The 13th Symposium on Accelerator Science arid Technology, Suita, Osaka, Japan, October 2001

Diagnostics of Sub-picosecond Electron Pulse Using the Fluctuation Method
K. Nakamura, T. Watanabe, T. Ueda, K. Yoshii, M. Uesaka
Nuclear Engineering Research Laboratory, University of Tokyo,22-2 Shirakata-Shirane, Tokai, Naka, Ibaraki 319-1188, Japan

Abstract
Diagnostics .of longitudinal bunch length of subpicoand picosecond electron beams by the fluctuation method
has been carried out at the S-hand twin linear
accelerators at Nuclear Engineering Research Laboratory(NERL), University of Tokyo. The diagnostics method
utilizes a statistical analysis of shot-noise-driven
fluctuations in incoherent radiation. Experiment wasperformed on Cherenkov light emitted from 1.0 ps(FWHM), 20 MeV bunch. As a result, the fluctuation
method indicated pulse duration four times longer thanthat by the streak camera. Its discrepancy attributes aspatial effect neglected in the theory. Thus, numericalanalysis is extended to 2-dimensional one.

1 INTRODUCTION
Measurement of the longitudinal bunch distribution ofa relativistic electron beam is of great importance inadvanced accelerators, for example, X-ray FEL, linear
collider, and laser-plasma cathode. So far, thefemtosecond streak camera has been the most reliable
tool for the measurement [1-3]. However, newtechniques for the generation of ultrashort electron pulse(~ 10 fs ), such as the plasma cathode [4-6], have been
proposed. In order to diagnose such a short pulse, wehave to use an alternative method, since the time
resolution of the streak camera, 200 fs, is not enough. AtNERL, the coherent transition/diffraction radiations(CTR/CDR) emitted at the wavelengths longer than orequal to the bunch length were used for the diagnostics
of subpico- and picosecond electron pulses [1-2].
Recently, a new novel technique was proposed by M.S.
Zolotorev, et al [7]. The method is based on observing
the intensity and spectral fluctuations of incoherent
radiation.

In the paper, the measurement of fluctuations in thepicosecond time domain is performed, and the reliabilityof the method is discussed. As showed in Fig. 1, it isimportant to try alternative methods based on different
physics and check their precision.

2 THEORY AND lD-SIMULATION
The fluctuations in both the time domain and thefrequency domain allow us to obtain the longitudinalbunch length. In case of the measurements in the time
domain, by using the band pass filter (BPF) withbandwidth 11m, the incoherent radiation has coherencetime 'rcoh''f coh oc

1/11m.

(1)

The pulse is consists of N independent coherent parts asshown in Fig. 2. N can be described as follows,(2)
where'i bis bunch length with full width halfmaximum. In the experiment, the detector measures thetime-integrated intensity of incoherent radiation as,

I=JIE(tt dt,(3)E(!} is the electric field of radiation. Since eachwherecoherent part has random amplitude and phase, the valueof the Eq. (3) would show fluctuations from one pulse toanother with the relative variation of the order of N 112•
The pulse-to-pulse fluctuation u can be expressed as,u[%] = 1/JN oct/ ~Tbl1m

Making use of a certain band pass filter, the bunch lengthis acquired.

'ib

2.5 ,-------------------·------"b = 500fs(FWHM)
IL0 = 700nm
I1IL = 15nm

2,.....,

Picosubpico

incoherent

IIFemtosecond
streak camera
200fs
Fluctuation
method:3~1.5~

coherent

CTR(4).,'rcoh ~ 50fs

1:-~

linac
(240fs)

-~·~-

1

0.5

CTR
-400

0400time[fs]* There are many other methods.

Fig. 2 Intensity of radiation through the BPF

Fig. 1 Diagnostics schemes and their time resolutions-361-800

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

In case of the frequency domain measurement, thepulse length can be deduced by a single shot from thespike width of the spectrum of incoherent radiation t5mby,(5)Fig. 4 Simulation result of measurement of pulse shape
We have performed computer simulation of the pulse
measurements based in the fluctuation method. In case oftime region measurements, the code simulates theincoherent radiation with Eq. (8) is,N,

Figure 3 shows the simulation result of the power
spectrum of incoherent radiation.

E(t )= L:e(t -tk)

(8)

k=l

where Ne is the number of radiation sources,

1.5r b = 500fs(FWHM)t k thetime of arrival of the kth particle at the observation point,
and e(t) electric field from one radiation source as in~::i~

Eq.(9),

Z''iiie(t) = RelJe(m )exp(imt }tmj,(9)where e(m) is decided by the transmittance of BPF,c::

1l 0.5

.5

0680

690

700

710

720

Wavelength [nm]Fig. 3 Power spectrum of incoherent radiation
Equation (5) indicates that the width of the spike become
wider as the pulse length is shorter. It is worth noticingthat wider one is easier to be observed on the detector.
Fourier transform of the power spectrum gives thecorrelation function, which can be defined as Eq. (6),r(r)= [E(t)E*(t-r)/t.

l(t)=l0 exp[-ln2~)
The result is shown with Ne = 500 in Fig. 2.

In case of the frequency region, the code generates theFourier component of the electric field with Eq. (11),N,E(m )= e(m )L:exp(imtk ).

dr(r)= (/r(r)- (r(r))/ 2 )IK(;t d; x [ dtl(t )I(t- r ),We assume a standard spectrometer with dispersion ofabout 2.3nm/mm and a CCD with 1100 channels of
about 24 micrometers. The simulation result ofmeasurement and pulse shape acquirement are shown inFig. 3 and 4.

3 EXPERIMENTThe experimental setup is shown in Fig. 5. Cherenkov
radiation emitted by the electron bunch in the Xechamber was introduced to the photodiode and the streak
camera through the band pass filter (BPF). The
photodiode detects the time-integrated intensity of the..

LINAC

30 ·'

Theoretical curve

2520i*i

15
10500(11)k=l(7)

where the angular brackets denote the ensemble average.
The simulation results of the measurement of dr (r) isshown in Fig.4. Only the averaged beam distribution canbe obtained as the convolution of the radiation intensity
by Eq. (7). It should be noticed that the infinitesimal
diameter of beam is assumed throughout the above
theory.
35(10)

rh/2(6)

Finally, from the dispersion of the correlation function,
the longitudinal bunch distribution can be acquired asfollows,= [and assumed to be Gaussian. It is assumed that thedistribution of radiation sources is Gaussian, and theaverage intensity of incoherent radiation is given by Eq.
(10) as,

200

400

600

800

1000time[fs]Fig. 5 experimental setup-362-The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

Cherenkov radiation as stated in the theory, and theshot-by-shot fluctuations are evaluated. Time-variationof the electron beam intensity detected by the photodiodeis automatically compensated by use of the Faraday cup.
The fluctuations measured as a function of the bandwidth
are shown in Fig. 6. By fitting the experimental data withthe calculated value from Eq. (4), the bunch length bythe fluctuation method was estimated to be 4.5 ps,whereas the bunch length measured independently by thestreak camera was 1.0 ps.

E(t, x) ~t. R{

fe(w )exp+• -';'

J].

{12)

where, lk is the length decided by the transverse
electron position.
The 2D-simulation of fluctuation is performed andshown in Fig.8. It is shown that the fluctuation issuppressed as the transverse bunch size is enlarged, asexpected.
60
50~40
t:

000'"iil30::::!

.....

Dg2oq::!> D"10D"

01010010000bandwidth [nm]The main source of this discrepancy can be understood
to be the influence of a large transverse size of theelectron bunch. It is assumed throughout the theory thatelectron pulse has an infinitesimal diameter. From theexperiment, we concluded that the spatial effect was not
negligible in our experiment.

4 2D-SIMULATION
To take into consideration the transverse spatial effectin calculation, the simulation code is upgraded to2-dimensional one. The transverse distribution isassumed to be Gaussian. The radiation from each source
spreads spatially. The radiation intensity has spatial
distribution on the detector. Only averaged signal on thedetector can be acquired. The calculated model is shownin Fig. 7.

Electron pulse

4060
bandwidth [nm]

80

100

Fig. 8 Simulation results of 2-dimensional fluctuations

Fig. 6 experimental result

Optical pass

20

DA

5SUMMARY
The lD-simulation of the fluctuation method wasachieved. The measurement of 1.0 ps electron pulses by
the fluctuation method and the comparison with thestreak camera have been done. There was a discrepancyof a few-ps between the two methods. The influence ofthe transverse beam size upon the fluctuation has to betaken into consideration. The simulation is upgraded to2-dimensional one. It is shown that the fluctuation issuppressed as the transverse bunch size increases.
To achieve the quantitative comparison between
calculation and experimental results and improve ouranalysis, we should develop the 3D simulation offluctuation. We also plan to try developing thecalculation and perform the frequency domain
measurement to obtain pulse shape information.

REFERENCEX

radiation

Radiation pointFig. 7 Two-dimensional calculation model
Electric field of radiation is given as the function of x on
the detector. The calculation is done following Eq. (12),[1] M. Uesaka et al., Nuclear Instruments and Methods A 406(1998) 371.
[2] T. Watanabe, et al., Nuclear Instruments and Methods A
437 (1999) 1.
[3] T. Watanabe, et al., Nuclear Instruments and Methods A (inpress).
[4] D. Umstadter, et al., Science. 273 (1996) 472.
[5] E. Esarey, et al., Nuclear Instruments and Methods A 331(1993) 545.
[6] H. Nasr, et al., Nuclear Instruments and Methods A 455(2000) 148.
[7] M. S. Zolotorev and G. V. Stupakov, SLAC-PUB-7132,(1996).

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