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Stable femtosecond X-ray generation through Thomson scattering Stable femtosecond X-ray generation through Thomson scattering
Fumio Sakai, Jinfeng Yang, Masafumi Yorozu, Yasuhiro Okada, Tatsuya
Yanagida
Sumitomo Heavy Industries, Ltd., Ltd., 2-1-1 Yatocho, Nishitokyo, Tokyo 188-8585,
Japan
Shinji Ito, Kazuya Takasago, Akira Endo
The Femtosecond Technology Research Association, 5-5 Tokodai, Tsukuba, Ibaraki 300-
2635, Japan

Femtosecond X ray pulses were generated through Thomson scattering between a few
picosecond electron bunches and 100fs Ti:sapphire laser lights in a 90-degree interaction
configuration. Electron bunches were generated from a photocathode RF gun with a copper
cathode. The electron bunches (0.5nC/pulse) were accelerated to 14MeV by a linac and
focused by quadrupole magnets to a beam radius of 100
µ
m (rms). The energy and pulse
duration of the Ti:sapphire laser used for the scattering experiments were typically 50mJ and
100fs. The femtosecond X-ray beam was observed by a micro-channel plate. The number of
X-ray photons generated at the interaction points was estimated to be 1.4x10
4
. The energy and
pulse width of the X-ray beam were calculated as 2.3keV and 400 fs (rms) using the
measured beam parameters of the electron and the laser beams, respectively. The system was
operated at 10Hz with good pulse-to-pulse stability.
PACS Codes: Femtosecond x-ray, Thomson scattering, photocathode, femtosecond laser

1. Introduction
A short pulse X-ray source is an important tool for studying the dynamics of materials in the
fundamental time scale. The development of femtosecond lasers made it possible to study short
time reactions in the femtosecond region. However, this optical probe is limited to studying
extended electronic levels in solids due to the low photon energy. X-rays are important probes
for studying the structure of solids through their interactions with core electronic levels in atoms.
A femtosecond X-ray pulse can be used to observe structural dynamics on a femtosecond time
scale by utilizing various techniques, such as X-ray diffraction and extended x-ray absorption fine
structure (EXAFS). The short pulse X-ray is also useful for industrial applications such as non-
destructive inspection of high-speed rotating materials, and for medical imaging applications.
A femtosecond X-ray pulse was generated by 90-degree Thomson scattering between a tightly
focused electron beam and a femtosecond laser light
1
. The generation of X-rays through
Thomson scattering between relativistic electrons and short-pulse laser light has some
advantages, such as good directional radiation, high brightness, wavelength tunability of and a
short-pulse in the picosecond and femtosecond regions. The generation of a femtosecond X-ray
pulse requires femtosecond laser pulses in 90-degree scattering geometry with a picosecond-
duration electron beam pulse, or in a normal incidence with femtosecond electron pulses. The
beam sizes of both the electron and laser pulses must be small in the 90-degree configuration to
reduce the interaction time between the electron and laser pulses to the femtosecond region.
We developed a stable high-brightness electron beam
2
and a stable femtosecond tera-watt laser.
3

We successfully performed the first X-ray generation by Thomson scattering, using a picosecond
laser to confirm the performance of the whole system without the femtosecond laser.
4
A
femtosecond X-ray was generated by a 90-degree collision using the femtosecond laser and
presented in this paper.
The theoretical background of Thomson scattering between relativistic electron beams and laser
beams is reviewed in the next section. The experimental system and the recent results of femtosecond X-ray generation in the 90-degree configuration are then presented and discussed as
well as the stability of the scattering X-ray.

2. Theoretical Background
In Thomson scattering between a relativistic electron pulse and a laser light, the energy of the
scattered photons under the Thomson limit ( Ep<<mc
2
) is given by
3

Ep
Ex
)
cos(
1
)
cos(
1
=
(1)
where Ex is the energy of the scattered X-ray photon, Ep is the energy of the incident laser light
photon,

is the incidence angle between the laser light beam and the electron beam in the
laboratory frame, is the emitting angle between the X-ray and the electron beam, m is the
electron mass, is the ratio between v (the electron velocity) and c (the velocity of light). The
coordinate system is defined in Fig. 1, where =180 indicates a head-on interaction and = /2
indicates a 90-degree interaction. The maximum energy of the photon ( 2 2
Ep for
=90
and
4 2
Ep for
=
180, where

is a Lorentz factor) is obtained when =0
The number of X-ray photons produced by Thomson scattering in the laboratory frame is given
by L
dt
dN
x
=
(2)
where represents the total cross section of the Thomson scattering and, L is the luminosity,
determined by the collision geometry of the electron pulse and laser light pulse. The luminosity
represents the density of the electrons and laser photons in the overlapping volume between the
electron pulse and laser light pulse.
The pulse length of an X-ray generated by Thomson scattering is determined by the interaction
time between the electron pulse and the laser pulse. We assume that both the electron and laser
light profiles satisfy the Gaussian profile. The pulse length of a scattering X-ray in a 90-degree
interaction is given by
5

2
2
2
2
2
2
2
Lp
Le
Wp
We
Lp
Wp
We
Le +
+
+
+
+
= .
(3)
The pulse length of the electrons exceeds the other parameters in many cases. Equation (3) is
represented as
2
2
2
Lp
Wp
We
x
+
+
=
for Le2 >> We2+ Wp2+ Lp2
. The laser pulse length is
typically 100fs for a Ti:sapphire, thus, it is very important to focus the electron beam and laser
beam tightly to generate a femtosecond X-ray pulse.
The stability of the X-ray is dependent on the stability of the electron and the laser beam
parameters. The luminosity in the laboratory frame is expressed
5
by
)
)(
2
(
sin
)
)(
2
(
cos
2
2
2
2
2
2
2
2
Lp
Le
Wp
We
Wp
We
L
e
N
N
L
+
+
+
+
=
(4)
where Ne is the number of electrons and, Np is the number of laser photons. The fluctuation of
the number of X-ray photons due to the fluctuation of the beam parameter is derived by
differentiating eq.(4) and is expressed for a 90-degree collision ( =90) by

Ne
Ne
Nx
Nx
=
(5) Np
Np
Nx
Nx
=
(5)








+
+
+
+
+ =
We
We
Lp
Le
Wp
We
We
Wp
We
We
Nx
Nx )
(
)
(
2
2
2
2
2
2
2
2
(6)
Equation (5) indicates the effect of the electron beam size fluctuation. If
We
and
Wp
are
exchanged, eq. (5) shows one of the laser beam size fluctuation. If
Le
and
Lp
are zero, eq.(6)
represents the effect in the head-on collision.
The X-ray intensity is determined by the luminosity of the interaction between the electron and
the laser beams. The intensity of an X-ray with y displacement between the electron and laser
beams is expressed by eq. (6). The intensity of an X-ray in a 90-degree collision with x
displacement between the electron and laser beams is expressed by eq. (6).





+ =
)
(
2
exp
)
(
2
2
2
0
Wp
We
y
N
y
Nx
(7)




+
+
+ =
)
(
2
exp
)
(
2
2
2
2
2
0
Lp
Le
Wp
We
x
N
x
Nx
(7)
where N
o
is the number of scattering X-rays when y=0 and x=0. Equation (7) represents the
X-ray intensity in a head-on collision if
Le
and
Lp
are zero,
We consider the X-ray intensity with a time delay ( t) in the same way as eq. (7) and it is
expressed by




+
+
+ =
)
(
2
)
(
exp
)
(
2
2
2
2
2
0
Lp
Le
Wp
We
t
c
N
t
Nx
(8)
The fluctuation of Nx is estimated from eqs. (7)-(8) and the fluctuation of the parameters, x, y
and t. As can be seen from eqs.