1. INTRODUCTION
The success of inertial fusion energy depends, to a large degree, on a
detailed understanding of material properties under extreme conditions,
and the ability to manufacture sophisticated targets (Borisenko et al., 2003; Sadot et al., 2003). Laser interactions with
low-density plastic foams of supercritical density, with electron density
ne in the fully ionized and homogenized foam, greater
than the laser critical density, are important, as foam layers can be used
for improvement of the spherical symmetry of direct-drive inertial fusion.
Most approaches to implosion symmetry improvement are based on smoothing
of laser imprint by thermal conductivity, in a relatively thick,
relatively hot low-density outer layer of the target (Desselberger et al., 1992; Gus'kov et al., 1995; Gus'kov, 2005). An alternative approach to the
mitigation of laser imprint is based on density tailoring of a layered
target, consisting of low-density porous matter on top of a higher-density
payload. A distant laser prepulse is used here as a shaping pulse that can
provide impedance matching between foam and payload, and thus,
Rayleigh-Taylor instability is suppressed (Metzler
et al., 1999). While many experiments (Hall et al., 2002) use foams with micron or
submicron pore size, interactions of laser pulses several nanosecond long,
with foams of typical pore, and radius comparable or greater than 10
μm, was studied in other experiments (Gus'kov et al.,
1996, 1999, 2000; Caruso et al.,
2000). This study succeeds our previous work (Kalal et al., 2003), and the distinctive
feature of these experiments is the interaction of subnanosecond laser
pulses with foams containing large pores, when laser pulse is shorter than
the time needed for full homogenization of the foam matter.
The main goal of our work is to study energy transport through
low-density porous matter and to demonstrate a sufficient efficiency of
thin foil acceleration, together with a substantial smoothing effect of
the low-density foam absorber. The experimental setup will be explained in
Section 2, while the results of X-ray and optical diagnostics are
presented and discussed in Section 3. Our two-dimensional hydrodynamic
simulations are described in Section 4, where analytical estimates are
also presented, and compared with experiments and simulations in Section
5. The conclusions are drawn and discussed in the last section.
2. EXPERIMENTAL SETUP
Experiments were conducted on the PALS iodine laser facility in Prague
(Jungwirth et al., 2001; Jungwirth, 2005). The laser provided 400 ps (FWHM)
pulses with energy up to 600 J at the basic frequency (λ1 =
1.32 μm). The laser was incident normally on the target; the best
radius focus spot was RL ≈ 40 μm.
Here, the target was placed out of the best focus, and the laser spot
radius RL ≈ 150 μm was used. Thus, the
laser spot radius, RL, is large compared to
the pore diameter Dp. Laser irradiances were
varied from I ≈ 1014 W/cm2 to
I ≈ 1015 W/cm2. No method of optical
smoothing was used, the laser beam focus was not quite uniform, and
contained small-scale intensity non-uniformities.
Several types of foam targets were used. Most experiments were done
with thick layers of polystyrene foam, with density in the range of
8–10 mg/cm3, and typical pore diameter,
Dp ≈ 50–70 μm. Other polystyrene
foams of density ρ ≈ 30 mg/cm3, with pore diameter
Dp ≈ 10 μm, and also of ρ ≈ 20
mg/cm3, and Dp ≈ 5 μm,
as well as polyvinylalcohol (PVA) foam of density ρ ≈ 5
mg/cm3, and of typical pore diameter
Dp ≈ 5 μm were used. A 2 or 0.8 μm
thick aluminum foil was placed at the foam rear side in the majority of
foam targets.
The diagnostic system included observation of target emission and
target optical probing. Side-view slit image of plasma emission in the
X-ray region (photon energy > 1.5 keV) was observed, with the KENTECH
(low magnification) X-ray streak camera. The temporal resolution was
either 30 or 70 ps, spatial resolution of 50 μm, was in the direction
normal to the target surface (target depth). We present here also
preliminary results on measurement of shock wave arrival at the target
rear side via self-emission observed by optical streak camera. Optical
interferometer and shadowgraphs were carried out by means of a three-frame
interferometer system with automated image processing technique, described
in detail by Pisarczyk et al. (1994).
Each of the three recording channels was equipped with a CCD camera
(Pulnix TM-1300), with a matrix of 1300 × 1030 pixels. The
diagnostic system used a probing beam at the third harmonic frequency with
similar, but slightly shorter pulse duration than that of the main beam.
Interferogram processing included parasitic noise filtering, comparison of
object and reference interferograms, and a subsequent reconstruction of
radial electron density distributions.
3. EXPERIMENTAL RESULTS
The target self-emission was imaged (magnified 11-fold) by 50 μm
wide slit, providing a spatial resolution along the target depth, on the
entrance slit of X-ray streak camera. The recording channel included 17
μm of Mylar and 40 nm of aluminum, the transmission was negligible for
photons of energy ≤1.1 keV, while the transmission was approximately
20% for 1.7 keV photons. As plastic foams containing only light elements
were used, the amount of X-ray emission was rather low. The only usable
pictures (weak, but significantly above X-ray streak sensitivity limit)
were recorded for the foams with the largest pore diameter (50–70
μm). From the recordings presented in Figure
1, the upper estimate of the laser penetration depth is about 120
μm of the immediately heated layer. The laser penetration is
consequently no more than two pore layers in this foam. Later, heat wave
propagates into the foam material with velocity of approximately 1.4
× 107 cm/s, and the rear side of the heated X-ray
emitting area is denoted by a solid white line in Figure 1. The X-ray signal lasts for nearly 3 ns, the
X-ray emitting zone covers only about two-thirds of the foam thickness,
and no emission near the Al foil at the target rear side is detected.
X-ray streak record of lateral slit picture of interaction of 400 ps
iodine laser (λ = 1.32 μm) pulse of energy 92 J and beam radius
150 μm with 400 μm thick polystyrene foam of density ρ ≈ 9
mg/cm3 and pore diameter Dp
≈ 50–70 μm, 2 μm thick Al foil is placed at the target
rear side.
Experimental sequences of three interferometric pictures taken in one
laser shot are presented in Figure 2. A sharp
rear boundary of 400 μm-thick polystyrene target with 2 μm Al foil
is observed, with no signs of low density plasma behind the target. On the
other hand, 0.8 μm-thick Al foil at the rear side of 100 μm-thick
PVA foam is heated and its expansion is later apparent.
Sequence of 3 interferograms recorded in one shot in time instants 1,
4, and 7 ns after the main 400 ps FWHM laser pulse maximum. Laser
wavelength 1.32 μm and beam radius 150 μm on the targets.
Parasitic effects of the target holder are denoted in the left pictures.
(a) Polystyrene foam of ρ ∼ 9 mg/cm3,
Dp ∼ 50–70 μm, 400 μm thick
and 2 μm thick Al foil at its rear side. Laser energy 173 J.
(b) PVA foam of ρ ∼ 5 mg/cm3,
Dp ∼ 5 μm, 100 μm thick and 0.8
μm thick Al foil at its rear side. Laser energy was 238
J.
The position of point P (rear side opposite to the laser beam
centre) is measured with the precision of 5–10 μm; the results
are summarized in Figure 3. The speed of the
accelerated Al foil can be determined from the difference in point
P positions in different frames. The speed of accelerated foil
grows with the laser energy. Foil acceleration during the laser pulse is
inferred for 100 μm thick PVA foam. For 400 μm-thick polystyrene
foams, the shock wave reaches the foil only 2 to 4 ns after the laser
pulse, and the delay decreases with laser energy. The above delay is
larger by about 2 ns than in simulations for homogeneous material of the
same density as the foam, and the difference is tentatively explained by
foam homogenization process.
Experimentally measured position of point P versus time after the
laser pulse maximum for two laser energies and 2 μm Al foil on
polystyrene foam of ρ ≈ 8–10 mg/cm3, pore
diameter Dp ≈ 50–70 μm and
thickness Δ = 400 μm. Points are also plotted for 0.8 μm Al
foil on PVA foam of ρ ≈ 5 mg/cm3,
Dp ≈ 5 μm, Δ = 100 μm and
laser energy 238 J.
In order to verify the measurement of time and form of the shock wave
arrival on the target rear side, we conducted preliminary experiments
where self-emission in the normal direction from the target rear side was
imaged (with magnification of 10) on the entrance slit of an optical
streak camera. The result is presented in Figure
4 where the absolute timing of the shock wave arrival is determined
by the fiducial in the left upper corner. The shock wave arrival delay
grows smoothly with the distance from the central point. No macroscopic
spatial features are registered, which is also consistent with smooth
shape of the accelerated part of the foil observed in optical
interferometer. This preliminary measurement was carried out during other
experiments on the PALS laser and third harmonics frequency of iodine
laser was used. Consequently, direct comparison of this measurement with
the other results presented here is not possible due to different
experimental conditions. However, the delay in shock wave arrival on the
target rear side is considerably smaller than in interferometric
measurements conducted for the laser basic frequency. This is tentatively
explained by the fact that the foam used is underdense for the third
harmonic of iodine laser while it is overdense for the laser basic
frequency.
Optical streak record of self-emission of the target rear side with
fiducial in the upper left corner. Third harmonic of iodine laser pulse
(wavelength λ = 432 nm, energy EL = 264
J, pulse length 350 ps FWHM) is focused to a spot of radius 200 μm on
700 μm thick polystyrene foam of density ρ ≈ 9
mg/cm3 and pore diameter Dp
≈ 50–70 μm, 5 μm thick Al foil is placed at the target
rear side. Time zero denotes laser pulse maximum.
4. COMPUTATIONAL SIMULATIONS AND ANALYTICAL
MODEL
Simulations were performed in cylindrical geometry by two-dimensional
Lagrangian hydrodynamics code ATLANT-HE, including advanced treatment of
laser propagation and absorption (Iskakov et
al., 2003). The code does not take into account fine scale
structure of the foam and thus the time of the hydrothermal wave transit
through the foam may be underestimated.
The calculated laser absorption was approximately 50%. Plasma radius
essentially exceeds the laser beam radius on the target (radius of laser
produced plasma reaches approximately 1000 μm for laser beam of radius
150 μm on the target) due to fast lateral heat transport in the
low-density porous matter. A smooth shape of the accelerated foil is
observed in simulations with the width considerably larger than the laser
beam diameter. The fast electrons do not preheat unevaporated Al layer in
simulations significantly for the laser intensities ≤ 1015
W/cm2.
Analytical model is based on the assumption of spherical hydrothermal
wave (Gus'kov et al., 2000)
propagating from laser absorption region. Time instants when the
hydrothermal wave reaches the target rear side are in a good agreement
with numerical simulations. However, the experimental time delays are
about 2 ns greater for 400 μm thick polystyrene foam. According to our
opinion, such a fact is caused by the direct influence of the initial
structure of foam on the target dynamics. The pressure accelerating the Al
foil is calculated and the derived hydrodynamic efficiency is η ≈
0.12.
The foil velocities measured in the experiment, calculated in our
simulations, and via analytical model are compared in Table 1. The Al foil in PVA foam target is heated up
to 800 eV in the simulations and its expansion leads to an excessive
velocity of the rear boundary.
(CH)n is 400 μm thick polystyrene foam of density 9
mg/cm3 with 2 μm Al foil and PVA is 100 μm thick
PVA foam of density 5 mg/cm3 with 0.8 μm Al foil.
Experimental and simulation velocities are represented by average values
in the interval 4–7 ns after the laser maximum
5. CONCLUSIONS
Interactions of laser beam of iodine laser “PALS” with
low-density foam targets have been investigated, both experimentally, and
theoretically. The speed of the heat wave inside polystyrene foam was
estimated to be ∼ 1.4 × 107 cm/s from the X-ray
streak measurements.
Velocities of the accelerated foil at the target rear side, measured
by three-frame optical interferometer, are in a good agreement with our
two-dimensional hydrodynamic calculations, and with analytical model.
However, a delay in the shock wave propagation in the foam is observed in
our experiments in comparison with our theoretical calculations that do
not take foam structure into account. This is explained here by the
phenomenon of non-equilibrium foam homogenization. This delay may
influence laser imprint mitigation. A smooth arrival of the shock wave on
the target rear side detected by optical streak camera is in agreement
with a smooth shape of the accelerated foil observed
interferometrically.
ACKNOWLEDGMENTS
This work was partly funded by project INTAS-01-572 and by IAEA
Research Project No. 11655/RBF. Partial support of the Czech
participants by the Czech Ministry of Education, Youth and Sports under
project LNA00100 “Laser Plasma Research Centre” is gratefully
acknowledged. The authors thank Dr. Dimitri Batani for his kind assistance
in preliminary optical streak measurements, and to the PALS staff for an
excellent experimental support.
