M. KOENIG1, T. VINCI1, A. BENUZZI-MOUNAIX1, S. LEPAPE1, N. OZAKI1,7, S. BOUQUET2, L. BOIREAU2,3, S. LEYGNAC3, C. MICHAUT3, C. STEHLE3,
J.-P. CHI `EZE4, D. BATANI5, T. HALL6, K. TANAKA7and M. YOSHIDA8 1Laboratoire pour l’Utilisation des Lasers Intenses, CNRS-CEA-Universit´e Paris VI-Ecole
Polytechnique, Palaiseau, France
2D´epartement de Physique Th´eorique et Appliqu´ee, CEA-DIF, BP 12, Bruy`eres-le-Chˆatel, France 3Laboratoire de l’Univers et de ses Th´eories, Observatoire de Paris, Meudon, France
4CEA – Saclay, DSM/DAPNIA and DSM/DRECAM, Gif-sur-Yvette Cedex, France 5Dipartimento di Fisica ‘G. Occhialini’, Universit`a di Milano-Bicocca and INFM, Piazza della
Scienza 3, Milano, Italy
6University of Essex, Colchester CO4 3SQ, United Kingdom
7Institute of Laser Engineering and the Graduate School of Engineering, Osaka University,
Osaka, Japan
8National Institute of Advanced Science and Technology (AIST), Tsukuba, Japan (Received 21 April 2004; accepted 6 June 2004)
Abstract. We present the set-up and the results of a supercritical radiative shock experiment performed
with the LULI nanosecond laser facility. Using specific designed targets filled with xenon gaz at low pressure, the propagation of a strong shock with a radiative precursor is evidenced. The main measured quantities related to the shock (electronic density, propagation velocities, temperature, radial dimension) are presented and compared with various numerical simulations.
Keywords: radiative shocks, laser plasmas
Radiative hydrodynamic processes (Mihalas and Mihalas, 1984; Zeldovich and Raizer, 1967) are very important in several physics areas such as ICF (Lindl, 1995) and astrophysics (Drake et al., 2002). Recently, several experiments have been per-formed to simulate radiative hydrodynamic flows of astrophysical interest like jets or blast waves (Edwards et al., 2001; Grun et al., 1991; Lebedev et al., 2002) and radiative shocks (Bouquet et al., 2004; Bozier et al., 1986; Keiter et al., 2002). In most astrophysical environments, a radiative shock (RS) is essentially character-ized by: 1) a hot ioncharacter-ized precursor in the upstream material, heated by radiation coming from the high temperature shocked gas, 2) a shock front followed by a short extension region where relaxation between ions, electrons and photons takes place, and 3) a recombination zone in the downstream flow. In the vicinity of the shock
and, provided its velocity is sufficiently high, Dcr, the precursor is heated up to a
temperature Tcrequal to that of the shocked material. Shocks satisfying D > Dcr
are often called “supercritical” (Zeldovich and Raizer, 1967). The understanding of the properties and structures of these shocks are very sensitive to the treatment
Astrophysics and Space Science 298: 69–74, 2005. C
of radiation transport and to its coupling with hydrodynamics. Consequently, labo-ratory experiments are relevant benchmarks for modeling as well as for validating theoretical predictions.
In order to be in the radiative regime, we first designed our target characteristics according to semi-analytical models such as the supercritical shock (Zeldovich and Raizer, 1967) or the steady radiative shock (Boireau et al., 2003; Bouquet
et al., 2000). The critical velocity, Dcr , above which a radiative shock enters the
supercritical regime is given by power laws Dcr≈ρa/Abwhereρand A are mass
density and atomic number respectively.
To strengthen radiative effects against thermal ones, a low-density material, with high atomic mass, is suitable to achieve radiative regime. Previous experi-ments, have shown that shock velocities about 50 km/s in a low density medium are achievable with the LULI nanosecond laser facility (Koenig et al., 1999). Accord-ing to the power laws mentioned above it is, therefore, quite appropriate to generate supercritical shocks in low density xenon gas (0.1 and 0.2 bar). The quantitative design of the whole experiment has been carried out with radiation hydro-codes. An optimized three layer-pusher drives the shock into the xenon gas cell. This pusher
is made of a 2µm CH ablator, a 3µm Ti X-rays screen and a 25µm CH foam
accelerator.
Our main goals regarding the experimental diagnostics were to focus on the time-dependent properties of the radiative shock and precursor. It concerns namely piston and shock velocities (Up, Us), precursor velocity (Vp), electron density in the
precursor (Ne), their radial extension (R) and the electron temperature (Te). In order
to fulfilled these goals, we implemented several diagnostics as shown in Figure 1. The self-emission diagnostic records time evolution of the emitted light from the
rear surface of the target and gives the temperature (Te). Two VISAR (Celliers et al.,
1998), with different sensitivities measure the shock velocity in the foam and/or
the foam-xenon interface velocity (Up). Finally, a Mach-Zehnder interferometer is
implemented to determine Us, Vpand Ne. Two streak cameras are used, one looking
at the fringes longitudinally (LONG), the other one providing a transverse image at a given position in the gas (TRANS) leading to the determination of the radius
R (Figure 1b). Electronic densities ranging from 1018to 1020cm−3in the precursor can be inferred from the interferometer. With the VISAR, we measured on some
shots the piston velocity Up (foam/gas interface), which drives the shock in the
xenon as pointed out in recent papers (Bouquet et al., 2004).
From measured Up, using SESAME EOS tables (1992) we deduced the shock
velocity Us which mean value was roughly 67 km/s with modulations at the shock
breakout during 1 ns (due to a reflection on the pusher interfaces) and a smooth decaying shock after (Figure 2). The computed velocities are in good agreement with this experimental value.
From the Mach-Zehnder interferometer pattern (Figure 3a), one may distinguish two different perturbations propagating in the gas. The first one (dashed curve) sep-arates the region where the electronic density is high enough to reflect or absorb
Figure 2. (a) Shock velocities: experimental results obtained with VISAR (—·) and longitudinal interferometer (——),· · ·corresponds to 1D hydro simulation. (b) precursor velocities: experimental results obtained with longitudinal interferometer (——).· · ·1D hydro simulation.
Figure 3. (a) Longitudinal interferometry along the direction of the shock propagation. Dashed and
solid lines define the shock and precursor front trajectories, respectively. (b) Transverse diagnostic gives the radial extension R(t).
the probe beam, its frequency being greater than the plasma frequency (overcrit-ical) from the zone in the front part of the cell. It corresponds to the shock front and provides its velocity. When compared to the VISAR data and 1D simulations (Figure 2a) we find a fairly good agreement with these values. During the first 0.4 ns, the value is 68 km/s and decays down to 60 km/s when averaged over the first 3 ns. This value is very close to the VISAR result (67 km/s). After those 3 ns, it slows down. This is mainly due to the laser pulse duration that is shorter than the time scale evolution of the shock. In addition, on Figure 3a, we also observe clearly fringe shifts, ahead the shock front, due to a change in the electron density. We associate the region located in between the two lines with the radiative precursor and the full curve represents the position of its front. At the beginning, its velocity is close to 140 km/s and decreases with time due to the piston deceleration. Indeed we do measure precursor velocity which is quite in a rather good agreement with the simulations (Figure 2b). The fringe shift gives the electron density change through
the relation: Ne = λNπcd whereφis the phase change related to the fringe shift,
λthe probe beam laser wavelength, Nc the critical density above which the laser
probe beam cannot penetrate, d the radial size of the shock/precursor. The latter have been assessed by the transverse diagnostic (TRANS). Indeed, looking at a
given longitudinal position in the cell (≈100–200µm away from the foam
inter-face), we get a picture of the shape of the shock-front in the transverse direction (departure from the plane geometry).
According to the transverse imaging system, a 300µm wide plasma is created
by the precursor so that one can deduce the variation of Ne(t) (Figure 4).
Here we did take into account the increase in R(t) as deduced from Figure 3b and the temperature measurement (Vinci et al., 2004). Using these data, we can
therefore deduce Neand compare it to numerical simulations. In Figure 4, we show
the variation of Ne along the cell at a given time (4.5 ns after the laser maximum).
We clearly observe that the precursor has a few hundreds microns extension in a good agreement with the code.
The last parameter we measured was the shock temperature. Among the methods existing for its determination (Collins et al., 2001; Hall et al., 1997), we adopted
Figure 5. Deduced temperatures: (——) 0.1 bar 70J, (· · ·) 0.2 bar, 70 J (—-) 0.2 bar 50 J and (•••)
1D hydro simulation for the first case.
an absolute photon counting technique. This implied a precise measurement of the total transmission efficiency of the rear side imaging system and the response of
the detector (streak+CCD) at a given wavelength. Therefore we can associate to
the counts on the CCD to a brightness temperature. However, we have to extract
the temperature Te by fitting intensity I(λ) to a grey body Planck spectrum. In
Figure 5, we show various Te measurements with different initial conditions. As
expected, increasing laser intensity or decreasing initial Xe pressure lead to higher temperatures. Also our results are in quite good agreement with simulations.
Finally, with the new LULI Facility (LULI2000) we shall be able to drive shocks in Xenon at much higher velocities typically ranging from 120–250 km/s depending on the adopted target scheme. Due to the much higher intensity on target (2–
4×1014W/cm2), one has to pay attention to preheating effects. For that purpose,
the flyer plate technique as developed many years ago at LULI and more recently at ILE (Tanaka et al., 2000) seems to be a promising alternative. This technique consists (Figure 6 (left)) to accelerate a multilayer foil which impinge a second one, generating a very high pressure. In a recent experiment, performed on the Hyper
facility at ILE, we were able to accelerate a multilayer foil (350µm foam−10µm
tantalum) to a 70 km/s velocity. In Figure 6 (right), we observe the shock trajectory in the foam and the Ta free surface using a transverse x-ray radiography coupled to
a streak camera. Such a velocity could produce, when impacting a 10µm aluminum
foil embedded in Xe gaz, a piston velocity up to 120 km/s.
Figure 6. Target scheme (left). Experimental shock trajectory in foam and Ta free surface velocity
As a conclusion, we have observed the development of a radiative precursor ahead a strong supercritical shock wave, in a xenon gas cell at low pressure. Our experimental results are in good agreement with numerical simulations either re-garding hydrodynamical (Us, Vp) or plasma parameters (Ne, Te). In the next future,
the upgraded laser facility at LULI will allow to explore a further step into the study
of the radiating shock to the full radiative regime where Eradand Pradbegin to play
a significant role.
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