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Observation of Laser Driven Supercritical Radiative
Shock Precursors
S. Bouquet, C. Stéhlé, M. Koenig, J. -P. Chièze, A. Benuzzi-Mounaix, D.
Batani, S. Leygnac, X. Fleury, H. Merdji, Claire Michaut, et al.
To cite this version:
S. Bouquet, C. Stéhlé, M. Koenig, J. -P. Chièze, A. Benuzzi-Mounaix, et al.. Observation of Laser
Driven Supercritical Radiative Shock Precursors. Physical Review Letters, American Physical Society,
2004, 92 (22), pp.225001. �10.1103/PhysRevLett.92.225001�. �hal-00508786�
Observation of Laser Driven Supercritical Radiative Shock Precursors
S. Bouquet,
1
C. Ste
´
hle
´
,
2
M. Koenig,
3
J.-P. Chie
`
ze,
4
A. Benuzzi-Mounaix,
3
D. Batani,
5
S. Leygnac,
2
X. Fleury,
1
H. Merdji,
6
C. Michaut,
2
F. Thais,
4,6
N. Grandjouan,
3
T. Hall,
7
E. Henry,
3,5
V. M a l k a ,
3
and J.-P. J. Lafon
8
1
De
´
partement de Physique The
´
orique et Applique
´
e (DPTA), CEA-DIF, BP 12, 91680 Bruye
`
res-le-Cha
ˆ
tel, France
2
Laboratoire de l’Univers et de ses The
´
ories (LUTH), Observatoire de Paris, 92195 Meudon, France
3
Laboratoire pour l’Utilisation des Lasers Intenses (LULI), CNRS–CEA–Universite
´
Paris VI–Ecole Polytechnique,
91128 Palaiseau, France
4
Service d’Astrophysique (SAp), CEA–Saclay, DSM/DAPNIA, 91191 Gif-sur-Yvette cedex, France
5
Dipartimento di Fisica ‘‘G. Occhialini,’’ Universita
`
di Milano-Bicocca and INFM, Piazza della Scienza 3, 20126 Milano, Italy
6
Service Photons Atomes et Mole
´
cules (SPAM), CEA–Saclay, DSM/DRECAM, 91191 Gif-sur-Yvette cedex, France
7
University of Essex, Colchester CO4 3SQ, United Kingdom
8
Galaxies, Etoiles, Physique et Instrumentation (GEPI), Obervatoire de Paris, 92195 Meudon Cedex, France
(Received 5 June 2002; published 2 June 2004)
We present a supercritical radiative shock experiment performed with the LULI nanosecond laser
facility. Using targets filled with xenon gas at low pressure, the propagation of a strong shock with a
radiative precursor is evidenced. The main measured shock quantities (electronic density and propa-
gation velocity) are shown to be in good agreement with theory and numerical simulations.
DOI: 10.1103/PhysRevLett.92.225001 PACS numbers: 52.72.+v, 95.30.Jx
Radiative hydrodynamic processes [1–3] are very
important in inertial confinement fusion [4] and astro-
physics [1,5–7]. Recent experiments have reproduced
hydroradiative astrophysical flows (jets or blast waves)
[8–14] and radiative shocks (RS) [15–19]. In most
astrophysical environments, such as envelopes of post-
asymptotic giant branch stars, a RS is characterized by
(1) an ionized precursor, ahead of the shock, 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 down-
stream flow. In the vicinity of the shock and, provided its
velocity D is larger than D
cr
, the precursor is heated up to
a temperature T
cr
equal to that of the shocked gas. Shocks
satisfying D>D
cr
are called ‘‘supercritical’’ (SC) [1,3]
and their structures are very sensitive to the treatment of
radiation transport and to its coupling with hydrodynam-
ics. Consequently, laboratory experiments [8–19] are very
relevant test beds for validating models and theoretical
predictions.
The critical velocity (D
cr
) above which a RS enters the
SC regime is the solution of the implicit equation
[1,3] T
cr
1
;D
cr
4
1
D
cr
"
1
;T
cr
1
;D
cr
, where
"; T is the internal energy, per unit mass, of the fluid
(mass density
1
) ahead of the shock. This steady relation
assumes that the photon flux emerging at the shock front
is entirely absorbed to ionize and to heat, up to the post
shock temperature, the unperturbed gas ahead.
In this Letter, new aspects of the RS are raised
compared to previous published results [8–19].
Radiative precursors have also been produced earlier
[9,13,14,16,19]; however, regimes differ from the one
we get. The goals differ also on at least two points.
First, most of the former experiments deal with gas jets
containing atomic clusters [9,14,19]. They are rapidly
heated by the laser beam and the radiation they emit
propagates ahead of the shock, producing a photoionized
precursor mostly not heated since the very low density
medium let the radiation escape (in our case, it is heated
up to 15 eV). Second, Taylor-Sedov blast waves, i.e.,
shock waves created by instantaneous, zero spatial exten-
sion explosions, are produced [9,13,14,16]. While it is
propagating, the shock decays rapidly since no more en-
ergy is supplied. Moreover, the blast wave generates an
inner cavity with a decreasing mass density. In our study,
energy is continuously injected (piston with velocity V
p
)
in the wave and the material is highly compressed behind
the shock. This is quite the opposite of the blast wave
evolution.
In this Letter we present measurements of the velocity
U
p
and ionization of the precursor of a SC-RS and they
are compared to simulations. In order to strengthen ra-
diative effects against thermal ones, a low-density me-
dium with a high atomic mass is prescribed, and xenon
gas at 0.1 and 0.2 bar (1 order of magnitude lower than in
Ref. [15]) is chosen. Using a screened hydrogenic-type
equation of state (EOS) for Xe and taking an initial
density
1
10
3
g=cm
3
, the critical velocity is as low
as D
cr
15 km=s, leading to T
cr
7eV.ThislowD
cr
is
partly due to the large heat capacity of Xe. Former experi-
ments at LULI have shown that shock with D 50 km=s
in low-density media are achievable with the nanosecond
laser facility [20] and it is, therefore, quite suitable to
generate RS in low-density Xe gas.
Experiments are performed in small, millimeter size
targets and the shock is far from equilibrium, at least
regarding its radiative properties. The length L of a sta-
tionary precursor generated by a shock with a constant
velocity D can be derived by equating the diffusion time
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of photons (mean free path ) across the precursor to the
time for the material to cover L. One gets L c=D (c
is the velocity of light) and, for the present experi-
ments, L 1m. The corresponding equilibrium time is
of the order of L=D, i.e., tens of microseconds. A
time-dependent model based on self-similar solutions
of the nonlinear heat equation [17] shows that in
the transient phase the length lt of the precursor grows
up to L according to the law lt8:7
10
7
1
kg=m
3
11=36
Dm=s
13=6
ts
31=36
; lt is
in meters. For D 65 km=s and
1
10
3
g=cm
3
,we
obtain l 1m for t 10 s, in agreement with the
above result. In addition, according to the Xe shock
adiabat, the compression rate
2
=
1
achieved for this
shock velocity is about 11 in an idealized situation (pla-
nar geometry). This result assumes a stationary RS with
D const and a precursor with constant length L.
However, at earlier time the precursor grows and the value
of the radiation flux should be larger than its stationary
value. Indeed, in the stationary regime, the energy sup-
plied by the flux is used only to maintain the propagation
of the precursor (heating and ionization) while in the
early transient phase the flux should provide energy for
both its propagation plus its growth, until the steady state
can be obtained. In the transient stage, more energy than
in the steady one is radiated ahead of the discontinuity
and, consequently, the temperature of the shocked gas is
lower than in the final state with a compression rate larger
than 11, depending on the magnitude of the emissivity.
This property explains, to some extent, the high compres-
sions achieved by strong shocks propagating in optically
thin media.
The design of the experiment has been carried out with
the radiation hydrocodes
MULTI [21] and FCI [22] (CEA
code). A RS is produced at 100 J of pulsed laser light. A
three-layer pusher drives the shock into the Xe gas ini-
tially at rest in a quartz cell (1mm
3
volume). This
pusher is made of a polyethylene ablator (2 m), a tita-
nium x-ray screen (3 m), and a polyethylene foam ac-
celerator (25 m). The laser beams focus on the ablator
and the foam/Xe interface acts as a piston moving at
V
p
70 km=s. This high velocity produces the RS to-
gether with its radiative precursor (Fig. 1).
Experiments have been carried out using three of the
six available beams of the LULI’s Nd-glass laser. The
beams were converted at 0:53 m, providing a
maximum total energy E
2!
100 J focused in a
500 m [full width at half maximum (FWHM)] diameter
spot with a 250 m flat center. The spatially averaged
intensity is 4–6 10
13
W=cm
2
depending upon the
laser energy. The laser square pulse has a 120 ps rise
time with a 720 ps FWHM. Each beam is focused with
a 500 mm lens and phase zone plates [23] are used to
remove large-scale spatial modulations and to obtain a
uniform intensity in the spot [24].
The experimental diagnostics are shown in Fig. 2. They
focus on the time-dependent properties of the precursor.
A streak camera records the self-emitted light from
the rear surface of the target at shock breakout and two
velocity interferometer systems for any reflector
(VISARs) [25] with different sensitivities (16.63 and
3:39 km=s per fringe) measure D in the foam or in the
gas provided the electron density n
e
becomes overcritical.
Finally, a Mach-Zehnder interferometer provides n
e
along the shock propagation. Two streak cameras are
used, one looking at the fringes longitudinally (LONG),
the other giving a transverse image at a given position in
the xenon (TRANS). Assuming a transverse plasma
thickness 200 m, a range n
e
10
18
–10
20
cm
3
in
the precursor is inferred from the interferometer. With
the VISAR, we measure V
p
(foam/gas interface, i.e.,
piston) provided the gas remains transparent to the probe
laser light. As we can see in Fig. 3, the fringes shift first to
the left (velocity jump due to a slight deceleration), then
to the right (small acceleration), and finally back to the
left. The mean measured shock velocity is D 67 km=s,
i.e., D 4D
cr
. In addition to the fact that numerical
simulations show a shock with a precursor (Fig. 1), the
computed velocities are in good agreement with this
experimental value. The above three stages correspond
to a first shock breaking through the foam-Xe interface,
then a second shock arrives (due to reflections on the
pusher interfaces) and catches the first one and, finally,
the piston decelerates slowly (see below).
FIG. 1. MULTI simulations [21] (I 6 10
13
Wcm
2
) with
and without radiation (dashed and solid curve, respectively).
FIG. 2. Experimental setup and diagnostics.
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According to the expected shock temperature (T
2
20 eV) and the associated ionization state, the shock
front in Xe is overcritical (n
e
10
21
cm
3
) while the
precursor is much less than critical (n
e
10
20
cm
3
);
see Fig. 1. The Mach-Zehnder interferometer pattern
(Fig. 4) shows two different perturbations propagating
in the gas. The first (dashed curve) separates the region
where n
e
is overcritical (left side of the curve) from the
zone in the rear part of the cell where n
e
is subcritical. It
corresponds to the shock front and we can deduce D
again. For the first 0.4 ns, it is 68 km=s and decays
down to 60 km=s when averaged over the first 3 ns. This
value is very close to theVISAR measurement (67 km=s).
After t 3ns, it slows down since the laser pulse is only
1nslong. In Fig. 4 we also clearly observe fringe shifts
(solid line) due to a change in n
e
ahead of the shock. We
associate the zone in between the two lines with the
precursor and the solid curve gives the position of its
front. In accordance with the analytical expression for
lt, the precursor grows roughly linearly with t.Overthe
first 2 ns, its velocity (slope of the solid line) is U
p
130 km=s, i.e., U
p
2D. Later on, a decrease of U
p
occurs due to the piston deceleration and 2D effects.
These effects have been assessed by the diagnostic
TRANS by looking at 100–200 m ahead of the
foam surface. We get a shock front picture and its shape
is not quite planar. Moreover, according to this system,
the plasma width in the precursor is d 200 m. Since
the shift depends also on the electron density per unit
plasma length 4:5 10
21
cm
3
m
1
=fringe we de-
duce n
e
t; see Fig. 5.
Numerical simulations clearly show (see below) that
the precursor is, in fact, an ionized zone where the plasma
is at rest (the gas moves significantly only after the
passage of the shock). The spatial profiles n
e
x; t at a
given time can be derived using a reconstruction proce-
dure from the interferograms. The deduced ionization
wave velocity is 70 130 km =s for isodensity contours
n
e
10
20
n
e
10
19
cm
3
. These results agree rather
well with the values of U
p
and D given above.
The formation of the precursor requires a careful nu-
merical treatment of radiation transport with a very high
spatial resolution. In order to estimate the nonequilibrium
effects that govern the early propagation of the precursor,
numerical simulations with V
p
const driven SC shock
have been performed with the radiative hydrocode
ASTROLABE [26]. This fully implicit, moving grid code
uses the two-moment radiative transfer approximation
and takes into account non-local-thermal-equilibrium
effects. With V
p
65 km=s, the precursor plasma enters
the RS with a 2 keV kinetic energy per ion and, according
to the Xe-EOS, dissipation of this energy results in a
plasma with a mean ionization equal to 15 with T
2
32–37 eV for
1
10
3
–10
2
g=cm
3
.
Figure 6 displays the structure of the nonstationary RS
in the vicinity of the discontinuity. The temperature in the
dense shocked gas and in the precursor is 20 eV,i.e.,
less than 32 eV. The latter would be achieved only for a
steady state. The sharp T
i
spike at the shock front is
specific to SC shocks. A moving grid numerical resolu-
tion of the spike shows that it consists in three zones,
through which the gas compression rises up to a final
value 55 (depending, actually, on the gas opacity).
Shortly after the viscous shock high heating of the Xe
ions (the end of this first step is shown by the X on the
curve; compression is 4), a first relaxation (second step)
occurs with T
i
T
e
. A second relaxation (third step)
happens where matter thermal energy moves to photons
on a distance shorter than until gas and radiation rise to
the same temperature. This zone is the source of the
radiative flux (shock luminosity) that heats the gas ahead
of the shock and creates the precursor. Its length is
500 m at t 5ns and cannot be shown in Fig. 6.
Unfortunately, the experimental study of the spike prop-
erties is not yet possible with our detector capabilities.
FIG. 3. VISAR image for a 0.2 bar filled gas cell.
FIG. 4. Interferometry (LONG) in Xe gas. The dashed (solid)
line defines the shock (precursor) front trajectory.
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Experiments have also been simulated with two more
Lagrangian radiative 1D hydrocodes,
MULTI [21] and FCI1
[22]. Both take into account the laser-matter interaction,
the target design and a multigroup radiative transfer in
the diffusion approximation. A detailed comparison (i.e.,
experiment versus computation) of the precursor dynam-
ics is not easy because it depends upon the value of n
e
which, in turn, depends on d (known to within about
20%). However, the similarity between the calculated
and the observed precursor is rather promising (see
Fig. 5). For example, 4 ns after the shock breakout in
Xe gas, we get U
p
100 km=s from TRANS (see Fig. 4)
for the isovalue n
e
3 10
19
cm
3
and for d
200 m. In the same conditions,
MULTI (FCI1) gives 120
300 km =s. These values have the same order of magni-
tude but the
FCI1 one is overestimated. With V
p
65 km=s,
ASTROLABE provides U
p
that decreases with
time from 170 to 130 km=s.Att 4ns, U
p
150 km=s.
In conclusion, we have observed, at the LULI facility,
the development of a radiative precursor ahead of a strong
SC-RS in low pressure Xe gas. Using various diagnostics,
the experimental results are in good agreement with
numerical simulations. In particular, the measured value
of D is very close to the numerical one. The experimental
value of U
p
remains within the range obtained with the
three codes. This discrepancy shows that much theoretical
and experimental work is required to get a better and
more reliable model of RSs. The resolution of the diag-
nostics will be improved and multidimensional effects
will be studied (hydrodynamics and radiative transfer). In
the near future, the upgraded laser facility at LULI will
allow one to explore the physics of stronger RSs.
The authors are grateful to B. Marchet, J. Grenier
(CEA), and Ph. Moreau (LULI) for their significant con-
tribution to the success of these experiments. We thank
the target designer groups: F. Gex and P. Barroso (GEPI/
Observatoire de Paris) and L. Pole
`
s, P. Sys, F. David,
J. Tidu, P. Di Nicola, and B. Cathala (CEA). The authors
acknowledge the Programme National de Physique
Stellaire (CNRS), the Observatoire de Paris, and CEA
for their financial support.
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FIG. 6. Blowup of the SC-RS at t 5ns for a 65 km=s
moving piston with position x
p
. These results come from
ASTROLABE for
1
1:3 10
3
g=cm
3
and T
1
300 K.
FIG. 5. Experimental and simulated values of n
e
(dashed and
solid curve, respectively) in xenon, 200 m away from the
foam surface.
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![FIG. 1. MULTI simulations [21] (I 6 1013 W cm 2) with and without radiation (dashed and solid curve, respectively).](/figures/fig-1-multi-simulations-21-i-6-1013-w-cm-2-with-and-without-109t73jn.webp)
