST MAX-I NSLS-VUV BESSY MIT Bates And others
Model predictions
Burst threshold (mA)
Energy (GeV)
J. Byrd, et. al. PRL 89, 224801, (2002).
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Bessy-II Microbunching
Bursting threshold
Agrees well with predicted microbunching
thresholds
G. Wuestefeld, Napa CSR Workshop, Oct. 2002
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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).

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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.
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ALS and Slicing Parameters
Parameter BL 5.3.1 BL 1.4
Modulation-observation point distance m 8.4 149.5
Energy GeV 1.5 1.5
Current per bunch mA 1- 10 1- 10
Ring length m 196.7 196.7
Dipole bending radius m 4.957 4.957
Momentum compaction 0.00137 0.00137
Relative energy spread 0.001 0.001
Relative energy modulation 0.006 0.006
Laser pulse duration FWHM fs 75 75
Laser repetition rate pps 1000 1000
BL 1.4 ALS IR beamline
BL 5.3.1 emergency THz Port
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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).

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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
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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.

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Slicing Synchronized Bursts
Slicing laser repetition rate is 1 kHz
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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
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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)

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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
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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.
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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.
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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
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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 timeslt1 turn)

Optical stochastic cooling schematic
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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 (gt3-4
  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