Measurement and Timing-Control Techniques of
Femtosecond Electron Pulse
Takahiro Watanabe, Kei Nakamura, Hokuto lijima, Yusa Muroya,
Tomonao Hosokai, Kenichi Kinoshita, Koji Yoshii, Toru Ueda
and Mitsuru Uesaka
Nuclear Engineering Research Laboratory, the University of Tokyo, 319-1188, Ibaraki, Japan
Abstract. Updated techniques and results on the measurement and timing-control of
femtosecond electron pulses are presented. Radiation emitted by an electron pulse was measured
by a femtosecond streak camera, a Michelson interferometer, a 10-channel polychromator and a
fluctuation method in order to estimate a longitudinal pulse shape of the electron pulse.
Measurements by the streak camera, the interferometer and the polychromator agree with one
another within the error of 20 %, while that by the fluctuation method was different. The
numerical simulation explained the reason for it that the transverse emittance of the electron
pulse affects the fluctuation of incoherent Cherenkov radiation. The synchronization of the
electron pulse with the femtosecond laser pulse was also carried out. The timing jitter was 330
fs in rms and the hours-long drift was more than 1 ps. The suppression of the drift is under way
by introducing a stable water cooler (within 0.01 °C) for the accelerator tubes and RF gun, and
an air-conditioner (within 2 °C).
INTRODUCTION
Generation, measurement and control of ultra-short electron pulses are continuing
challenges in accelerators [1], Femtosecond pulses have already been available
via a high-quality beam generation from a photo-injector [2], A brand-new technique,
i.e., a plasma cathode, is expected to reduce the bunch length another order of
magnitude [3,4]. Once such an ultra-short pulse has been generated, one has to verify
the success of the generation by a reliable measurement way. The conventional timedomain technique, such as a streak camera, may not be able to catch up with
the reduction of the pulse duration into 10-femtosecond regime. It is therefore necessary
to develop an alternative measurement scheme. Further, even for the picosecond pulse
that can be measured by the streak camera, it is beneficial to construct a simple and
inexpensive measurement instrument. One more basic technique, i.e. timing-control of
electron pulses, is equally important. The time resolution of the pump-probe experiment
is dominated not by the speed of the mechanical shutter and the detector, but by the
pulse duration and the precision of the timing-control of pulses. In the paper, the
measurement and the timing-control of femtosecond electron pulses are studied.
Incoherent and coherent radiations emitted from an electron pulse are measured by a
several independent techniques and their results are compared with one another [5. 6].
The characteristics and error sources of the four methods are qualitatively discussed.
The timing-control systems for femtosecond laser and electron pulses have been
modified and the improvement is shown.
MEASUREMENT THEORY
Properties of electromagnetic radiation from charged particles depend greatly on the
actual particle density distribution. The spectrum of the radiation from the pulse has a
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
869
cutoff frequency determined by the inverse of the bunch duration. The degree of
coherence changes dramatically across the boundary. The frequency-domain diagnostics
of electron pulses, which are so-called coherent radiation technique, are based on the
finding of the boundary [5-12]. Once one can observe the enhancement of the degree of
coherence, it enables to estimate the bunch duration from the relation between the
wavelength of the cutoff and the bunch duration. Incoherent radiation, which has much
higher frequency of the cutoff, has been used for time-domain diagnostics such as a
streak camera. Such a short wavelength radiation does not provide the information on
the cutoff. However, as M.S. Zolotorev et al. proposed [13, 14], incoherent radiation is
also useful for the frequency-domain measurement. They proposed to observe the
relation between the bunch duration and the spectral width, instead of the frequency
itself. Further, the relation is obtained not directly from the spectrum but from the
statistical analysis of the fluctuation in the spectrum. Here we synthesize the
measurement theories for coherent and incoherent radiations.
The electric field of the radiation pulse E(CD) can be described as the superposition
of radiation emitted from each electron [15]:
p(icott),
(1)
where e(co) is the spectrum from a single electron and N is the number of electrons.
The difference of position of each electron numbered k gives rise to the phase
difference cotk. The first-order spectral correlation function between different energies
can be written as,
where the angular brackets denotes the ensemble average over bunches. By expanding
Eq.(2),
(E(co)E(co')) =
=l
N(N - l}F(co)F*(co'}}.
(3)
Here Aa> = CD - CD' and F is the Fourier transform of the bunch distribution. The
function is connected to the bunch form factor / by \F\2 = f . The first term consists of
a single N and is known to be the incoherent term. The second term is proportional to
the square of N and known to be the coherent term. Another important feature of Eq.(3)
is related to the function F. In the first term, there exists a single F, which is a function
of Ao>. The second term includes two Fs, which is a function of co. These
characteristic features of incoherent and coherent terms reflect the measurement
principles for incoherent and coherent radiation techniques as discussed in the following.
By substituting o) = a)f in Eq.(3), the important equation for the diagnostics using
coherent radiation can be derived as,
The bunch distribution can then be obtained from the bunch form factor f(co) .
Therefore the relation between the bunch duration and the frequency co is the key to the
measurement for coherent radiation. On the other hand, the second term vanishes for the
incoherent radiation. In order to obtain the bunch form factor from the first term in
Eq.(3), one has to introduce the second-order correlation function. By using the Siegert
relation, the second-order correlation function g2(co,co') can be described by the bunch
870
form factor as,
(5)
Eq.(5) gives the understanding of the diagnostic method using incoherent radiation.
Not the power spectrum of incoherent radiation but its correlation or fluctuation carries
the information on the bunch distribution. Further, the important key is the relation
between the bunch duration and the spectral width LCD .
MEASUREMENS USING COHERENT RADIATION
We introduced a Michelson interferometer and a 10-channel polychromator to
resolve coherent radiation. The experimental setup is shown in Fig. 1. Transition
radiation is sent to the two apparatus from the thin-Al radiator. Cherenkov radiation
emitted in air is sent to the femtosecond streak camera by the retractable Al mirror.
Figure 2 indicates the typical output of the two apparatus; (a) the interferogram obtained
by the interferometer (b) output of the polychromator. The reconstruction of the bunch
shape is calculated from the experimental results by using Eq.(4). As one can see in Fig.
3, three bunch distributions obtained from the streak camera, the Michelson
interferometer and the polychromator were compared with each other. As a result, good
agreements within 20 % were obtained.
Streak
Camera
=1——— N^
———————— 1
II
Alfoil
6-stage
x-stage
rn——
4—————— &± \ \ -II LINAC 35L
'\\
1
\^
i
*^°^-^i
> /"^A-^j
v
Oi/ ^^^^\ \ \/
'J
Michelson
Interferometer r^
W
Figure 1. Experimental setup for measurements of electron pulses.
(b)
2.0
0.07
1.5
r
1.0
0.5
0
0.01
-0.5
10
Optical Path Difference (mm)
15
20
25
Wavenumber (cirr
Figure 2. Interferogram and output of the polychromator.
871
30
The good agreement can be obtained only with careful thought of error sources [4],
When the longitudinal bunch form factor fL(o)) is evaluated from the experimental data,
the spectrum from the electron pulse 1(0)), the number of electrons N9 the transverse
bunch form factor / r (o>), the divergence angle of the electron pulse x> and the
spectrum from an electron I0(co) have to be considered as follows:
fT((o)X(N-l)
l0(a>)N
-1
(6)
~ /r(fl>)ArVoM '
All quantities on RHS in Eq.(6) can be an error source. When it is assumed that each
error is much smaller than the actual value, the total error is estimated by,
A/ L (ftj)^ A/(ftj) A/ 0 (ftj) ^AJV AX A/ r (ftj)
(7)
fL(co) * I(co]
I(co)
IIn0(co]
(co)
N
The misalignment of the interferometer or the polychromator yields the error of the
spectrum. The transverse emittance of the electron pulse should be taken into
consideration for the estimation of fT(co) and x- The current error is enlarged twice to
the error of the longitudinal bunch form factor under the assumption of small error. The
spectrum contributed by a single electron, I0(co), is calculated under several
assumptions, such that the radiator is an ideal conductor without dispersion and has a
finite dimension. In consequence, one has to be careful about these factors.
It is worth noticing that all the error factors discussed above does not effect on the
measurement limit. Even though the total error A/ r (o>) exists, the short pulse can be
estimated if the bunch form factor fL(co) is acquired within an appropriate range. The
appropriate range for the bunch form factor is around 0.1 as shown in Ref. [4],
Streak camera
(FWHM = 1.0ps)
Interferometer
(FWHM=1.2ps)
Polychromator
(FWHM=1.0ps)
-
2
0
2
4
Time (ps)
Figure 3. Bunch distributions by three methods.
MEASUREMENTS USING INCOHERENT RADIATION
There have been two remarkable achievements of the experimental results using
incoherent radiation [16,17]. Both of them observed the spectral fluctuation of undulator
radiation. P. Catravas et al., reported first measurements of the full single shot spectra
with 100 % fluctuations and the extraction of the bunch duration [16]. V. Sajaev
872
reported the reconstruction of the bunch distribution from the shot noise [17]. In our
case, the time-integrated power fluctuation of Cherenkov radiation was observed. The
radiation is limited by the band-pass filter and detected by the photo-diode shot-by-shot.
The fluctuations were measured as a function of the bandwidth. The experimental
results are shown in Fig. 4. There were big discrepancies of the bunch duration between
the streak camera and the fluctuation method. The 1.0 ps pulse from the 18 MeV linac
was measured to be 4.5 ps. The 1.5 ps pulse from the 35 MeV linac was measured as 30
ps. In order to investigate the reason for the discrepancies, we developed the threedimensional numerical simulation. The electrons are placed at the three-dimensional
position in the pulse and emit Cherenkov radiation. The radiation can be imaged onto
the focal plane as a ring. The three-dimensional code gives the intensity profile on the
focal plane, from which the intensity fluctuation can be estimated. Here the pulse
duration is 300 fs and the energy is 20 MeV. The total fluctuation as a function of
transverse beam emittance is shown in Fig. 5. One can see in Fig. 5 that the fluctuation
is suppressed as the emittance becomes larger. The enhancement of transverse modes by
the emittance is summarized in Fig. 6. The horizontal line in Fig. 6 indicates the
threshold of the measurable range under the assumption that 10 modes are the largest
transverse size. Consequently, typical emittances of our linacs are found to be out of the
measurable range. The dependence of the transverse emittance upon the transverse
modes of Cherenkov radiation is quite large compared with that of other radiations. It
comes from the fact that Cherenkov radiation is not a spherical wave but a shock wave.
Fluctuations
40
10
100
1000
vi \
1 5ps
- ^3Qps
® Experiirrental data
\
\
10
"^
0
10
">
100
1000
Band width [nm]
Band width [nm]
Figure 4. Power fluctuation of Cherenkov radiation.
Another important feature in Cherenkov radiation is pointed out by M.S. Zolotorev [18].
When Cherenkov radiation is used in the experiment, the radiator length is usually
much larger than the formation zone in order to make the intensity enough large. Then
the electron emits Cherenkov radiation at each formation zone independently, which
suppresses the fluctuation.
The radiation lengths of undulator radiation and transition radiation are equal or
smaller than the formation zone. Hence one can see that these two radiations are more
appropriate than Cherenkov radiation.
873
40
H-\J
Sf
1
3
E
i
30
30
20
20
*
10
10
•
n
0
i
0.1
11
10
0.1
10
Normalized emittance
emittance [p
Normalized
[JT mm.mrad]
mm.mrad]
Figure 5.
5. Fluctuation
Fluctuation as
as aa function
function of
Figure
of normalized
normalized emittance.
emittance.
10000
10000
Available
100
Difficult
18 MeV
linac
35 MeV
linac
10
1
0.001
0.01
0.001 0.01
0.1
0.1
11
10
10
100
100
Unnormalized emittance
emittance [p
Unnormalized
[jt mm.mrad]
mm.mrad]
Figure 6. The number of transverse modes as a function of unnormalized emittance.
Figure 6. The number of transverse modes as a function of unnormalized emittance.
CHARACTERISTICS OF MEASUREMENT METHODS
MEASUREMENT
METHODS
We CHARACTERISTICS
have so far demonstrated theOF
measurements
by the femtosecond
streak camera,
have so interferometer,
far demonstrated
the measurements
by the and
femtosecond
streak method.
camera,
theWe
Michelson
10-channel
polychromator
the fluctuation
the
Michelson
interferometer,
10-channel
polychromator
and
the
fluctuation
method.
Here let us summarize characteristics of these four schemes as shown in Table 1. Since
Here
let us
characteristics
of these four
schemes
as shownconsideration
in Table 1. Since
we have
notsummarize
yet achieved
reliable experimental
results,
the theoretical
and
we
yet achievedbyreliable
experimental
results,
theoretical
and
twohave
othernot
achievements
P. Catravas
et al., [16]
and V.the
Sajaev
[17] areconsideration
referred.
two other
achievements
by
P.
Catravas
et
al.,
[16]
and
V.
Sajaev
[17]
are
referred.
The streak camera and the fluctuation method resolve the incoherent radiation, while
streak camera
fluctuation method
resolve
the incoherent
theThe
interferometer
andand
thethepolychromator
observe
coherent
radiation.radiation,
A single while
shot
the
interferometer
and
the
polychromator
observe
coherent
radiation.
A That
singleof shot
measurement of the pulse duration is available except for the interferometer.
the
measurement
of theispulse
duration
forAlthough
the interferometer.
That ofhas
the
pulse distribution
available
only is
byavailable
the steakexcept
camera.
the streak camera
pulse
distribution
is
available
only
by
the
steak
camera.
Although
the
streak
camera
has
the apparent time resolution of 200 fs, other three methods can measure down to less
the
time resolution
200 important
fs, other three
methods
canfactors
measure
downscheme.
to less
thanapparent
tens of femtosecond.
It isofquite
to know
the error
of each
than
tens
of
femtosecond.
It
is
quite
important
to
know
the
error
factors
of
each
scheme.
The time resolution of the streak camera is distorted by the large light intensity and
The
time resolution
the streak aberrations,
camera is distorted
the large light
intensity and
aberrations
such as ofachromatic
sphericalbyaberrations.
As discussed
in
aberrations
such
as
achromatic
aberrations,
spherical
aberrations.
As
discussedthe
in
Ref.[5], the coherent radiation technique is influenced by the optical alignment,
Ref.[5],
the coherent
radiation
technique
is influenced
by the the
optical
alignment,
the
measurement
of electron
charge,
transverse
beam emittance,
assumption
of the
measurement
electron
charge,
beam
emittance,
the assumption
the
radiation fromofa single
electron,
andtransverse
aberrations.
As for
the fluctuation
method, weofhave
radiation
from a single
electron, and
As for the
method,
have
not investigated
experimentally
yet. aberrations.
One can measure
the fluctuation
bunch duration
withwethreenot
investigated
experimentally
yet.ofOne
can measure
the bunch
duration with
orders
of magnitude
from hundreds
femtosecond
to hundreds
of picosecond
by threeusing
orders
of magnitude
from camera.
hundredsThe
of femtosecond
to hundreds
of picosecond
by using
the femtosecond
streak
coherent radiation
technique
requires that
one
the femtosecond streak camera. The coherent radiation technique requires that one
874
should know the bunch duration in advance so that the bunch form factor should be
around 0.1. The dynamic ranee of the fluctuation method is determined by that of the
spectrometer. The value 10 written in Table 1 is an example. The timing-jitter
measurement is available only in the measurement by the streak camera.
Table 1. Characteristics of measurement schemes.
Radiation
Single shot
(Duration)
(Distribution)
Time
resolution
Error factors
Dynamic
range
Timing jitter
Streak Camera
Incoherent
Interferometer
Coherent
Polychromator
Coherent
Flue. Method
Incoherent
available
available
200 fs
not available
not available
« tens fs
available
difficult
« tens fs
available
not available
« tens fs
Intensity
Aberrations
Alignment
Electron charge
Beam size
Theory
Aberrations
103
10
10
102
available
not available
not available
not available
TIMING CONTROL
Timing-control systems for the linacs and the terawatt lasers have been modified.
The linac is controlled by the photo-injection and the rf in cavities. The laser is
controlled by the timing stabilizer for the oscillator and the pockel's cell. Currently the
timing jitter of the system is 1.9 ps at rms, most of which comes from the drift. It took
two hours to take all data. The instantaneous timing fluctuates 2 ps at peak-to-peak,
which corresponds to 330 fs at rms. Therefore, we have worked for suppression on the
drift. The main factor for the drift is the thermal expansion of the optical table, the wall
and other large devices. Hence a new water cooler for the accelerating tubes and RF
guns supply and a new air-conditioner were introduced. The water temperature is
controlled within 0.01 °C and the air is controlled within 2 °C. As a result, the
compressed electron pulse keeps its duration at least within 30 shots (12 minutes) as
shown in Fig. 7 (a). In the timing-jitter measurement, however, the large drift still
remains as shown in Fig. 7 (b). It took an hour to complete the measurement of 180
shots. The drift can attribute to the 3-m optical delay with 12 mirrors. The optical delay
was installed before the compressor of the injection pulse in order to tune pump- and
probe-pulses at the same timing in the measurement of Fig. 7 (b). Here the bunch
duration fluctuates largely again. The detailed performance of the current timing system
with the temperature control is now under investigation.
875
(a)
(a)
15
10
1
£?!
u
12
1 2 minutes
minutes
<————————————————— >*
5
5
0
~J\^^^^
/
P -5
/
e-bunch duration x 3
-10
-15
0
0
10
20
30
(b)
time difference
difference
(b)
time
e-bunch duration
duration xx 33
e-bunch
hour
30
30r—^———
11 hour
25
20
15
10
5
00
50
100
180
150
150180
Shot number
number
Shot
Shot number
Figure 7. Stability
of the
the timing
timing system,
system. (a)
(a) bunch
bunch duration
duration without
without the
the 3-m
3-m long
long optical
optical delay,
delay. (b)
(b)
Figure
Stability of
bunch duration
duration and
and time
time difference
difference between
between the
the electron
electron and
and the
the laser
laser pulses
pulses with
with the
the 3-m
3-m long
long
bunch
optical delay.
delay.
optical
SUMMARY
SUMMARY
We have
have developed
developed the
the measurements
measurements and
and the
the timing-control
timing-control techniques
techniques of
of
We
subpicosecond electron pulses. The Michelson
Michelson interferometer
interferometer and
and the
the 10-channel
10-channel
results with
with the
the femtosecond
femtosecond streak
streak camera
camera
polychromator provided the consistent results
factors were
were pointed
pointed out.
out. We
We could
could not
not get
get good
good
within 20-% errors. Several error factors
agreement between the streak
streak camera
camera and
and the
the fluctuation
fluctuation method.
method. The
The threethreedimensional numerical analysis showed the
the effect
effect of
of the
the transverse
transverse beam
beam emittance
emittance
upon the fluctuation,
fluctuation, remaining
remaining the
the discussion
discussion on
on the
the formation
formation zone.
zone.
Suppression of hours-long drift
drift in the
the current
current timing
timing system
system is
is under
under way
way by
by
o
running the new water
C) and
and air-conditioner
air-conditioner(within
(within
water cooler
cooler for
for the
the linacs
linacs (within
(within 0.01
0.01°C)
2 o°C).
C). We are still facing
facing with the
the serious
serious drift
drift (>
(> 10 ps
ps for
for 1 hours)
hours) and
and investigating
investigating its
its
source. The timing system has
has already
already been
been supplied
supplied to
to the
the pulse
pulse radiolysis
radiolysis experiment
experiment
for radiation chemistry [19].
for
[19].
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
We would like to thank Y. Shibata, K. Ishi, S. Sasaki,
Sasaki, Y.
Y. Sugiyama,
Sugiyama, T. Yoshimatsu
Yoshimatsu
and Y. Kondo (Tohoku Univ.), M. S. Zolotorev,
Zolotorev, W.P.
W.P. Leemans,
Leemans, P.
P. Catravas,
Catravas, E.
E. Esarey
Esarey
and S. Chattopadhyay (LBNL) for useful
useful supports
supports and
and numerous
numerous discussions
discussions in
in the
the
measurements of electron pulses. We would also
also like
like to
to thank
thank K.
K. Takasago
Takasago and
and K.
K.
Kobayashi (FESTA) for helpful
helpful supports
supports in
in the
the development
development of
of the
the timing-control
timing-control
system.
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