Fermilab, Jan. 16, 2007

Longitudinal Diagnostics of Electron Bunches Using

Coherent Transition Radiation

Daniel Mihalcea

Northern Illinois University

Department of Physics

•Fermilab/NICADD overview

• Michelson interferometer

• Bunch shape determination

• Experimental results

• Conclusions

Outline:

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 Detectors: - Molectron pyro-electric

- Golay cell (opto-acoustic)

Data Flow

Interferometer

ICT Detectors Stepping motor

Scope

Controller

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)

222

22

03

22

)cos1(

sin

4

c

e

dd

UdIe

Ginsburg-Franck:

)(fIe

Detector aperture 1 cm

Backward transition radiation

Basic Principle (2)

2)()1()( fINNI eIntensity of Optical Transition Radiation:

Coherent part N2

Form factor )(f related to longitudinal charge distribution: dzczizf )/exp()()(

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

dttEctEI2

1 )()/(

dttE

dtctEtE

I

IS 2

2

1

)(

)/()(Re)(

dE

deES

ci

2

/2

)(

)(Re)( deSEI ci

/2)()()(

Kramers-Kröning technique

Coherence condition

z mm3max

Due to detector sensitivity:

Acceptable resolution: mmz 6.0 Need bunch compression !

Bunch Compression RF field in booster cavity

Electron bunch before compression

Energy-Position correlation

Head

Tail

After compression

mm1

mm15.0

2566 c

Tt f

Measurement Steps

Ideal apparatus

mmz 19.0

2/

FT

K-K

mmz 18.0

Kramers-Kröning method:

dczIc

z

x

IxIdx

/)(cos)(1

)(

)(/)(ln)(

0

022

Experimental results (1)

Path difference (mm)

Frequency (THz)c

ndE

22 sin||

Molectron pyro-electric detectors

Interference effect Missing frequencies

Experimental results (2)

Golay detectors: no problem with interference !

Still need to account for:

low detector sensitivity at low frequencies

diffraction at low frequencies

absorption at large frequencies

Experimental results (3)

Low detector sensitivity

DiffractionAbsorption

Interference

Apparatus response function:

)(

)()(

simulation

measured

I

IR

Beam conditions:

Q = 0.5 nC

maximum compression

Experimental results (4)

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.

21)( aI

)(I

Molectron pyroelectric detectors

Experimental results (5)

• Molectron pyroelectric detectors

• Kramers-Kroning method

Head

Tail

Parmela simulation

Head-Tail ambiguity

Experimental results (6)

FT

Spectrum correction with R()

Spectrum completion for:

andzc /0 0

Beam conditions:

Q = 3.0 nC

moderate compression

K-K

Golay cell

Start point

z 1ps

Complicated bunch shapes

Stack 4 laser pulses

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

Before compression

After compression

(Parmela simulations)

Experimental results (7)

Double-peaked bunch shapes

Beam conditions:

Q = 0.5 nC each pulse

15 ps initial separation between the two pulses

both pulses moderately compressed

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.