Longitudinal Diagnostics of Electron Bunches Using Coherent Transition Radiation

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Longitudinal Diagnostics of Electron Bunches Using Coherent Transition Radiation

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Longitudinal Diagnostics of Electron Bunches Using Coherent Transition Radiation

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Longitudinal Diagnostics of Electron Bunches Using Coherent Transition Radiation

Daniel Mihalcea

Northern Illinois University

Department of Physics

Fermilab, Jan. 16, 2007

Outline:

- Fermilab/NICADD overview
- Michelson interferometer
- Bunch shape determination
- Experimental results
- Conclusions

Fermilab NICADD Photo-injector Laboratory

- FNPL is a collaborative effort of several institutes and universities to operate a high-brightness photo-injector dedicated to accelerator and beam physics research.
- Collaborators include:

U. of Chicago, U. of Rochester, UCLA, U. of Indiana, U. of Michigan, LBNL, NIU, U. of Georgia, Jlab, Cornell University

DESY, INFN-Milano, IPN-Orsay, CEA-Saclay

FNPL layout

Michelson interferometer for longitudinal diagnostics

Michelson Interferometer

(University of Georgia & NIU)

Autocorrelation = I1/I2

- Molectron pyro-electric

- Golay cell (opto-acoustic)

Detectors:

Interferometer

Stepping motor

Scope

Detectors

ICT

Controller

Data Flow

Get Q

Get I1 and I2

LabView code:

- Advances stepping motor between x1 and x2 with adjustable step size (50 m)
- At each position there are N readings (5)
- A reading is valid if bunch charge is within some narrow window (Ex: 1nC 0.1 nC)
- Position, average values of I1 and I2 and their ’s are recorded.
- Autocorrelation function is displayed.

Basic Principle (1)

Backward transition radiation

Ginsburg-Franck:

Detector aperture 1 cm

Form factor

related to longitudinal charge distribution:

Basic Principle (2)

Intensity of Optical Transition Radiation:

Coherent part N2

To determine (z) need to know I() and the phase of f()

Kramers-Kröning technique

Coherence condition

Due to detector sensitivity:

Acceptable resolution:

Need bunch compression !

Bunch Compression

RF field in booster cavity

Energy-Position correlation

Electron bunch before compression

Tail

After compression

Head

Kramers-Kröning method:

Measurement Steps

FT

Ideal apparatus

K-K

Molectron pyro-electric detectors

Path difference (mm)

Frequency (THz)

Interference effect

Missing frequencies

Experimental results (1)

Experimental results (2)

Still need to account for:

- low detector sensitivity at low frequencies
- diffraction at low frequencies
- absorption at large frequencies

Golay detectors: no problem with interference !

Beam conditions:

- Q = 0.5 nC
- maximum compression

Experimental results (3)

Interference

Apparatus response function:

Absorption

Diffraction

Low detector sensitivity

Auto-correlation function:

- Q = 3nC
- 9-cell phase was 3 degrees from maximum compression

Power spectrum:

- Asymptotic behavior
low frequencies:

high frequencies:

- Least square fit.

Experimental results (4)

Molectron pyroelectric detectors

Experimental results (5)

- Molectron pyroelectric detectors
- Kramers-Kroning method

Head-Tail ambiguity

Parmela simulation

Head

Tail

Beam conditions:

- Q = 3.0 nC
- moderate compression

Experimental results (6)

Golay cell

- FT
- Spectrum correction with R()
- Spectrum completion for:

and

Start point

K-K

z 1ps

Complicated bunch shapes

Stack 4 laser pulses

Select 1st and 4th pulses (t 15ps)

After compression

Before compression

(Parmela simulations)

Beam conditions:

- Q = 0.5 nC each pulse
- 15 ps initial separation between the two pulses
- both pulses moderately compressed

Experimental results (7)

Double-peaked bunch shapes

K-K method may not be accurate for complicate bunch shapes !

K-K method accuracy

R. Lai and A. J. Sievers, Physical Review E, 52, 4576, (1995)

Generated

Reconstructed

K-K method accurate if:

- Simple bunch structure
- Stronger component comes first

Calculated widths are still correct !

Other approaches

Major problem: the response function is not flat.

1. Complete I() based on some assumptions at low and high frequencies.

R. Lai, et al. Physical Review E, 50, R4294, (1994).

S. Zhang, et al. JLAB-TN-04-024, (2004).

2. Avoid K-K method by assuming that bunches have a predefined shape and make some assumptions about I() at low frequencies.

A. Murokh, et al. NIM A410, 452-460, (1998).

M. Geitz, et al. Proceedings PAC99, p2172, (1999).

This work:

D. Mihalcea, C. L. Bohn, U. Happek and P. Piot, Phys. Rev. ST Accel. Beams 9, 082801 (2006).

Conclusions:

- Longitudinal profiles with bunch lengths less than 0.6 mm can
be measured.

- Systematic uncertainties dominated by approximate knowledge of response function and completion procedure.
- Golay cells are better because the response function is more uniform.
- Some complicate shapes (like double-peaked bunches) can be measured.