Laser smoothing and imprint reduction with a foam layer in the multikilojoule regime.

Abstract

This Letter presents first experimental results of the laser imprint reduction in fusion scale plasmas using a low-density foam layer. The experiments were conducted on the LIL facility at the energy level of 12 kJ with millimeter-size plasmas, reproducing the conditions of the initial interaction phase in the direct-drive scheme. The results include the generation of a supersonic ionization wave in the foam and the reduction of the initial laser fluctuations after propagation through 500 mum of foam with limited levels of stimulated Brillouin and Raman scattering. The smoothing mechanisms are analyzed and explained.

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Laser Smoothing and Imprint Reduction with a Foam Layer in the Multikilojoule Regime
S. Depierreux,1C. Labaune,2D.T. Michel,1C. Stenz,3P. Nicolaı ¨,3M. Grech,3,4G. Riazuelo,1S. Weber,3C. Riconda,2
V.T. Tikhonchuk,3P. Loiseau,1N.G. Borisenko,5W. Nazarov,6S. Hu ¨ller,7D. Pesme,7M. Casanova,1J. Limpouch,8
C. Meyer,9P. Di-Nicola,9R. Wrobel,1E. Alozy,1P. Romary,9G. Thiell,9G. Soullie ´,1C. Reverdin,1and B. Villette1
1CEA, DAM, DIF, F-91297 Arpajon, France
2Laboratoire pour l’Utilisation des Lasers Intenses, Ecole Polytechnique, Palaiseau, France
3Centre Lasers Intenses et Applications, Universite ´ Bordeaux 1, CEA, CNRS, Talence, France
4Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
5P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia
6University of St. Andrews, Fife KY16 9ST, Scotland, United Kingdom
7Centre de Physique The ´orique, Ecole Polytechnique, 91128 Palaiseau cedex, France
8FNSPE, Czech Technical University in Prague, 115 19 Prague 1, Czech Republic
9CEA, DAM,CESTA, F-33114 Le Barp, France
(Received 25 January 2009; published 14 May 2009)
This Letter presents first experimental results of the laser imprint reduction in fusion scale plasmas
using a low-density foam layer. The experiments were conducted on the LIL facility at the energy level of
12 kJ with millimeter-size plasmas, reproducing the conditions of the initial interaction phase in the
direct-drive scheme. The results include the generation of a supersonic ionization wave in the foam and
the reduction of the initial laser fluctuations after propagation through 500 ?m of foam with limited levels
of stimulated Brillouin and Raman scattering. The smoothing mechanisms are analyzed and explained.
DOI: 10.1103/PhysRevLett.102.195005 PACS numbers: 52.38.Hb, 52.38.Bv, 52.57.Bc, 52.57.Fg
Inhomogeneities of the intensity distribution of the in-
cident laser beam can be a source of fast growing pertur-
bations of the target shell during the acceleration and
deceleration phases of direct thermonuclear target com-
pression [1]. Development of efficient and robust methods
of control of Rayleigh-Taylor instabilities is one of the
outstanding problems in inertial confinement fusion
(ICF). The diffusive heat conduction smooths the ablation
pressure front and ensures its homogeneity if the distance
between the ablation and the absorption surfaces, Dac, is
larger than the perturbation wavelength ?p[2] and if the
heat diffusion time is larger than the laser beam correlation
time [3]. The most dangerous intensity perturbations are
those during the first few hundreds of picoseconds of the
laser pulse, when the thickness of the heat conduction zone
is very small and the temporal beam smoothing is not yet
efficient. This is the so-called problem of ‘‘laser imprint’’
[4], where the initial laser pulse intensity fluctuations are
imprinted in the target shell and are amplified later on,
during the acceleration and deceleration phases. Optical
smoothing techniques are inefficient to avoid this early
imprint because the instantaneous laser intensity distribu-
tion always remains highly nonuniform and fast variation
of the laser intensity distribution requires a very large laser
bandwidth [3].
To reduce the laser imprint, it has been suggested to
cover the target shell with an overcritical foam through
which a supersonic heat wavewas created by an x-ray flash
[5]. This supersonic heat wave enabled the creation of a
conduction zone (Dacalmost set by the foam thickness,
typically of a few tenths of microns) before the laser
reached the target, thus ensuring the thermal smoothing
of perturbations of the ablative pressure with wavelength
?p< Dac. Although this idea was confirmed in experi-
ments [6], it has been abandoned because the x-ray flash
introduced undesired entropy in the fuel and spoiled the
compression efficiency.
The idea of the approach presentedinthis Letter is touse
a foam not for smoothing the pressure inhomogeneities
directly, but the laser intensity itself. In this new scheme, a
low-density (undercritical) foam is ionized directly by the
laser beam. It is important to choose the interaction pa-
rameters so that the ionization wave in the foam is super-
sonic [7], thus avoiding the creation of pressure
perturbations at the ablation surface. This idea follows
from plasma induced beam smoothing that has been ob-
served in different experiments [8] and interpreted with
theory and simulations [9]. Two plasma-smoothing re-
gimes have been identified: at high intensity, the combina-
tion of filamentation, self-focusing (SF) and the filament
instability (FI), and at low laser intensity, stimulated for-
ward Brillouin scattering (FSBS), are responsible for the
smoothing effect [10].
The purpose of the experiments presented in this Letter
is to test this type of smoothing under conditions close to
those anticipated with the Laser MegaJoule (LMJ) and to
demonstrate how it can provide a reduced imprint of the
laser inhomogeneities while reflectivities associated with
parametric instabilities were kept at an acceptable level.
The results demonstrate for the first time the smoothing of
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initial intensity perturbations of a multikilojoule laser
beam by propagation through a few hundreds microns of
a low-density (<10 mg=cc) foam layer and its conse-
quence on the reduction of ablation pressure inhomogene-
ities on a foil with limited levels of stimulated scattering.
The four beams of the LIL (Ligne d’Integration Laser)
laserwereused toirradiateatargetcomposedofathickfoil
with a low-density material deposited on it. The scheme of
the experiment is shown in Fig. 1(a). The total laser energy
was 12 kJ in 2.7 ns square pulse at the wavelength 351 nm.
Each beam in the quadruplet had a square shape of 36 cm
in the near field, and they were focused all together with an
optical system of 8 m focal length through random phase
plates (RPP).Inpurpose,weused anarrowlaserbandwidth
of 2 GHz created by the SSD (smoothing by spectral
dispersion [11]) which is set up to suppress stimulated
Brillouin scattering in the laser optics. The target was
placed 5 mm in front of the focal plane to increase the
beam spot size and to produce large-scale inhomogeneities
(? few tenths of?m) of intensity due to a slight separation
of the four beams as shown in Fig. 1(b). The shape of the
focalspotwasapproximatelyasquare of1mmsideandthe
average intensity was hIi ? 4 ? 1014W=cm2. Shots used
alternatively thick copper foils (10 ?m thickness), foams,
and composed targets (foam þ foil). The foams were low-
density polymer C15H20O6with small (?1 ?m) cell struc-
tures. They were doped with 1% Cl to increase the x-ray
emissivity for diagnostic purposes. The foam was hold in a
cylinder of 2.5 mm in diameter and 0.5–1 mm long sup-
ported by a washer of a 6 mm diameter with a 1 mm slit for
side view diagnostics, as shown in Fig. 1(c).
Five diagnostics provided complementary informations
on the laser propagation through the foam. The space and
time-resolved evolution of the side x-ray emission was
recorded to measure the velocity of the ionization front
in the foam. The smoothing effect was studied with
(i) temporally resolved two-dimensional x-ray images of
the foil emission with an eight-frame camera and by
(ii) measurements of the angular distribution of the beam
transmitted through the foam. The intensity, spectral and
angular distribution of stimulated Brillouin and Raman
scattering were measured in backward and near backward
directions as well as the total energy budget.
The first result concerns the speed of the ionization
process. The foam density was chosen according to nu-
merical simulations carried out with the nonlinear hydro-
dynamiccode
CHIC
[12]
combination of a 10 mg=cc foam density with a few
1014W=cm2irradiation intensity provided a supersonic
ionization wave, sustained for more than 2 ns, with a
velocity exceeding 0:5 mm=ns. The temporal evolution
of the x-ray emission as a function of the distance along
the target is shown in Fig. 2(a) for a target composed of
950 ?m of 10 mg=cc foam in front of a copper foil.
Because of partial absorption of the laser light in the
foam plasma, the front velocity, shown in Fig. 2(b), de-
creased as a function of time from 0:7 mm=ns initially to
0:4 mm=nsatthemomentwhenitarrivedattherearsideof
the foam. It significantly exceeded the acoustic velocity,
cs? 0:32 mm=ns, which was deduced from the trajectory
of the rarefaction wave front in Fig. 2(a). This value agrees
well with the electron temperature T ? 1:8 keV estimated
from the stimulated Brillouin scattering spectra and from
the energy balance, as well as from the hydrodynamic
simulations. This result demonstrates the supersonic
whichindicated thata
FIG. 1 (color online).
main diagnostics. (b) Far field image of the laser beam at the
target plane. (c) View of a foam target with the support and a slit
for side observations.
(a) Scheme of the experiment with theFIG. 2 (color online).
the foam along the direction of propagation, showing the propa-
gation of the ionization front. (b) Temporal evolution of the
ionization front velocity as extracted from panel (a).
(a) Time-resolved x-ray emission from
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propagation of the ionization wave, which is supported by
a direct laser energy deposition at the ionization front. This
ionization front velocity is approximately the same as the
one measured on the PALS laser facility [13] for similar
irradiation conditions, but with a shorter pulse duration of
350 ps.
The observation of the laser intensity smoothing came
first from the x-ray framing images of the emission of the
copper foil placed behind the foam. Two images of a
copper foil alone and of the same foil covered with
500 ?m of 10 mg=cc foam are presented in Fig. 3. The
images are integrated over 200 ps and are recorded at the
very beginning of the foil emission, i.e., when the laser
beam reached the foil. With no foam, Fig. 3(a), at the
beginning of the laser pulse, t ¼ 0, we observe large
intensity fluctuations with same spatial scale as in the focal
spot distribution in vacuum [see Fig. 1(b)]. The foam,
Fig. 3(b), becomes transparent for the laser beam after
1.2 ns which is in agreement with both the previously
discussed result and the time-resolved transmitted light
through a free standing foam target and with CHIC simula-
tions. The copper foil emission behind the foam plasma is
much smoother than in the previous case. The inhomoge-
neities of size ?50 ?m have been removed, and the am-
plitude of small-scale fluctuations was strongly reduced.
The modification of the angular distribution of the trans-
mitted laser beam confirms the foam spatial smoothing
effect. In Fig. 4, the time-integrated forward near field
images of the beam are compared for vacuum, Fig. 4(a),
and after propagation through 900 ?m of 6:5 mg=ccfoam,
Fig. 4(b). In vacuum, the four beams of the quadruplet are
clearly separated, each having a divergence of 2.6?. After
propagation through the foam, the angular divergence has
increased by morethan 2 timesas compared tovacuum and
the overall large-scale contrast of the intensity distribution
was strongly reduced to the level of less than 10% inside
and outside the beam area.
An important concern with such a smoothing technique
was the possiblegrowth of stimulated Brillouin and Raman
scattering in the quasihomogeneous plasma produced from
the foam. The detailed analysis of stimulated Brillouin and
Raman backscattering showed that the reflectivity levels
FIG. 3 (color online).
integrated over 200 ps and recorded at the very beginning of the
emission. (a) Cu foil alone; (b) Cu foil þ500 ?m of foam.
2D x-ray images of the Cu foil emission
FIG. 4 (color online).
near field images of the laser beam. (a) in
vacuum; (b) after propagation through
the 900 ?m long, 6:5 mg=cc, foam.
Time-integrated
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were below 8% and 4%, respectively. These levels of
backscattering are affordable because they concern only
a small part of the laser energy at the beginning of an
ignition pulse. The detailed energy balance shows that
around 1 kJ of laser light was needed to ionize and heat a
foam volume of 0:5 mm3. Approximately 70% goes into
the plasma internal energy, 15% in its kinetic energy, and
15% is radiated. Therefore such a smoothing technique
requires about 12 kJ of laser energy for a 1 mm radius
target, which is a relatively minor part of the energy budget
in an LMJ-scale experiment.
We estimated that beam smoothing due to multiple
scattering on either decaying density fluctuations produced
in the homogenization stage of the foam ionization or
density perturbations driven by the speckles themselves
was marginal. Indeed, the ion acoustic waves damping in
C15H20O6foam plasma is mainly due to collisions between
the heavy carbon and oxygen ions and to Landau damping
from the light hydrogen ions. Under our experimental
conditions, the normalized ion acoustic damping rate for
wavelength of a few microns, which are of interest for the
observed smoothing, is ?s=!s? 0:1. The ion acoustic
perturbations are therefore damped in a few periods.
Considering wave period of ?10 ps, their damping time
is of the order of 100 ps, which is much shorter than the
foam burnthrough time. These fluctuations therefore exist
only in a very close vicinity of the ionization front.
Assuming that this front propagates toward the foil with
a velocity of the order of 0:5 mm=ps, one can estimate this
region to have a width of ?50 ?m. On such a distance,
strong density perturbations (?n=nc? 0:15) might con-
tribute to the beam angular spreading and consequently
to the homogenization of the ionization front. However,
their effect is not maintained on a time long enough to
allow the laser beam smoothing to be efficient during the
few hundred picoseconds after the foam burnthrough re-
quired to create the conduction zone in the foil.
Plasma induced smoothing can also follow from laser
light multiple scattering on laser induced density perturba-
tions due to FSBS, FI or the speckle SF. The relative
importance of each of these processes depends on the ratio
of the average power ina speckle P to the critical power for
SF [14] PC¼ 34ð1 ? ne=ncÞ1=2ðne=ncÞ?1Tkev. For an
electron density of ð0:25–0:35Þnc, estimated from the com-
plete ionizationof thefoam, and aplasmatemperature T ¼
1:8 keV, we find a critical power Pc¼ 136 MW for a
foam density of 10 mg=cc and 246 MW for a density of
7 mg=cc. The speckle pattern was calculated using the
code MIRO in which the real laser parameters were intro-
duced. Because of defocusing, two speckle mean radii
coexist in the focal volume: ? ¼ ?0f ? 7:8 and 3:1 ?m
for f ? 22:2 and 8.9, respectively, corresponding to inde-
pendent or superimposed beams [15]. The corresponding
average powers in a speckle were P ¼ ?2hIi ? 240 MW
and 38 MW. Most of the speckles in the first case carry a
power above the critical power PCand are unstable with
regards to SF and FI. Strong SF and associated beam spray
are therefore expected. In the second case, P ? 38 MW ?
ð15%–28%Þ PC. In this regime, plasma induced beam-
smoothing follows from collective FSBS. It is shown in a
recent work [16] that spectral broadening and beam spray
occur if ?ðP=PcÞð!s=?sÞ > 1, where the factor ? ? ð2–8Þ
accounts for both ponderomotive and thermal effects on
the excitation of acoustic waves by the laser. This criterion
is satisfied for our conditions.
Three-dimensional simulations with the laser-plasma
interaction code PARAX [17], using plasma parameters
provided by the code CHIC, confirm the effect of both SF
and FSBS on the induced spatiotemporal incoherence of
the laser light. As can be observed in Fig. 5, the power
threshold is strongly exceeded for our experimental con-
ditions and the beam angular aperture is increased by a
factor 2–3 during the beam propagation. The reduction of
the spatial coherence of the laser light allows smoothing of
structures with wavelengths larger than a few microns
while the broadening of the temporal spectrum (up to
cs=?0? 80 GHz) provides a homogeneous fluence of the
transmitted light. Moreover, hydrodynamic simulations
show that a conduction zone in the CH foil with a width
Dac? 40 ?m was created 600 ps after the burnthrough
(similar results have been obtained in Ref. [5]). It was
observed in our simulations that the smoothing remained
efficient until this time.
In conclusion, we have reported the first observation of
laser beam smoothing and reduced imprint in the multi-
FIG. 5 (color online).
aperture angle ? normalized to the incident aperture ?0(solid
curves) as a function of the propagation distance (z) at two
different times: t ¼ 100 ps (black) and 500 ps (blue) after the
laser burnthrough; (ii) the figure of merit for collective FSBS as
introduced in Ref. [14]: C ¼ ?ðP=PCÞð!s=?sÞ (dashed curves).
FSBS-induced beam spray is expected to happen for C > 1. The
foam density is 10 mg=cc.
Numerical evolution of (i) the laser
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kilojoule regime, using a thin (?500 ?m) low-density
(?10 mg=cc) foam in front of a solid target. The super-
sonic ionization wave propagates faster than the shock and
reduces the pressure fluctuations at the ablation surface.
The foam plasma provides laser beam smoothing before
the absorption zone and a homogeneous ablation pressure
during the time offoam decay. This time is long enough for
creating the thermal conduction zone inside the target. It
has also been demonstrated that stimulated scattering re-
flectivities remained at an acceptable level. These experi-
mental results validate a new scheme for direct-drive ICF
targets where a thin layer foam reduces the laser imprint.
This work was coordinated under the auspice of the
Institute Lasers and Plasmas. The authors acknowledge
the support of the ANR contract and the operation team
of the LIL facility who made these experiments possible.
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