Study of plasma heating induced by fast electrons

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Study of plasma heating induced by fast electrons
A. Morace,1A. Magunov,2D. Batani,1R. Redaelli,1C. Fourment,3J. J. Santos,3G. Malka,3
A. Boscheron,4A. Casner,5W. Nazarov,6T. Vinci,7Y. Okano,8Y. Inubushi,8
H. Nishimura,8A. Flacco,9C. Spindloe,10and M. Tolley10
1University of Milano Bicocca, Milano 20126, Italy
2General Physics Institute, Russian Academy of Sciences, Moscow, Russia
3Université de Bordeaux-CNRS-CEA, CELIA, Talence, France
4CEA/CESTA, Le Barp, France
5CEA-DAM, Bruyeres-le-Chatel, France
6University of St. Andrews, St. Andrews, United Kingdom
7CEA, Bruyeres le Chatel, France
8Institute of Laser Engineering, Osaka University, Osaka, Japan
9LOA, Ecole Polytechnique, Palaiseau, France
10Rutherford Appleton Laboratory, Didcot, United Kingdom
?Received 28 May 2009; accepted 19 October 2009; published online 18 December 2009?
We studied the induced plasma heating in three different kinds of targets: mass limited, foam targets,
and large mass targets. The experiment was performed at Alisé Laser Facility of CEA/CESTA. The
laser system emitted a ?1 ps pulse with ?10 J energy at a wavelength of ?1 ?m. Mass limited
targets had three layers with thicknesses of 10 ?m C8H8, 1 ?m C8H7Cl, and 10 ?m C8H8with
size of 100?100 ?m2. Detailed spectroscopic analysis of x rays emitted from the Cl tracer showed
that it was possible to heat up the plasma from mass limited targets to a temperature of ?250 eV
with density of ?1021cm−3. The plasma heating is only produced by fast electron transport in the
target, being the 10 ?m C8H8overcoating thick enough to prevent any possible direct irradiation of
the tracer layer even taking into account mass-ablation due to the prepulse. These results
demonstrate that with mass limited targets, it is possible to generate a plasma heated up to several
hundreds eV. It is also very important for research concerning high energy density phenomena and
for fast ignition ?in particular for the study of fast electrons transport and induced heating?. © 2009
American Institute of Physics. ?doi:10.1063/1.3261807?
I. INTRODUCTION
The study of strongly coupled plasmas1is of crucial im-
portance for several fields of physics, including inertial con-
finement fusion ?ICF? research and astrophysics.2,3More
specifically, in the fast ignition approach to ICF,2the heating
of the shock compressed plasma is expected to be produced
by a fast electron beam produced by ultrahigh intensity
?UHI? laser pulses. Therefore the study of fast electron in-
duced heating is of fundamental importance for the develop-
ment of this science. The use of mass limited targets4–7per-
mits to concentrate the fast electron energy in small regions,
confining them via the huge electric fields produced by
charge separation at the target surfaces. This leads to the fast
electron refluxing back and forth in the target, resulting in a
more uniform material heating to higher temperatures.4,6,8
Previous works showed that is possible to generate high en-
ergy density states characterized by high densities and tem-
peratures using mass limited targets and funnel shaped cone
targets.5However, the influence of the prepulse on the mea-
surements is determinant, as demonstrated in Ref. 5. The
prepulse, in fact, produces a preplasma that influences the
laser energy absorption and, at the same time, generates a
shock propagating in the target. The shock produced by the
pre pulse propagates, releasing its energy into the target and
causing the subsequent material expansion. The advent of
ultrashort pulse laser in principle allowed to deliver the
energy on target much faster than the typical temporal scale
length of plasma expansion, but in fact this is true only if we
neglect the presence of the prepulse. In many works what is
reported as “isochoric” heating has instead probably to be
referred to a lower density plasma. The misinterpretation is
probably due to the lack of diagnostics capable to measure
the prepulse effects and the target expansion, i.e., typically
interferometric or shadowgraphy diagnostics. In any case,
x-ray spectroscopy represents a key diagnostic to infer the
material temperature and density. High density plasma spec-
tra are characterized by broadened redshifted resonance
lines, with the appearance of new satellite structures, very
different from the usual low contrast or nanosecond laser
plasmas. This spectral behavior is explained with the dielec-
tronic satellite accumulation6and dense plasma line shift7,9
model. Measurements that do not show these features have
certainly not to be assimilated to high density states.
In this paper we present the experimental results on low
Z ?C8H8? plasma heating obtained from mass limited target
and induced by fast electrons produced in laser matter inter-
action in UHI regime. A buried chlorinated plastic thin layer
was used as a tracer. The x-ray emission was collected by a
high resolution Bragg spectrometer, and the spectral analysis
was mainly based on the Cl He-? line and its Li-like satel-
lites. Complementary optical, x-ray, and proton diagnostics
have been used to measure the pre pulse effects on target
?i.e., preplasma formation and target expansion?. The target
heating is only produced by fast electron refluxing in the
PHYSICS OF PLASMAS 16, 122701 ?2009?
1070-664X/2009/16?12?/122701/9/$25.00© 2009 American Institute of Physics
16, 122701-1

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target, being the 10 ?m C8H8overcoating thick enough to
prevent any possible direct irradiation of the tracer layer
even taking into account mass-ablation due to the prepulse.
II. EXPERIMENTAL SETUP
The experiment has been performed at CEA/CESTA us-
ing the 100 TW Alisé Laser Facility.10The laser delivered
12 J and 1053 nm pulses with ?1 ps duration. Pulses were
focused on target using a f/3 off axis parabola. The laser
focal spot was measured at low energy using an optical di-
agnostic ?imaging system coupled to a CCD?, showing that
the 50% of laser energy was contained in 15 ?m spot size
with an expected mean intensity ?for a similar energy distri-
bution in the main pulse? of ?3?1018W/cm2.At high laser
energy we used a x-ray pin hole camera to estimate the
plasma size and therefore get indirect information on focal
spot size. At the same time we looked at proton emission
versus focal position using from target with radio chromic
films ?RCFs?.11We found that the best focus position at high
laser energy was shifted by 200 ?m with respect to the
focus at low energy and showed maximum proton emis-
sion and plasma size of ?50 ?m. Assuming this as an indi-
cation of spot size we get a laser intensity on target
?6?1017W/cm2. It is important to notice that the pin hole
camera filter was 6 ?m thick Al, allowing the transmission
of soft x rays in the range of 1–1.5 keV produced by the laser
wings and thermal radial conduction. In this sense, our in-
tensity evaluation has to be assumed as an average over the
measured x-ray spot size, while a larger peak intensity can be
expected. The prepulse was 6 ns long growing linearly from
the noise to a final contrast ratio of ?5?10−5. The
s-polarized laser was focused with a 7° incidence angle to
the target normal. Several diagnostics have been used to get
crossed information on plasma parameters.
The chlorine x-ray spectrum has been collected by a to-
roidally bent Bragg quartz crystal spectrometer12looking at
the target front side and recorded on a back illuminated
CCD. The spectrometer was operated in the second order of
reflection, giving spectral range from 4.40 to 4.75 Å and
recording Cl lines from the “cold” K-? at 4.7286 Å to the
He-? at 4.4438 Å, the He-? line being reflected at 41.7°
Bragg angle. The viewing angle of the spectrometer was 5°
to the target front surface.
A gated optical imager ?GOI? ?Ref. 13? looked at the
target rear side with an angle of 38° to the normal. The
temporal window was 120 ps, and the images were filtered
with a 2?-530 nm interferential filter, cutting any scattered
laser light as well as laser shining through the target at very
early times. The gate was opened at different time delays,
before and after the arrival of the main pulse, in order to
measure the target expansion. Plasma extension has also
been measured using a transverse shadowgraphy technique
with a 1 ps-2? probe beam. Of course these two diagnostics
also allow to determine the extension of preplasma if syn-
chronized before the arrival of the main pulse. The shadow-
graph images were filtered by a 2?-530 nm interferential
filter and recorded on a 8 bit CCD. The x-ray emission from
the front side plasma has been recorded by an x-ray pin hole
looking at the target surface with an angle of 61° to the target
normal. The filter was 6 ?m Al layer, the pin hole diameter
was 5 or 30 ?m, and the magnification has been varied from
2.5 to 10. The image has been recorded on direct exposure
film ?Kodak?. Finally, radio chromic film stack ?Gafchromic
HD 810?, 28 mm far from the target rear surface, has been
used for proton diagnostic target.
In the experiment we used four different kinds of
multilayer targets and a single layer target, namely,
?1? mass limited targets, 100?100 ?m2, 230 ng, and com-
posed by three layers, 10 ?m C8H8, 1 ?m C8H7Cl
tracer layer, and 10 ?m C8H8;
?2? massive targets, 2?2?2 mm3, made of C8H8with
C2H3Cl tracer layer buried at 10.5 ?m depth;
?3? foam targets composed of 50 ?m thick C8H8 and
0.05 g/cm3foam with 1 ?m C8H7Cl tracer layer on
the back ?the laser being focused onto the foam layer?;
and
?4? pureC2H3Cl
?polyvinylchloride
200 ?m thick, used for x-ray diagnostics alignment.
?PVC??
targets,
Mass limited and foam targets have been fabricated by
Rutherford Appleton Laboratory target preparation team,
while the massive and pure PVC targets have been prepared
at ILE. The schematic of the experimental setup is shown in
Fig. 1.
III. EXPERIMENTAL RESULTS
This paper is mainly devoted to the analysis of
results obtained with mass limited targets. Results obtained
with massive targets and foam targets are only used for
comparison.
The experimental results manifestly show the action of
the prepulse on mass limited targets, inducing the target ex-
pansion before the arrival of the main pulse. The expansion
is clearly seen on GOI and x-ray pin hole images as well as
in shadowgraphy, and its effects influences the shape of RCF
signals and x-ray spectra.
FIG. 1. ?Color online? Schematic of the experimental setup.
122701-2Morace et al.Phys. Plasmas 16, 122701 ?2009?

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A. Expansion measurements
GOI shows the target expansion 100 ps before the main
pulse arrival ?Fig. 2, right?. Pin hole images show similar
results ?Fig. 3?. For massive and foam targets, the pin hole
images are characterized by a well defined single spot ?of
average size of 50 ?m at best focus?. Mass limited target
images are instead characterized by multiple spots distrib-
uted on a surface, which is much larger than the original
target size ?Fig. 3, center?. Due to the fact that x rays are
emitted only from very hot regions in the target, we attribute
these images to the arrival of the main pulse on the already
expanded target. Also, due to the short duration of the laser
pulse, as well as the very fast time of x-ray emission, these
pin hole images give an instantaneous image at the arrival
time. The size of the emitting area is compatible with the
GOI data.
In order to calculate the target volume from a two-
dimensional image, several assumptions have to be made.
The expansion has been considered as a composition be-
tween a “preferential” expansion toward the laser incoming
direction and an isotropic component due to thermal expan-
sion. It is indeed expected that plasma expansion is larger on
the laser axis due to interaction with target front surface. The
isotropic expansion involves the three dimensions in the
same way and is estimated by measuring the image size nor-
mal to the laser propagation. Preferential expansion is esti-
mated from the difference between the horizontal size of the
experimental image and the calculated target size after iso-
tropic expansion, taking into account the 38° viewing angle
to the target normal ?Fig. 4?. In this way the volume has been
calculated to be two orders of magnitude larger than the ini-
tial target volume.
Finally shadowgraphy images also qualitatively show
the same behavior; a large preplasma is extended toward the
laser direction. Figure 5 shows a shadowgraph of foam target
100 ps before the main pulse arrival. The preplasma exten-
sion toward the laser direction is ?75 ?m. This value is in
fair agreement with the value observed with mass limited
targets. Unfortunately no mass limited shadowgraphs have
been recorded due to problems in the diagnostics.
B. RCF
The expansion of mass limited targets before the arrival
of the main pulse is also confirmed by analysis of the proton
signal obtained on the RCF stack. As it is well known14
protons are accelerated due to the sheath potential formed by
charge separation at the target rear side by the fast electrons.
Usually emission is normal to the target rear surface, with an
energy dependent angular spreading of by 40°–50° disper-
sion at low energies and 10°–15° at higher energies. Indeed
RCF data obtained from foam targets show a quite colli-
mated proton emission, with energy-dependent spreading of
proton beam ?Fig. 6? and a maximum energy of ?6 MeV.
For mass limited targets, results change dramatically.
The proton signal is distributed on the entire RCF film sur-
face, and their energy is limited to 1 MeV ?Fig. 7?. Both the
large proton spreading and the lower energy can be explained
by assuming that target has already expanded at the arrival of
FIG. 2. ?Color online? X-ray pin hole images. Left: massive target ?the spot
size is 54 ?m?. Center: mass limited target showing the multiple spots.
Right: the same image compared with the original target size as seen from
the x-ray pin hole.
FIG. 3. ?Color online? GOI images of mass limited targets Left: mass limited target reference image before the main pulse arrival. Right: image of target 100
ps before the main pulse arrival, clearly showing a significant target expansion.
122701-3Study of plasma heating induced by fast electronsPhys. Plasmas 16, 122701 ?2009?

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the main beam when protons are emitted. The accelerating
quasistatic field is related to both the fast electron energy and
the scale length of plasma by the relation
E =
Te
eLn
,
?1?
where E is the electric field, Tethe fast electron temperature,
and Lnis a typical scale length.
In the case of solid target, Lnis the hot electron Debye
length, which is typically of the order of 1 ?m. In the case
of an expanding plasma, the scale length is determined by
the density gradient L given by
Ln= cs?,
?2?
where csis the plasma sound velocity and ? is the temporal
scale length. In this case L??hotand the accelerating electric
field decreases and the consequent proton energy gets
smaller. At the same time this also explains the geometrical
shape of emission. In a solid target, the rear surface is planar
and protons are emitted perpendicularly to it. In the case of
mass limited target, the large beam divergence is a conse-
quence of the plasma expansion, modifying the shape of tar-
get rear surface and then the emission direction of protons.15
C. X-ray spectroscopy
Obtained experimental x-ray spectra strongly differ for
the different types of targets, showing a larger ionization for
mass limited targets compared with massive and foam tar-
gets. Figure 8 shows the Cl x-ray spectrum obtained from
C2H3Cl ?PVC? target. The spectrum is ranging from the cold
K-? line to the He?1resonance line corresponding to the
Cl15+ionization state and its Li-like satellites corresponding
to electronic transitions in the Cl14+state. The K-? line is a
superposition of eight unresolved lines for ionization states
from Cl1+to Cl8+.16
By comparing the spectra obtained with different targets
?Fig. 9?, it is clear that the higher ionization is reached in the
mass limited targets, implying a higher temperature. Instead
the massive targets show a lower ionization, and foam targets
only show cold K-? line signal.
IV. SIMULATIONS OF PREPLASMA EXPANSION
A 2D radiative hydrodynamic code ?DUED? ?Ref. 17? has
been used to perform a simulation to study the mass limited
target expansion under the action of the prepulse. The case
that was simulated implied that a simulated prepulse was
growing linearly from 0 to 5?1012W/cm2.
The result for density and at 6 ns is shown in Fig. 7. At
the end of the prepulse, the mass limited target appears al-
ready expanded, with an overall density much lower than the
solid one. Let us notice that the real prepulse is even larger
than the simulated one ?Fig. 10?. Therefore expansion is ex-
pected to be even larger, confirming the results on expansion,
which were obtained by GOI and pin hole X.
V. SIMULATIONS AND DISCUSSION
OF SPECTROSCOPIC RESULTS
We performed a detailed kinetic simulation of the x-ray
line emission spectra to estimate the relevant plasma param-
eters ?electron density and temperature? corresponding to the
experimental observations. The spectral lines of highly
charged ions are clearly visible both in the mass limited tar-
get and in the alignment shots involving pure PVC targets.
The spectral analysis is based on the intensity ratio between
the resonance and intercombinational lines of the He-like ion
?He?1,?2? and the dielectronic satellite lines of the Li-like
ion, while the K-? signal is related to the fast electron trans-
port in lower ionized matter.
The collisional-radiation kinetic level population model
used for spectra simulations corresponds to the scheme of
energy levels for Cl ions shown in Fig. 11. The model is
based on the 1s-2p transitions between the ground and ex-
FIG. 4. ?Color online? Schematic of target expansion. The small central box
represents the original target, the semitransparent box on the right represents
the isotropic expansion, and finally the semitransparent box on the left rep-
resents the preferential expansion due to laser interaction on the front
surface.
FIG. 5. ?Color online? Foam target shadowgraph 100 ps before the main
pulse arrival. The preplasma extension toward the front target surface is
?75 ?m.
FIG. 6. RCF data obtained for foam target and correspondent proton energy.
The first RCF is on the left. We clearly see how larger energy protons are
characterized by smaller opening angles.
122701-4Morace et al.Phys. Plasmas 16, 122701 ?2009?

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cited states of He- and Li-like ions. For the Li-like ions tran-
sitions to the autoionizing states 1s2l2l? are also included to
account for the dielectronic satellite structure of the spectra.
Optically allowed dipole transitions between the autoioniz-
ing states are included as well. The quasistationary condition
for the excited states population densities Nn
charge Z is valid as if their relaxation time is much shorter
than those for the ground states and their populations relate
as Nn
algebraic equation set for the population densities of the ex-
cited levels arranged by ascending energy reads
Zof ions with the
Z?N1
Z?see, e.g., Ref. 18 and references therein?. The
Kn
ZNn
Z=?
n??n
Knn?
ZNn?
Z+ Kn1
ZN1
Z+ Kn1
Z,Z+1N1
Z+1+ Kn1
Z,Z−1N1
Z−1,
?3?
where the relaxation rates Kn
?Knn?
density and the energy and fraction of hot electrons in the
form
Zand the transition rates
Z,Knn?
ZZ?? depend on the bulk electron temperature and
Kn
Z=?
n??n
An?n
ZNe+?
Z
+ ?n
Z+?
n??n
Vn?n
n? ? n,?
ZNe+ V1n
Z+1,ZNe,
?4?
Knn?
Z
= Vnn?
Ann?
0,
Z,
n? ? n
?5?
Kn1
Z,Z+1= Vn1
Z,Z+1Ne
2+ ?Cn1
Z,Z+1+ Rn1
Z,Z+1?Ne,
?6?
Kn1
Z,Z−1= Vn1
Z,Z−1Ne.
?7?
The rates in Eqs. ?4?–?7? contain the radiation Ann?
ionization
?n
probabilities,
excitation rates Vnn?
mal electron bulk and hot fraction, the electron impact
Z
and auto-
excitation/de-
Z?Ehot? by the ther-
Z
theimpact
Z=?1−f?Vnn?
Z?Te?+fVnn?
ionization rates V1n
the recombination rates including the three-body recombina-
tion Vn1
tronic capture Cn1
The ground state population densities in Eq. ?3? are con-
sidered as a parametric dependence or in the stationary re-
gime as well. Thus the excited level population in Eq. ?3?
depends on the bulk electron temperature, the electron den-
sity, the hot electron fraction, and the hot electron average
energy in smaller degree. The values Nn
spectrum of the x-ray line emission for the optically thin
plasma in the form
Z+1,Z=?1−f?V1n
Z+1,Z?Te?+fV1n
Z+1,Z?Ehot?, and
Z,Z+1?Te?, photo recombination Rn1
Z,Z+1?Te? processes.
Z,Z+1?Te?, and dielec-
Zdefine the synthetic
FIG. 7. RCF image for mass limited target; the protons are distributed on
the whole film and their energy is low. All protons stop at the first layer
corresponding to energies of ?1.1 MeV.
FIG. 8. ?Color online? ?Top? Chlorine high energy spectrum from the K-?
line ?right? to the He?1resonance line ?left?. The He?2line is overlapped to
some Li-like satellite lines. ?Bottom? The experimental spectrum as recorded
on the x-ray CCD.
FIG. 9. ?Color online? Typical Cl x-ray spectra for mass limited targets, pure
PVC targets, and massive and foam targets.
122701-5Study of plasma heating induced by fast electronsPhys. Plasmas 16, 122701 ?2009?

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I??? = C?−1?
Znn?
Ann?
ZNn?
ZS?? − ?nn?
Z?,
?8?
where S?x? is the spectral function and C is the normalization
factor.
Figure 12 presents the result of calculations by Eqs. ?3?
and ?8?, demonstrating the effect of the hot electron fraction
f on the line intensities for different values of the bulk elec-
tron temperature Teat the electron density Ne=1021cm−3
that is close to the critical value for the Nd-laser radiation.
The hot electron energy was fixed at 100 keV. In fact its
value in the range from 50 keV to a few hundreds keV does
not strongly change the shape of the x-ray spectrum. The
reason is in a smooth variation in the ionization rates and the
excitation rates of the autoionizing states in Li-like ions from
the ground and low lying excited states in this energy
range. This also allows considering a monochromatic energy
spectrum of hot electrons. We used the spectral function S
that corresponds to the Doppler line broadening for ions with
the effective temperature Ti=1.5 keV that accounts for the
macroscopic plasma expansion. The stationary ion charge
distribution was used. The spectroscopic constants for the
lines indicated in Fig. 11 were taken from Ref. 19, while the
collisional rates are from Refs. 20 and 21.
At low values of the hot electron fraction f?0.01%, the
satellite lines k and j from the 1s?2p21D?2DJautoionizing
states that are populated mainly through the dielectronic cap-
ture from the ground state of the He-like ion dominate in the
emission spectra since the electron excitation of the reso-
nance He?1and the He?2lines is weak even at higher
Te=250 eV in Fig. 12?c?. By increasing the hot electron
fraction, the intensities of the He?1,?2and those satellites
populated via the electron excitation channel are growing up,
which agrees with the results for a similar spectrum of Ar in
Ref. 22. Note that the intensity of He?2dominates in the
overlapped group of lines. At f?0.05% the intensities of
“excited” satellites exceed over the “captured” ones espe-
cially for Te?200 eV ?Figs. 12?a? and 12?b??. At higher Te
?Fig. 12?c?? the k and j satellites are enhanced due to addi-
tional population of the He-like ion by thermal electrons. In
this case the satellites from the right side group have similar
intensities.
The dependence of the satellite structure on the electron
density is much weaker in agreement with the calculations in
Ref. 22. Thus the results presented in Fig. 12 provide
guidance for the modeling of the experimentally observed
spectra.
In Fig. 13 the experimental spectrum for the mass lim-
ited target is compared with calculation that gives a good
agreement at plasma parameters indicated on the plot. In
addition the optical thickness was taken into account with the
effective plasma size of 75 ?m. It gives the optical density
for the He?1line ?=3.8 that leads to additional width of the
line. The visible difference in the He?1 wings is partly due
to contribution of satellites from 1s2p3l autoionizing states22
that are omitted in present calculations. The optical depth for
other lines is considerably lower. Note that the electron den-
sity of 1021cm−3is in fair agreement with our expectations
based on the evaluation of target expansion before the arrival
of the main high intensity pulse.
Temperature and density for mass limited targets have
been determined by comparing the experimental results with
simulations ?Fig. 13?. The best agreement is obtained when
the mass limited targets reach a temperature of 250 eV and a
density of 1021cm−3, with a fast electron fraction of 0.05%.
Let us notice that a density of 1021cm−3is in fair agreement
with our expectations based on the evaluation of target ex-
pansion before the arrival of the short-high intensity pulse.
To check the consistency of the analysis, energy conser-
vation is required. We made several simplifying assumptions.
FIG. 10. ?Color online? Mass limited target density at the end of the
prepulse. The mass limited target is completely deformed, and the rear side
is expanding.
FIG. 11. ?Color online? Graphical scheme of model kinetic matrix. ?Left?
The Li-like Cl ion transitions. ?Right? The He-like transitions.
122701-6Morace et al.Phys. Plasmas 16, 122701 ?2009?

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Fast electron average energy was fixed using the Beg’s scal-
ing law23
Thot= 100 keV?
I?W/cm2?
1017W/cm2?
1/3
? 200 keV.
?9?
The total number of electrons in the mass limited target is
N=7?1016, and the number of ions is ?N/3; both species
are assumed to have the same temperature Te=250 eV de-
termined from spectroscopic analysis, corresponding to a to-
tal energy of 4.48 J. The fast electron fraction of 0.05% gives
a total number of fast electrons of 3.5?1013with a total
energy of 1.12 J. This corresponds to a conversion efficiency
laser-fast electrons of 9%, in agreement with other works
performed at the same laser intensity.24The energy contained
in the pre pulse corresponds to 1.8 J, and the ionization en-
ergy is 0.74 J.
Summing all the contributions we find a total energy of
7.5 J, compatible with the total laser energy of 12 J. It must
be pointed that in the calculation, the hydrodynamic work
and the radiative energy dissipation have not been taken into
account, and then the real energy value can be closer to 12 J.
Finally, comparing the mass limited and the pure PVC
target spectra, both the spectra are relative to a plasma,
whose density is 1021cm−3, but for PVC target this corre-
sponds to the emission from the plane critical layer, while for
mass limited targets, it is the average density of the material
?the tracer layer being inside the target?. Figure 9 shows the
comparison between these two spectra.
Let us also notice that the PVC target spectrum is ?5
times more intense than the mass limited target one. This
result can be explained by considering the number of radiat-
ing Cl atoms in the two targets and taking into account op-
tical thickness effects. The number of radiating atoms for
PVC target is evaluated assuming that the x-ray radiation
comes from the ablated mass. The ablation rate is
(a)
(b)
(c)
FIG. 12. ?Color online? Spectra simulation results varying the fast electron fraction to total electrons from 0% to 0.08%. ?a? Plasma electron temperature of
Te=150 eV. ?b? Te=200 eV. ?c? Te=250 eV.
122701-7Study of plasma heating induced by fast electronsPhys. Plasmas 16, 122701 ?2009?

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m ˙?
kg
cm2s?= 150?I?W/cm2?
= 109?
1014 ????m?−4/3?
cm2s?,
A
2Z?
kg
?10?
where A is the atomic mass and Z is the ion charge.
The ablated thickness over the focal spot surface
?25 ?m radius? is therefore given by
d =m ˙ ?
?
= 4.7 ?m,
?11?
where ? is the pre pulse duration and ? is the PVC density
corresponding to 1390 Kg/m3. Being the PVC ?C2H3Cl?
molar mass equal to 62 g/mol, the total number of Cl atoms
in the ablated mass is 1.2?1014.
Instead the Cl atoms in the mass limited target tracer
layer ?C8H7Cl? are 5.63?1013; then the radiating Cl atoms
in PVC target are ?2 times larger than the Cl atoms in the
tracer layer. The optical thickness of the C8H8overcoating
layer in the mass limited target, taking into account the spec-
trometer viewing angle, allows ?50% of x-ray transmission
in the range of 2.6–2.8 keV. Then the signal form pure PVC
target is ?5 times larger the one coming from mass limited
targets.
Concerning the spectral structure, the He?2line is mani-
festly more intense for the PVC target as it is also true for the
for the cold K-? line signal, which for the mass limited tar-
get is practically absent. In fact for the PVC target the fast
electron beam passes through a mostly nonionized matter
producing K-? signal. In mass limited targets instead, most
of the matter is highly ionized due to high energy density,
and then the K-? signal disappears.
VI. CONCLUSIONS
Low Z plasmas from mass limited targets were uni-
formly heated to large temperature ??250 eV? via fast elec-
trons. X-ray spectroscopy was used as a diagnostic tool to
measure plasma temperature and density. We have demon-
strated that the fast electrons are suitable to heat up plasmas
to a very large temperature, as required to generate high
energy density states. The plasma heating is only produced
by fast electron transport in the target, being the 10 ?m
C8H8overcoating thick enough to prevent any possible direct
irradiation of the tracer layer even taking into account mass-
ablation due to the prepulse.
ACKNOWLEDGMENTS
This experiment has been performed within the frame-
work of the European Program of Access LaserLab. A. Ma-
gunov gratefully acknowledges the hospitality of the Univer-
sity of Milano Bicocca under the Fellowship of the Cariplo
Foundation through the Landau Network-Centro Volta.
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