Fundamental Study for Time-Resolved Imaging
by Laser Plasma X-rays
T. Ohkubo, K. Kinoshita, T. Hosokai, Y. Kanegae, A. Zhidkov and M. Uesaka
Nuclear Engineering Research Laboratory, University of Tokyo,
2-22 Shirakata-Shirane, Tokai-mura, Naka-gun, Ibaraki-ken, 319-1188 Japan
Abstract. Laser plasma X-ray, generated from solid targets irradiated by an intense short laser pulse, is an ultra-short
pulse with the time-duration of about 10ps and enables time-resolved measurements. For dynamic imaging using this
laboratory-scale source at Nuclear Engineering Research Laboratory (NERL), University of Tokyo, we have to increase
the X-ray intensity at least ten times more than present 3×104 photons/cm2/shot at a sample. We carried out simulations
of the interaction of a laser pulse with a solid target, which show that the number of hot electrons (>8keV for CuKα
emission) become larger by decreasing the intensity of laser Amplified Spontaneous Emission. We have a plan to take
time-resolved images of laser ablation of solids with the time resolution of 10ps.
results of the interaction of a laser pulse with a solid
target show that the X-ray intensity is considerably
sensitive to a distribution of the plasma density formed
by a long laser pulse (~5ns) of Amplified Spontaneous
Emission (ASE), which is accompanied by the main
pulse [11]. In the present study, we have carried out
measurements of influence of the X-ray CuKα
intensity on the plasma density distribution formed by
the 12TW 50fs Ti:Sapphire laser. It contains the prepulse of ASE with the focused power density of ~1013
W/cm2 and the pulse duration of 5ns. The power
density and pulse duration of the main pulse are ~1019
W/cm2 and 50fs, respectively. Further, we are
calculating the plasma density distribution, using the
hydrodynamics simulation code, HYADES [12]. Then,
by using the code based on the collisional particle-incell (PIC) method [13], we are simulating how many
hot electrons (>8keV for CuKα emission) are
generated from the different initial plasma density
distribution, and investigating its mechanism
quantitatively.
INTRODUCTION
Presently, large demand for hard X-rays (~10keV),
which penetrates through materials, is growing in
various fields such as medicine and nondestructive
testing. Some X-ray imaging techniques have been
developed with the third generation synchrotron
radiation source [1-4]. Accompanying recent
remarkable progresses in the technique of intense
ultra-short pulse lasers, pulse X-ray sources have been
under development [5,6]. Laser plasma X-rays (LPX),
generated from a solid target irradiated by an intense
short laser pulse, is in an ultra-short pulse with the
duration of about 10ps and a variety of time-resolved
measurements become possible. Pump-and-probe
time-resolved X-ray diffraction is used to observe
ultra-fast phenomena and to investigate motions of
atoms or molecules in pico- and subpicoseconds [7-9].
Using this compact source at NERL, University of
Tokyo, we succeeded in obtaining diffraction patterns
indicating atomic motions in a GaAs single crystal
during 300ps [10]. Now we have a plan to apply the
LPX source to time-resolved imaging with the time
resolution of 10ps. For this dynamic imaging, it is
necessary to obtain a single-shot image, namely one
image by one X-ray pulse. However, the low intensity
of CuKα emission, at present 3×104 photons/cm2/shot
at sample, does not allow us to do it. Recent calculated
MECHANISM OF LPX GENERATION
The LPX is generated from a solid target irradiated
by a focused laser pulse, which consists of the ASE
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
811
pre-pulse and the main pulse. First, the pre-pulse heats
the target surface and forms the plasma density
distribution as shown in Fig.1. In this distribution,
there is a critical point where the density is equal to the
critical density n cr = 4π 2 ε 0 m e c 2 λ L 2 e 2 where λ L
is the laser wavelength, ε 0 the vacuum permittivity,
m e the electron mass, e the elementary charge, c the
speed of light in vacuum. Second, at this point, the
following main pulse provides its energy to the plasma
on account of resonant absorption and produces hot
electrons, which interact with atoms of the target. Then,
these electrons emit continuous X-rays due to
Bremsstrahlung radiations, while they bring about
inner-shell excitation of target atoms and characteristic
X-rays are emitted by the transition from the excited
state to the ground state.
FIGURE 2. Schematic view of the experimental setup for
the radiography by the imaging plate and the X-ray intensity
measurement with the X-ray PIN photodiode.
Electron Density [/cm3]
1E+24
1E+23
1E+22
Critical
Point
(a)
1cm
(b)
1cm
Critical
Density
400µm
1E+21
470µm
1E+20
-50
0
50
100
Distance from Target Surface [μm]
FIGURE 1. Typical electron density distribution of the
plasma produced by the ASE pre-pulse with the power
density of 1013 W/cm2, at 2.5ns from the beginning of the
pre-pulse irradiation, with the copper target. At the critical
point, the main pulse energy is absorbed into the plasma due
to resonance of the laser frequency with the plasma
frequency.
(c)
1cm
Scattering X-rays
Direct X-rays
EXPERIMENT
200µm
FIGURE 3. Radiographs of (a) a LAN cable, (b) a floppy
disk and (c) a leaf, obtained by 300 pulses of the LPX. Inner
wires of 400µm thickness and the vains of the leaf of 200µm
thickness can be seen. The direct X-rays is twice more
intense than the scattering X-rays.
Using the LPX source with a copper target, we
obtained some radiographs and measured the intensity
of the X-rays of only CuKα1 (8.04778keV) and CuKα2
(8.02779keV) by the X-ray PIN photodiode. Fig.2
shows the schematic view of the experimental setup.
The pulse of the Ti:Sapphire laser (790nm, 50fs, 10pps,
3TW) is introduced into the vacuum chamber and is
focused onto the copper target with the off-axis
parabolic mirror in order to generate an X-ray pulse
that is used for radiography. Moreover, we select
CuKα1 and CuKα2 via Bragg diffraction by the LiF
crystal (200) and measure the intensity of those by the
X-ray PIN photodiode outside the chamber.
Radiographs shown in Fig.3 are obtained by 300
pulses of the LPX instead. In the radiographs of (a) a
LAN cable and (b) a floppy disk, inner wires with the
thickness of 400µm appear through the plastic part.
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main pulse energy. HYADES code solves the
following equations in the Lagrangian coordinate
system,
The vains of the leaf of 200µm thickness is resolved
clearly in (c). The intensity of the direct X-rays is
twice more than that of scattering X-rays in the
chamber. The spatial resolution of this radiography
system is about 200µm. Based on these images and
some others, we conclude that a metallic sample and a
biological one make clear contrast by ~10 shots and
~100 shots, respectively. So, we need the X-ray
intensity ten times more even for the metallic and a
hundred times more for the biological. As a
preliminary experiment to enhance the X-ray intensity,
we formed ~100nm thick gold film by the vacuum
evaporation onto the copper target. Then we make
different distribution of the plasma density, which is
very sensitive to the X-ray intensity. Fig.4 shows the
number of photons per shot generated from the copper
target with the gold film by the vacuum evaporation,
changing the plasma density distribution (cross) and
without that (circle), measured by the X-ray PIN
photodiode. The X-ray intensity has slightly decreased
with the film. This result of the measurements agrees
with the calculated one as shown in the next chapter.
the equation of continuity;
Dρ
(1)
= − ρ∇ ⋅ u ,
Dt
the equation of motion;
Du
1
= − ∇P ,
(2)
ρ
Dt
the equation of state;
(3)
P = f (ρ, T ) ,
the energy equation;
DP
(4)
= −γP∇ ⋅ u + ρ (γ − 1) S ,
Dt
where ρ is the density, u the velocity, P the
pressure, γ the specific heat ratio and S the heating
term. Time-differentiation in the Lagrangian
coordinate system is described as D Dt = ∂ ∂t + u ⋅ ∇ .
Fig.5 shows the calculated result of the plasma density
distribution formed by the ASE pre-pulse with the
power density of 1013 W/cm2, at 2.5ns from the
beginning of the pre-pulse irradiation. The plasma of
the gold target spread a little more than that of the
copper one. At this point, we should apply these
distributions to the PIC calculations. However, owing
to the large spread of these distributions, we cannot put
as many cells as sufficiently. Then, other four
distributions as shown in Fig.5 are employed as the
initial conditions for the PIC calculations. In the PIC
4E+09
3E+09
Cu
Au
2E+09
1E+24
1E+09
0E+00
2E+18
3E+18
4E+18
Laser power density [W/cm2]
Electron Density [/cm3]
X-ray intensity [photons/shot]
5E+09
5E+18
FIGURE 4. Number of photons per shot generated from the
copper target with the gold film by the vacuum evaporation,
changing the plasma density distribution (cross) and without
that (circle), measured by the X-ray PIN photodiode. The Xray intensity has slightly decreased with the film.
Au
Cu
(a)
(b)
(c)
(d)
1E+23
1E+22
Critical
Density
1E+21
(d)
SIMULATION
1E+20
-10
For the CuKα emission, the electron energy has to
become more than 8keV by resonant absorption of the
main pulse. As a matter of course, hotter electrons
produce more CuKα X-rays. We use the two codes, the
HYADES [12] to calculate the plasma density
distribution formed by the ASE pre-pulse and the
collisional particle-in-cell (PIC) code [13] to simulate
the electron dynamics due to the absorption of the
0
(a)
(c)
(b)
10
20
30
Distance from Target Surface [μm]
FIGURE 5. Numerical result of the plasma density
distribution by HYADES code with the pre-pulse power
density of 1013 W/cm2, at 2.5ns from the beginning of the
pre-pulse irradiation, with the gold target (dotted line) and
the copper one (solid line). The other four distributions (fine
lines) are the initial conditions for the PIC calculations,
named (a), (b), (c) and (d) in order of length of the plasma.
813
simulation, the following Langevin equation


p
dp k
= q k E(rk ) + k × H (rk ) + Pk (v k )
γ kc
dt


2 4
2
γ k = M k c + c pk
momentum, the position, the charge and the mass of
particle, E and H are the electric and the magnetic
fields, and Pk ( v k ) is the collisional term, respectively.
The outputs of the electron distributions with the main
pulse power density of 1019 W/cm2, just after the end
of the main pulse irradiation, are shown in Fig.6. As
the initial plasma distribution is spread, the electron
energy decreases. However, there is no clear
difference between (c) and (d). Therefore, we should
control the plasma distribution as (c) for the increase
of the X-ray intensity. We are going to calculate
CuKα1 and CuKα2 emissions by the Monte-Carlo code
for the atomic process soon later.
(5)
2
of 1D in space and 3D in velocity is solved under nonlocal thermodynamic equilibrium (non-LTE). It takes
into account the interaction of the plasma with the
main pulse, where p k , rk , q k and M k are the
Electron distribution [a.u.]
1E+00
(a)
(b)
(c)
(d)
1E-01
1E-02
SUMMARY AND SUBJECTS
1E-03
For the time-resolved X-ray imaging with the timeresolution of 10ps using the LPX source, we carried
out the measurements. The X-ray intensity is 3×104
photons/cm2/shot at the sample presently. We
simulated the interaction of a laser pulse with a solid
target, which show that the electron energy decreases
as the initial plasma distribution is spread. Decreasing
the ASE intensity, we can control the plasma
distribution as shown in Fig.7, and increase the X-ray
intensity. It allows us to obtain the single shot image
and to realize the dynamic imaging in picoseconds.
We will measure the intensity and pulse duration of
the ASE by cross-correlator and the X-ray pulse
duration by X-ray streak camera very soon.
Furthermore, we will apply the LPX source to timeresolved imaging of laser ablation of solids with the
time-resolution of 10ps.
1E-04
1E-05
0
20
40
60
80
Electron energy [keV]
100
FIGURE 6. Numerical results of the electron distributions
by the PIC simulation with the main pulse power density of
1019 W/cm2, at the time of just after the end of the main
pulse irradiation, corresponding to the four distributions of
(a) to (d) as shown in Fig.5. The distribution of (c) and (d)
show more hot electrons comparing to that of (a) and (b).
Electron Density [/cm3]
1E+24
1E+13
1E+12
1E+11
1E+23
REFERENCES
1. A. Momose, et al., Radiology 217, 593 (2000).
2. P. Cloetens, et al., Appl. Phys. Lett. 75, 2912 (1999).
3. Y. Kagoshima, et al., Jpn. J. Appl. Phys. 39, L433 (2000).
4. M. Tegze, et al., Nature 407, 38 (2000).
5. T. Guo, et al., Rev. Sci. Instrum. 72, 41 (2001).
6. M. Yoshida, et al., Appl. Phys. Lett. 73, 2393 (1998).
7. C. Rose-Petruck, et al., Nature 398, 310 (1999).
8. C. Rischel, et al., Nature 390, 490 (1997).
9. K. A. Nelson, Science 286, 1310 (1999).
10. K. Kinoshita, et al., Laser and Particle Beams 19, 125
(2001).
11. A. Zhidkov, et al., Phys. Rev. E 62, 7232 (2000).
12. J. T. Larsen, et al., J. Quant. Spectrosc. Radiat. Transf.
51, 179 (1994).
13. A. Zhidkov, et al., Phys. Rev. E 59, 7085 (1999).
1E+22
Critical
Density
1E+21
(d)
1E+20
-10
0
(a)
(c)
10
(b)
20
30
Distance from Target Surface [μm]
FIGURE 7. HYADES outputs of the plasma density
distributions with the ASE pre-pulse power density of 1013
W/cm2 (black dotted line), 1012 (gray dotted line) and 1011
(light gray dotted line) together with the inputs for the PIC
simulation. The pre-pulse with the intensity of 1011 may give
appropriate distribution.
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