sbsr nov 2005 page 1 john byrd seeding of the csr instability in storage rings john byrd lawrence...

SBSR Nov 2005page 1

John Byrd

Seeding of the CSR instability in storage rings

John Byrd Lawrence Berkeley National Laboratory

SBSR Nov 2005page 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 2005page 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 HaoBob Warnock, Sam Heifets, Gennady Stupakov - SLAC, Jim Murphy, Larry Carr- NSLS-BNL, Gode Wustefeld, Peter Kuske, Karsten Holldack- BESSY

Acknowledgements

SBSR Nov 2005page 4

John Byrd

A CSR Primer

Grazie, Caterina

SBSR Nov 2005page 5

John Byrd

Coherence of Synchrotron Radiation

rho=4.96732 mEb=1.52 GeVIb=41 µA, N=1.00e+00σt=20.42 ,6.13 fsec µm

/2=2 gap cm=1.02 , B T Ec=1567 eV

coherent

incoherent

Log

Flu

x

Log Frequency

long bunch (>σz)

short bunch (<σz)

∑=

−=N

kkttetE

1

)()(

⎟⎠⎞⎜

⎝⎛ +=

222

)(ˆ)(ˆ)( ωωω fNNeP

Total electric summed over N electrons distributed at time tk.

Incoherent Coherent

Bunch spectral distribution

long bunch with bumps (<σbump)

SBSR Nov 2005page 6

John Byrd

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• First comprehensive report on radiation effects in synchrotron/betatron’s is by Schwinger - 1945 unpublished manuscript.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)

In 1949 Schwinger published a paper on radiation in accelerators but left out any reference to coherent effects

Manuscript transcribedby M. Furman (1998)LBNL-39088

Manuscript transcribedby M. Furman (1998)LBNL-39088

First mentioned to me by Murphy at PAC 95

SBSR Nov 2005page 7

John Byrd

Radiation Force

In free space

e-

E

Eφ =Z0c4π

2e342 1 / 3

1s4 / 3

for s>0

Total voltage on a bunch

Front Back

nominal bunch distribution

wake accelerates bunch front

V(s) = 2πρ ds'Eφ(s – s')I(s')

– ∞

s

opening angle~ ψr~

2π

1 / 3

(de)focussing gradient

SBSR Nov 2005page 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

πσ<λ <2h hρ

1/ 2

h

effective source sizebeam size

vacuum chamberWhen 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!

Frequency

short bunch spectrum

long bunch spectrum

free space impedance

shielded impedance

SBSR Nov 2005page 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”)

3/2

3/1

)(R

kiAkZ −=

G. Stupakov and S. Heifets, PRST-AB 5 (2002) 054402

Can such an instability also account for the time structure of the measured signal?

Dispersion relation for sinusoidalperturbations to linearized Vlasov

equationRadiation impedancein free space

k = wavenumber of mode = frequency of mode

SBSR Nov 2005page 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.

10.5mA

28.8mA

100ms806040200

Time (msec)

40.0mA

10 mA

29 mA

40 mA

Time (msec)

Bolo

mete

r si

gnal

(V)

Bursts of far-IR CSR observed on a bolometer. Threshold depends on beam energy, bunch length, energy spread, and wavelength.

CSR Instabilities


John Byrd

Microbunching Model

S. Heifets and G. Stupakov, PRST-AB 5, 054402 (2002).M. Venturini and R. Warnock, PRL 89, 224802 (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/σ

/σ

Nonlinear effects cause the instability to saturate. Radiation damping damps the increased energy spread and bunch length, resulting in a ‘sawtooth’ instability.


John Byrd

ALS microbunching results

Instability thresholds in general agreement with modelProper scaling with energy and alpha

20

15

10

5

0

Bursting threshold (mA)

2.01.81.61.41.2

Energy (GeV)

2.0 mm threshold 3.2 mm threshold

Model predictions

Bu

rst

thre

shold

(m

A)

Energy (GeV)

J. Byrd, et. al. PRL 89, 224801, (2002).

32

3

31

31

σ zRFRF

SE

VfBDNN =≤

CSR bursts observed at several facilities:SURF-NISTMAX-INSLS-VUVBESSYMIT BatesAnd others…


John Byrd

Bessy-II Microbunching

G. Wuestefeld, Napa CSR Workshop, Oct. 2002

Agrees well with predicted microbunching

thresholds

Bursting threshold


John Byrd

Laser Slicing of Beams

• R.W. Schoenlein, et al., Science, Mar 24, (2000) 2237.•A. Zholents, M. Zolotorev, Phys. Rev. Lett. 76, 912, (1996).

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.


John Byrd

1.2

1.0

0.8

0.6

-0.4 -0.2 0.0 0.2 0.4 1086420

1.02

1.00

0.98

0.96

0.94

-6 -4 -2 0 2 4 6

Time (ps)

1.00.80.60.40.20.0

Frequency (THz)

AE=2 AE=4 AE=8

a) b)

c) d)

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)


John Byrd

ALS and Slicing ParametersALS and Slicing Parameters

Parameter BL 5.3.1

BL 1.4

Modulation-observationpoint distance [m]

8.4 149.5

Energy [GeV] 1.5

Current per bunch [mA] 1- 10

Ring length [m] 196.7

Dipole bending radius [m] 4.957

Momentum compaction 0.00137

Relative energy spread 0.001

Relative energymodulation

0.006

Laser pulse durationFWHM [fs]

75

Laser repetition rate [pps] 1000

BL BL 5.3.15.3.1

BL 1.4BL 1.4

Laser Modulation Laser Modulation RegionRegion

BL 5.3.1: ‘emergency’ THz PortBL 5.3.1: ‘emergency’ THz Port

BL 1.4: ALS IR beamlineBL 1.4: ALS IR beamline


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 bandwidthInstrumentation bandwidth• Vacuum chamber cutoffVacuum chamber cutoff

Only the high frequency part of Only the high frequency part of the spectrum can be measuredthe spectrum can be measured

•Fine structure due to water absorption.Fine structure due to water absorption.•Larger structure due to interference with Larger structure due to interference with the vacuum chamber (‘Waveguide effect’).the vacuum chamber (‘Waveguide effect’).


John Byrd

Slicing as a source?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 Energy per pulse: 8.5 JJ• Max reprate: 10 - 100 kHzMax reprate: 10 - 100 kHz

x-ray, visible and THz femtosecond pulses, x-ray, visible and THz femtosecond pulses, all synchronousall synchronous


John Byrd

An Unexpected ObservationAn Unexpected Observation

2.2. The average CSR power starts to grow larger than The average CSR power starts to grow larger than quadratically with the current per bunchquadratically with the current per bunch..

1.1. Most of the CSR bursts associated with the Most of the CSR bursts associated with the instability become synchronous with the 1 kHz instability become synchronous with the 1 kHz repetition rate of the slicing laser repetition rate of the slicing laser

ExpeExperimental observationrimental observation: : With a larger momentum With a larger momentum compaction lattice (~0.0027 instead of 0.0014) compaction lattice (~0.0027 instead of 0.0014) andand above above the microbunching instability threshold, we observe that:the microbunching instability threshold, we observe that:


John Byrd

Slicing Synchronized BurstsSlicing Synchronized Bursts

Slicing laser repetition rate is 1 kHzSlicing laser repetition rate is 1 kHz


John Byrd

CSR Power vs. Current per BunchCSR Power vs. Current per Bunch

The CSR power correlated The CSR power correlated with the laser slicing scales with the laser slicing scales

exponentiallyexponentially with the current with the current per bunch above MBI per bunch above MBI

threshold, quadratically threshold, quadratically belowbelow

N.B.: these are not CSR spectra. They are just the Fourier Transform of the time domain signals


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 withcurrent

Exponential growth withcurrent

Understanding saturation of instability


John Byrd

Particle density in phase space

Snapshot at time of saturation

exponential growth of mode saturates

exponential growth of mode saturates

energy-deviationdensity flattens

energy-deviationdensity flattens

q

p

Rad

iati

on

Pea

k P

ow

er

ALS measurements (Jan 2005)

Simple model of saturation

Saturation model

Simulation by Marco Venturini


John Byrd

Fast burst behaviorUsing a faster detector (hot electron bolometer) we can observe the structure of the stimulated burst.

ALS

Burst

BESSY-IIK. Holldack

Slicing signal

~45 µsec

Following the initial CSR signal from the slice, a burst grows within a synchrotron period.


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


John Byrd

High frequency beam ticklingBeam 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

Laser

ModulatorEtalon w/variable spacing

Modulated bunch

120

80

40

0

Amplitude (arb. units)

1086420

Frequency (THz)

Useful for single or multipass systems


John Byrd

Really broadband feedbackGiven 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?


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

sbsr nov 2005 page 1 john byrd seeding of the csr instability in storage rings john byrd lawrence...

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