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. Outline:. Fermilab/NICADD overview Michelson interferometer Bunch shape determination Experimental results Conclusions.

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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: Transition Radiation

  • Fermilab/NICADD overview

  • Michelson interferometer

  • Bunch shape determination

  • Experimental results

  • Conclusions

Fermilab NICADD Transition RadiationPhoto-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 Transition Radiation

Michelson interferometer for longitudinal diagnostics

Michelson Interferometer Transition Radiation

(University of Georgia & NIU)

Autocorrelation = I1/I2

- Molectron pyro-electric

- Golay cell (opto-acoustic)


Interferometer Transition Radiation

Stepping motor





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) Transition Radiation

Backward transition radiation


Detector aperture  1 cm

Form factor Transition Radiation

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 Transition Radiation

Due to detector sensitivity:

Acceptable resolution:

Need bunch compression !

Bunch Compression Transition Radiation

RF field in booster cavity

Energy-Position correlation

Electron bunch before compression


After compression


Kramers-Kröning method: Transition Radiation

Measurement Steps


Ideal apparatus


Molectron Transition Radiationpyro-electric detectors

Path difference (mm)

Frequency (THz)

Interference effect

Missing frequencies

Experimental results (1)

Experimental results (2) Transition Radiation

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: Transition Radiation

  • Q = 0.5 nC

  • maximum compression

Experimental results (3)


Apparatus response function:



Low detector sensitivity

Auto-correlation function: Transition Radiation

  • 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) Transition Radiation

  • Molectron pyroelectric detectors

  • Kramers-Kroning method

Head-Tail ambiguity

Parmela simulation



Beam conditions: Transition Radiation

  • Q = 3.0 nC

  • moderate compression

Experimental results (6)

Golay cell

  • FT

  • Spectrum correction with R()

  • Spectrum completion for:


Start point


z  1ps

Complicated bunch shapes Transition Radiation

Stack 4 laser pulses

Select 1st and 4th pulses (t 15ps)

After compression

Before compression

(Parmela simulations)

Beam conditions: Transition Radiation

  • 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 Transition Radiation

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



K-K method accurate if:

  • Simple bunch structure

  • Stronger component comes first

Calculated widths are still correct !

Other approaches Transition Radiation

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: Transition Radiation

  • 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.