M. Busquet et al- Effect of lateral radiative losses on radiative shock propagation

8/3/2019 M. Busquet et al- Effect of lateral radiative losses on radiative shock propagation

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Effect of lateral radiative losses on radiative shock propagation

M. Busquet a,*, E. Audit b, M. Gonzalez b, C. Stehle a, F. Thais b, O. Acef a, D. Bauduin a,P. Barroso a, B. Rus c, M. Kozlova c, J. Polan c, T. Mocek c

a LERMA, Observatoire de Paris, UPMC, CNRS, Place Jules Janssen, 92190 Meudon, Franceb Service d’Astrophysique, CEA-Saclay, Gif-sur-Yvette, Francec Institute of Physics, PALS Center, Prague, Czech Republic

Available online 4 February 2007

Abstract

Experimental and numerical studies of radiative shocks, of interest as scaled astrophysical objects, have been performed. Experiments were

conducted at the PALS facility in Prague with a xenon filled mini-shock tube using a laser accelerated plastic pusher. Numerical simulations of

the hydrodynamics including radiation effects have been performed with the 3D code HERACLES. Measurements have been made of the elec-

tronic density of the shocked gas and of the time history of the position of the radiative precursor. Simulations and experimental results show

good agreement when lateral radiative losses are taken into account, including a wall albedo of 40%.

Ó 2007 Elsevier B.V. All rights reserved.

Keywords: Radiative shocks; Laboratory astrophysics

1. Introduction

Radiative shocks can be defined as shocks of sufficient

strength that radiation arising from the compressed layer will

significantly alter the structure of the shock itself, with radiative

cooling of the downstream region and radiation heating and ion-

izing of a precursor. Radiative shocks are observed around astro-

nomical objects in a wide variety of environments, e.g.,

supernovae in their radiative cooling stage, bow shocks of stellar

jet in galactic medium, collision of interstellar clouds. Under-

standing the underlying physical phenomena is important for

the analysis of the time-dependence of these events. However,

each astronomical observation is unique and almost fixed in

time. Since the late 80s [1] there have been efforts by several

groups to scale these astrophysical events to accessible labora-

tory conditions for analytical and/or parametric studies. In this

study we explore radiative shocks produced by a laser in mini-

shock tube. [2e6]. In the experiment we performed on the

PALS laser facility in Prague, the aim was to study the time

history for a much longer time than in the experiment performed

inLULI [5] studying the slowing down of the radiative precursor

due to lateral radiative losses. As radiation emissivities and

opacities increase with the atomic number, we select xenon

for the medium in which the shock will propagate.

2. Target design, experimental setup and results

Thetargets aredesigned as mini-shock-tubes made of a 4 mm

long glass capillary with a square section of 700 mm filled with

xenon at 0.2 bar. A 1 cm3 reservoir prevents reduction of the xe-

non pressure during the 20 min between the filling and the lasershot. A 10 mm CH foil is glued at one end of the capillary and is

coated by a 0.5 mm layer of gold facing the xenon gas that pre-

vents preheating the gas by radiation and electrons created in the

expanding laser created corona. This foil is irradiated by the fre-

quencytripled( l ¼ 438 mm)iodine700 JPALSlaserwithapulse

duration of 0.35 ns, which is smoothed with a PZP-type random

phase plate to have a uniform focal spot of w650 mm with a re-

sulting intensity of up to 1.5Â 1014 W/cm2 on target. Laser ab-

lation of the front surface acceleratethe CH/Au pusher by rocket

effect and launches a strong shock in the gas. The laser pulse is* Corresponding author.

E-mail address: [email protected] (M. Busquet).

1574-1818/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.hedp.2007.01.002

High Energy Density Physics 3 (2007) 8e11www.elsevier.com/locate/hedp

mailto:[email protected]

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short enoughand the targetmassive enough that theback surface

of the pusher remains at solid density, launching a shock into the

unperturbed gas. The velocity of the pusher, which is computed

tobew65 km/s, atomic number and gas pressure give rise to the

formation of super-critical radiative shock [7e10]. To probe the

time evolution of the precursor front in the xenon gas we use

interferometric measurement of the electron density witha probebeam transverse to the cell, see Fig. 1. The interferometer uses

a Fresnel biprism and a 150 ns green laser beam, obtained

with a continuous 5 W Verdi laser operating at 1e2 W and an

acousto-optical switch. An astigmatic beam expander is used

to illuminate the cell with an 8 Â 0.1 mm line. A visible Hama-

matsu C5680 streak camera records green light fringes through

the cell along its axis for a period of 50 ns, however, they blur

shortly after the main beam laser pulse, which produces the

bright horizontal spot in Fig. 2 that we use as a time marker.

However, visible light going through the gas allows measure-

ment of the electron density by inverse bremsstrahlung absorp-

tion providing the precursor front position as a function of time,

displayed as black superimposed line in Fig. 2. The precursorregion is located at left of this line. The measured average inten-

sities in the averaging boxes displayed in Fig. 2 gives a trans-

mission of 70% in the precursor region compared to the

transmission in the unperturbed gas. With the transverse internal

dimension of the glass cell equal to 0.69 mm, we infer an elec-

tronic density of 1.1Â 1019 cmÀ3Æ 15%.

3. Numerical simulations and comparison with

experiment

We use the 1D Lagrangian hydrocode MULTI, [12] includ-

ing detailed physics (laser absorption, realistic ionization andEOS, non linear thermal conduction), to perform simulations

of the laser ablation of the pusher using the experimental

conditions (foil thickness, laser intensity versus time, xenon

pressure). The pusher is accelerated by rocket effect with

a rear surface velocity V p of 65 km/s without any noticeable

velocity change for more than 50 ns after the laser pulse, see

Fig. 3. Note that in the experimental conditions the pusher ve-

locity is roughly proportional to the mean laser intensity I L,

thus the accuracy of the velocity inference is equal to the pre-

cision on I L. As an ionizing Marshak wave, the front velocity

is not very sensitive to the pusher velocity from the time the

shock is launched into the medium until it reaches the

Fig. 1. Schematic layout of the experiment. The target is made of

a 4Â 0.7 mm glass tube, filled with xenon at 0.2 bar, closed at one end by

a gold coated CH pusher. A green 2 W laser, with an astigmatic imaging,

transverse too the cell probes the electronic density.

Fig. 2. False color enhancement (b) of the experimental image (a) of the

streaked interferogram. Time increases vertically for 50 ns, and distance

from the pusher goes from left to right with an accuracy of the origin estimated

to be 0.2 mm. Total observed length is 4 mm. The bright horizontal line occurs

during the 0.35 ns laser pulse. On the raw data (a), fringes are clearly seen be-

fore the laser pulse, and blur shortly after it. Although with a small contrast

(65%), an unambiguous absorbing front is seen with a parabolic shape. Super-

imposed in the false color image (b) is the computed position of the precursor

front. Boxes are the averaging areas to measure the relative intensity throughthe precursor and through the unperturbed gas.

9 M. Busquet et al. / High Energy Density Physics 3 (2007) 8e11



stationary limit, which happens after the region of interest. On

the contrary, the shock is very sensitive to the geometry (pla-

nar or spherical expansion) and to the lateral radiative los-

ses.[13] To address both points we use the hydrocode

HERACLES [14,15] developed in CEA-Service d’Astrophysi-

que. HERACLES is a three dimensional (3D) Eulerian hydro-

code including a gray M1 moment radiative transfer method,

and a state of art opacity for the low temperature xenon.[16]

This method allows a good angular description of the radiative

transfer. In fact it preserve shadows in contrast to usual P1 dif-fusion method [14,15,17]. As the pusher can be approximated

as a constant velocity wall, we use a constant velocity (at

65 km/s) at the bottom boundary of the simulation box. The

glass cell is reproduced with a non-moving solid wall for hy-

drodynamics, and a constant partial reflectivity (or albedo) R

for X-rays. HERACLES can also be used in two dimensional

(2D) configuration to save computing time. We have tested for

one set of conditions that the evolution of the radiative shock

computed in 3D mode in a square cell is well reproduced using

a 2D cylindrical geometry; thus, subsequent parametric studies

have been performed in 2D mode. A typical result of density

and temperature map at a given time is shown in Fig. 4. Fig. 4

displays half section of the cell, the symmetry axis on the left,the wall interface on the right, and the pusher interface at bot-

tom. The shock, shown at 1.7 mm from initial position of

pusher, remains planar, see Fig. 4a; although the density is

higher close to the glass wall, which is on the right in Fig. 4b,

as radiative losses induce decrease of temperature close to the

wall, thus increase compression. The temperature map in

Fig. 4b shows the radiative precursor, heated from radiation

emitted from the shock, which is also colder and denser close

to the wall.

The position of the shock and the precursor front is plotted as

a function of time in Fig. 5 for different value of albedo R. The

parabolic shape is a signature of the damping of the radiative

precursor through energy losses across the walls. At longertime, an asymptotic, stationary limit would finally be found

where the losses will be balanced by feeding from the shock,

with a constant distance between the shock and the precursor.

Here the rate of slowing down is related to the amount of losses.

Note that an albedo of 40% fits the experimental precursor front

position at all times and this is true evenfor slight adjustments of

the distance from the pusher, i.e., the Z -axis. This demonstrates

the effect of lateral radiative losses and provides the amount of

energy lost (here 60% of the X-rays hitting thewall). Finally, the

computed electronic densities in the precursor (1.2e1.3Â

1019 cmÀ3) agree with the measured value (Section 2).

4. Conclusion

We have been able to extract the essential information

about the radiative precursor, electronic density and position

of the front versus time from initial experiments at the

Fig. 3. Mesh positions versus time computed with the 1D Lagrangian codeMULTI for our conditions. Laser shines the pusher from the left.

Fig. 4. Half section of density (a) and temperature (b) maps computed with HERACLES in a cylindrical geometry. Ordinates are distances from pusher and

abscissas are distances from the symmetry axis. Left of plots are then the center of the cell, right of plots are the cell wall. Bottom is the pusher interface.




PALS laser facility. These data provide an indirect measure of

the wall albedo. For a glass cell and a gas temperature around

10 eV, we found a value of 40%. The 3D simulation of the

radiative shock in the gas performed with the code HERA-

CLES [14,15] shows that lateral radiative losses are the origin

of the slowing down, even if the shock remains planar. The

measured electron density in the precursor agrees with the

simulation. Analysis of the behavior of radiative shock in lab-

oratory experiments will contribute to our understanding of

radiative shocks in astrophysical objects.

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R=60%

R=40%

R=20 %

experiment

position (mm)

0 1 3 420

10

30

40

20

50

t i m e ( n s )

shock precursor front

(R=60%, 40%, 20%)

Fig. 5. Position versus time of the shock and the precursor front from exper-

iment (stars) and computed with HERACLES for different value of wallalbedo R (20%, 40% and 60% from right-faster to left-slower).


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M. Busquet et al- Effect of lateral radiative losses on radiative shock propagation