brookhaven science associates u.s. department of energy longitudinal space charge micro- bunching in...

Brookhaven Science AssociatesU.S. Department of Energy

Longitudinal Space Charge Micro-Longitudinal Space Charge Micro-bunching in SDL (DUV-FEL) bunching in SDL (DUV-FEL)

T. Shaftan, L. Carr, H. Loos, B. Sheehy, (BNL)Z. Huang, C. Limborg (SLAC)

W.S. Graves (MIT/BATES)

MICROBUNCHING AND BEAM BREAK-UP IN DUV-FEL ACCELERATOR,T. Shaftan, Z. Huang, L. Carr, W.S. Graves, C. Limborg, H. Loos, B. Sheehy,PAC 2003, Portland, Oregon

T.Shaftan, S2E Workshop, Aug. 20032

Positive RF slope

Accelerate bunch at RF zero-crossing of tank 4 Spectrometer

dipole

Zero RF slopeNegative RF slope

Size of the Size of the chirped beam chirped beam image at the image at the monitor 14monitor 14 is isproportional proportional to theto thebunch length !bunch length !

The DUVFEL AcceleratorThe DUVFEL AcceleratorThe DUVFEL AcceleratorThe DUVFEL Accelerator

RF gun 4.5 MeV

Tank 1Tank 2Tank 3Tank 435 MeV75 MeV135 MeV200 MeV

SpectrometerSpectrometerdipoledipole

Focusing tripletsFocusing triplets

ChicaneChicane

MonitorsMonitorsBeamDump 14 Drive

Laser

Electron beam longitudinal diagnostics

• For energy/time domain measurements we use TV monitor (Num. 14Num. 14) located after 72° spectrometer dipole

• ““Zero-phasing” method of the bunch Zero-phasing” method of the bunch length measurement (single-shot !)length measurement (single-shot !)

to FEL


MotivationMotivationMotivationMotivation

DUV FELDUV FEL

W.S. Graves, et al., PAC 2001, p. 2860

M. Huning et al., NIM A 475 (2001) p. 348

TTFTTF

• ““Zero-phasing” imagesZero-phasing” images from the spectrometer dipole revealed spiky structurewith sub-picosecond period in the chirped beam energy spectrum

• Assuming that chirped bunch energy spectrum represents longitudinal density distribution spikes could be treated as a spikes in the longitudinal bunch density (peak current)

• Calculating FEL slippage length for lasingat 266 nm as 70 um , follows that the spike width is comparable or less than slippage length must cause degradation of FEL performance

• Similar effect has been observed at TTF


Modulation in RF gun drive laserModulation in RF gun drive laserWe measure temporal profile of the laser (at 266 nm) by cross correlating it with the 120 fsec, 800 nm oscillator pulse in a nonlinear optical crystal (multi-shot measurement). This measurement has a resolution of ~200 fs, due to velocity mismatch in the crystal. Cross-correlation of the drive laser profile shows some amount of modulation (~5-10 %).


Structure with a Large Number SpikesStructure with a Large Number SpikesStructure with a Large Number SpikesStructure with a Large Number Spikes

Frequency spectrum (THz)

Time, ps

• “Zero-phasing” image of uncompressed bunch with a large number of sharp spikes

• Energy spectrum, derived from the image,horizontal axis is scaled in picoseconds

• Frequency spectrum of upper plot. Spectrumshows modulation with harmonics in THz range. Harmonics sharpness of the spikes.

0 1 2 3 4 5 6 7 8 90

50

100

0 3 6 9 12 15 180

1

2

3

4

5

2.6 5.2


Modulation dynamics with Compression (~300 pC)Modulation dynamics with Compression (~300 pC)Modulation dynamics with Compression (~300 pC)Modulation dynamics with Compression (~300 pC)

0 2 4 6 80

50

100

1.42 ps

0 1 2 3 4 50

50

1001.24 ps

0 0.5 1 1.5 2 2.50

2000.43 ps

0 1 2 3 40

100

2000.93 ps

• Dynamics at “high” (>200 pC) charge differs from the dynamics at “low” charge

•Uncompressed bunch profile is smooth

• Experiment on modulation dynamics:Keep chicane constant and increase chirpingtank phase (0-13-19-25 degrees)

Modulation shows up during compression Process

Compression: a} decreases modulation period (C times); b) increases bunch peak current (C times)

0°

-19°

-13°

-25°


Sensitivity to the Chicane StrengthSensitivity to the Chicane StrengthSensitivity to the Chicane StrengthSensitivity to the Chicane Strength CSR-related effect ? should be

sensitive to the bending radius in the chicane magnets

Experiment: maintain the final bunch length constant, while changing

chicane strength initial and final (post-compressed) bunch properties are the same for any chicane strength, so only collective effect should show up !

Compression factor is 1-hR56 there is always a combination of h and R56 that will maintain a constant compression ratio

Result of the experiment:

in general the modulation is insensitive to the chicane settings

5 10 15 20 25 30 35 40

10

20

30

40

50

60

70

Tank 2 Phase (Degree)

Chic

ane C

urr

ent

(A)

0.1

0.1

0.1

0.10.3

0.3

0.3

0.30.6

0.6

0.6

11

1

11.2

1.2

1.2

1.21.5

1.5

1.5

1.5

1.7

1.7

1.7

1.71.7

Isolines of constant bunch length


• For an energy-modulated bunch, the horizontal profile by rf zero-phasing is also modulated with an enhanced amplitude • Space charge oscillation connects energy modulation with current modulationHorizontal modulation appears much larger than the current modulation it intends to measure “gain” = (amplitude of final energy modulation)/(initial density modulation)

Space Charge Model (courtesy of Z. Huang)Space Charge Model (courtesy of Z. Huang)

Space charge impedance per unit length for transversely uniform coasting beam in free space:

- energy, rb – bunch radius, - modulation frequency

Z. Huang, SLAC-PUB-9788

),,()(1 120

||

bbb

b

rfc

rK

c

r

r

ZcZ


SimulationSimulationSimulationSimulationEn

ergy

, MeV

Time, ps

Beam parameters:E=65 MeVI=200 Arb=0.4 mmLdrift=15 m

mod=0.2 ps

Emod= 20 keV


Modulation analysisModulation analysis

An example of the chirped beam image. One of the interesting features here is evolution of the modulation wavelength along the bunch, corresponding to nonlinear chirp. Interpretation of double peaks on the left: “overmodulated” periods. Every couple of double spikes in this region represents a single modulation period. Tail of the bunch is folded back over, introducing bright region on the right side of the image (space charge).

“Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL preprint.


“Overmodulation” effect“Overmodulation” effect

Measuring distance E between “double spikes” we can determine amplitude of the energy modulation.

a

XX E

2

1)cot(

where

.arcsin,

aX

ha

is the energy modulation, is themodulation frequency

“Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL preprint.


Fourier spectrum of structure (with L.H. Yu)Fourier spectrum of structure (with L.H. Yu)Fourier spectrum of structure (with L.H. Yu)Fourier spectrum of structure (with L.H. Yu)

Harmonics in the Fourier transform of energy spectrum

Assuming chirped coasting beam with constant density and sinusoidal energy modulation, we can derive expression for the energy spectrum.

This expression is valid for the case of “overmodulated” bunch as well

Energy spectrum must contain a family of harmonics of modulation frequency

1

2

0 cos2

1exp21)(

nEn E

hn

hn

hnJ

h

IEg

Frequency spectrum (THz)

Time, ps0 1 2 3 4 5 6 7 8 9

0

50

100

0 3 6 9 12 15 180

1

2

3

4

5

2.6 5.2

“Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL-71490-2003-JA .


Sensitivity to the Transverse Beam SizeSensitivity to the Transverse Beam SizeSensitivity to the Transverse Beam SizeSensitivity to the Transverse Beam Size

Space charge force is a function of rb

Change the beam size of the compressed beam along the accelerator effect on modulation ?200 A

40 A

large linac beam (1 mm)

0 20 40 60 80 10005101520253035

G a

200 A

40 A

small linac beam (250 m)

Analytical calculations of “gain”in the modulation by Z. Huang

3 different lattice solutions 3 different RMS beam sizes along the accelerator


Results of the ExperimentResults of the ExperimentResults of the ExperimentResults of the Experiment

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

1401

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

1402

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

1403

Average RMS beam sizes along the accelerator: 0.25 mm, 0.5 mm, 1 mm

“Zero-phasing” profiles of the beam (300 pC) for different lattice solutions:


IR Radiation MeasurementsIR Radiation Measurements

0 50 100 150 2000

50

100

150

200

250a

1 2

Wavelength, um

>40 um >100 um >160 umFilters:

“Modulated”Modulated” bunch profile ““Non-modulated”Non-modulated” bunch profile

Does modulation enhance any bunching in the bunch longitudinal density ?

Experiment: Change the beam size

“modulated” and “non-modulated” bunch profiles

We measured CTR from metallic mirror, using IR detector and low-pass IR filters (cut-off of 40 µm, 100 µm, 160 µm)

Modulation wavelength = 90 µm (from “zero-phasing”) expect enhancement of the coherent IR power in this spectral region if bunching

Result of the experiment: No difference is found

between“modulated” and “non-modulated” beam conditions

Bolo

met

er s

igna

l, uV

s


Dependence on EnergyDependence on EnergyDependence on EnergyDependence on Energy

Space charge force is a function of Change the energy of the compressed

beam (300 pC) along the accelerator effect on modulation ?

Vary tank 3 energy, maintaining the same all other beam parameters (bunchlength, transverse beam size, charge)

60 MeV

80 MeV

110 MeV


0 1 2 3 40

50

100 a

0 1 2 3 40

50

100 a

0 1 2 3 40

50

100

a

0 1 2 3 40

50

100

a

0-phasing profiles without (a) and with chicane (b)Initial chirp = 0 in both situations (no compression)a)

+90°

-90°

b)

+90°

-90°

Initial chirped beam profiles (no compression)Initial chirped beam profiles (no compression)


(I) Results of the experiment(I) Results of the experiment

Number of modulation periods and modulation wavelength for different energies is different !Product is constant: bunch length is the same for different energiesWhy ?

“Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang, BNL-71491-2003-JA


“Final phase space”, spectrometer

“Initial phase space” Beam: 70 MeV and other parameters of the experiment

Space Charge “kicks”

3 m long linac section16 m

1 m

Slippage “kicks”

Model of “Modulation versus Energy” experimentModel of “Modulation versus Energy” experiment

Assumptions: 1) Do not take into consideration bunch prehistory before chicane. We did not change anything but energy using tank after chicane.

2) Initial conditions at the end of the chicane no initial energy modulation, certain amount of initial density modulation (spectral shape is unknown)


(II) Results of the experiment(II) Results of the experimentSimulated normalized spectra of energy and density modulations for 50 MeV and 110 MeVWith energy increase average spectral frequency of energy modulation shifts toward higher freq. rangeTherefore modulation wavelength decreases and number of modulation periods increases for higher energyAnother words:Plasma oscillations at different frequencies accumulate different phase advance while the bunch travels down to the accelerator.

Initial density modulation

Initial density modulation

Final density modulation

Final density modulation

Final energy modulation

Final energy modulation

50 MeV

110 MeV

“Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang,

BNL-71491-2003-JA


(III) Results of the experiment(III) Results of the experiment

Using technique for “overmodulated” bunch (#11), we processed measured data and found energy modulation amplitude for different energies.Dashed line: simulation, assuming 6 % density fluctuations (and no initial energy modulation) at the end of the chicane-compressor.

“Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang,BNL-71491-2003-JA


Summary & ConclusionsSummary & ConclusionsSummary & ConclusionsSummary & Conclusions We observed a peculiar phenomena in the longitudinal phase space Space charge oscillation transforms small longitudinal density

modulation into energy modulation along the bunch “Zero-phasing” shows spikes, corresponding to the energy modulation

in the chirped bunch energy spectrum. A space charge model of the phenomena is in fair agreement with

experimental data (based on several assumptions have been made) Complete understanding of the phenomena requires further analysis Is this structure dangerous for accelerator performance ? o It increases the projected energy spread in the bunch and distorts

longitudinal phase spaceo It does not affect compression for DUV FEL experimental conditionso magnetic system may convert this modulation into real spatial bunching


AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements

Research supported by DOE Contract No. DE-AC02-98CH10886

We wish to thank D. Dowell, A. Doyuran,P. Emma, S. Krinsky, J.B. Murphy, J. Rose, X.J. Wang, Z. Wu, L.H. Yu for their help and many stimulating discussions.

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