Hot Electrons Transverse Refluxing in Ultraintense Laser-Solid Interactions
S. Buffechoux,1,2J. Psikal,3,4M. Nakatsutsumi,1L. Romagnani,5A. Andreev,6K. Zeil,7M. Amin,8P. Antici,12
T. Burris-Mog,7A. Compant-La-Fontaine,9E. d’Humie `res,3S. Fourmaux,2S. Gaillard,7F. Gobet,10F. Hannachi,10
S. Kraft,7A. Mancic,1C. Plaisir,10G. Sarri,5M. Tarisien,10T. Toncian,8U. Schramm,7M. Tampo,11P. Audebert,1
O. Willi,8T.E. Cowan,7H. Pe ´pin,2V. Tikhonchuk,3M. Borghesi,5and J. Fuchs1,*
1LULI, E´cole Polytechnique, CNRS, CEA, UPMC, route de Saclay, 91128 Palaiseau, France
2INRS-EMT, Varennes, Que ´bec, Canada
3CELIA, Universite ´ de Bordeaux-CNRS-CEA, 351 Cours de la Liberation, 33405 Talence, France
4Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague, Czech Republic
5Centre for Plasma Physics, The Queen’s University, Belfast BT7 1NN, United Kingdom
6Max Born Institute, Berlin D-12489, Germany
7Forschsungszentrum Dresden Rossendorf, Postfach 510119, 01314 Dresden, Germany
8Institut fu ¨r Laser und Plasma Physik, Heinrich-Heine-Universita ¨t Du ¨sseldorf, Universita ¨tstrasse 1, 40225 Du ¨sseldorf, Germany
9CEA, DAM, DIF, 91297 Arpajon, France
10Universite ´ de Bordeaux, Centre d’Etudes Nucle ´aires Bordeaux Gradignan, UMR 5797 CNRS/IN2P3, Gradignan, 33175, France
11Kansai Photon Science Institute, Japan Atomic Energy Agency (JAEA), Kyoto 619-0215, Japan
12Istituto Nazionale di Fisica Nucleare, Via E. Fermi, 40-00044 Frascati, Italy
and ILE-Ecole Polytechnique-CNRS-ENSTA-Iogs-UP Sud, Batterie de l’Yvette, 91761 Palaiseau, France
(Received 26 February 2009; revised manuscript received 21 January 2010; published 2 July 2010)
We have analyzed the coupling of ultraintense lasers (at ?2 ? 1019W=cm2) with solid foils of limited
transverse extent (?10 s of ?m) by monitoring the electrons and ions emitted from the target. We observe
that reducing the target surface area allows electrons at the target surface to be reflected from the target
edges during or shortly after the laser pulse. This transverse refluxing can maintain a hotter, denser and
more homogeneous electron sheath around the target for a longer time. Consequently, when transverse
refluxing takes places within the acceleration time of associated ions, we observe increased maximum
proton energies (up to threefold), increased laser-to-ion conversion efficiency (up to a factor 30), and
reduced divergence which bodes well for a number of applications.
DOI: 10.1103/PhysRevLett.105.015005PACS numbers: 52.38.Kd, 41.85.Ew, 52.38.Dx, 52.65.Rr
The dynamics of MeV electrons generated in solids by
ultraintense lasers plays a crucial role in many applications
such as electron-driven fast ignition  or the production
of secondary sources, e.g., x rays , positrons , or ions
, all with important scientific or societal perspectives.
Understanding the hot electrons dynamics requires con-
sidering several aspects of their transport through the tar-
get. First, the target material  can induce filamentation
of the forward propagating MA electron current through its
interplay with the return current. Second, the recirculation
of the hot electrons, as they are reflected by the Debye
sheaths at the target front and rear surfaces, affects electron
transport through the target (longitudinal transport) [6,7].
If the targets are thin enough, this longitudinal recircula-
tion induces a transient electron density enhancement.
Finally, electrons will also spread laterally along the target
surfaces. This transverse transport was studied in the 1980s
 and has been revisited recently on large targets via
measurements of ion emission .
This Letter reports an investigation of the influence of
the target lateral dimensions on the dynamics of hot elec-
trons and associated energetic proton production. It is the
first to identify the important role played by the lateral
electron recirculation in small targets. As observed in the
simulations discussed here, electrons that are injected into
the target center at 45?are seen to spread along the target
surface with a velocity vt
target edges. They therefore transit from the center to the
edges and back in a time ?t¼ Ds=vt
the target transverse diameter. When ?tis of the order of
the laser pulse duration ?L, the hot electrons, refluxing
from the edges, are confined during or shortly after ?L.
This leads to a time-averaged denser, hotter, and more
homogeneous electron population.
The experiments were performed using the 100 TW
laser at LULI. The laser pulse (?L¼ 400 fs) was
frequency doubled and filtered at 529 nm in order to
enhance its temporal contrast. This was done to avoid
preplasma formation on the front surface that, hydrody-
namically expanding, could reach and perturb the rear
surface, hampering proton acceleration . As illustrated
inFig. 1, the laser was focusedto a spot offull width at half
maximum (FWHM) of ?6 ?m, in S polarization, at 45?
incidence, and at the targets’ center. The laser energy in
this focal spot was EL? 7 J, which led to a peak intensity
on target of I ? 2 ? 1019W ? cm?2. Wave front correction
was applied before every shot.
To explore the effect of the electrons transverse reflux-
ing, we used Au targets that had constant thickness
(2 ?m), but with variable surface areas. As shown in
hot? 0:7c and reflected at the
PRL 105, 015005 (2010)
2 JULY 2010
? 2010 The American Physical Society
Fig. 1, three diagnostics were used. The first uses radio-
chromic film (RCF) (with a central, millimeter-sized hole)
 in front of a magnetic spectrometer  to resolve in
energy and angle the protons that are electrostatically
accelerated by the electrons [4,13]. The second diagnostic
utilizes a stack of four calibrated image plates (IP) 
separated by 2 mm thick Al plates to resolve the energy of
hot electrons expanding into vacuum up to the stack.
During this expansion, the electrons cool down by trans-
ferring their energy to the ions, but nonetheless retain a hot
tail with the temperature of the initial population at the
target surface . It is this hot tail that is measured by the
stack. The third diagnostic records 2D time-resolved im-
ages ofthe thermalemission fromthebulkelectronsat
the target surface that are collisionally heated by the hot
We first analyze the effective (time-averaged) hot elec-
tron temperature (Thot) as a function of the target surface
area given by the first diagnostic. The proton beam energy
distribution is shaped by the characteristics (density, tem-
perature) of the accelerating electron sheath described by
dNp=d" ¼ 1:3Nhotcs=½cð2"ThotÞ1=2??
expð?½2"=Thot?1=2Þ . By fitting with this expression
the proton spectra measured from RCF data (by optical
calibration of the dose deposited in the RCFs as well as
through nuclear activation measurements ), we can
obtain [see the squares in Figs. 1(b) and 1(c)] Thot, the
electron sheath temperature, and Nhot;the effective num-
ber of electrons in the sheath, both time integrated over
the proton acceleration time ?acc(see below). Note that
the fitting used to obtain the results shown in Figs. 1(b) and
1(c) is a 1D picture assuming a homogeneous elec-
FIG. 2 (color online).
showing that the dose is more collimated when using small targets. The inset shows the RCF (dose in units of Gy) for a 300 ?
200 ?m2target. (b) FWHM of dose profiles for the same targets as in (a) for all proton energies. (c),(d) Thermal rear side emission
image (integrated over 30 ps) for two targets 4 ns after the interaction. The laser is incident on the tilted target from the right side of the
image, which explains the observed asymmetry. Note that the emission in (d) is, in absolute, 3 times brighter than in (c).
(a) Azimuthally averaged angular proton dose profiles extracted from RCFs for two targets at "="max? 0:6,
FIG. 1 (color online).
experiment. (b) Effective number of hot
electrons in the accelerating sheath Nhot,
and (c) effective hot electron tempera-
ture Thotas a function of surface area.
Squares are extracted from the RCF-
measured proton spectra.
(a) Setup of the
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tron population over the sheath. We observe in Figs. 1(b)
and 1(c) that both Nhotand Thotincrease for targets having
surface areas <3–4 ? 104?m2, corresponding to target
transverse diameters Ds< 170–200 ?m. For larger tar-
gets, both Thotand Nhotremain, on the contrary, constant.
With regard toThot,thedata areconsistentwith simulations
of sharp-interface plasmas irradiated at 45?with S polar-
ization . With regard to Nhot, the data are consistent
with measurements of hot electrons density (nhot) and
sheath surface  which, combined, yield a comparable
number of electrons contained in the sheath as shown here
in Fig. 1(b). The circles in Fig. 1(c) show complementary
results obtained fromthe second diagnostic, confirming the
trend for Thotobtained. Thotis here obtained by fitting the
electron dose measured in the IP stack by assuming a
Boltzmann distribution for the electrons with a given Thot
and using the Monte Carlo code GEANT4 , or similarly
MCNP . Finally, the thermal emission diagnostic con-
firmed that the energy density of the hot surface plasma
increases when reducing the target surface area [compare
Fig. 2(c) to Fig. 2(d)]. All of these results are consistent
with previous reports of bulk target heating increase when
reducing the target surface area [16,22].
We also observe that the hot electron sheath becomes
more uniform when we reduce the target surface area. This
result is obtained by analyzing the angular proton beam
profile as recorded on RCF. Indeed, the angular divergence
of the proton beam is determined [4,5,23] by the curvature
of the accelerating electron sheath. Figure 2(a) displays
proton beam angular profiles corresponding to a beam slice
at ?60% of the maximum proton energy collected on RCF
fortwodifferent targetsizes.Thisfigureand Fig.2(b)show
that the beam is more collimated when the target surface
area is reduced. This suggests a flatter electron sheath
along the target rear side for smaller targets, which is
consistent with the picture of geometrically confined elec-
trons. The measurement of the thermal emission from the
target rear side further confirms this. This is observed in
Figs. 2(c) and 2(d) where the lateral homogeneity of the
thermal emission increases when reducing the target sur-
As a result of the observed increase of Nhotand Thot
reducing the target surface area, we observe a clear im-
provement of the proton beam characteristics as shown in
Fig. 3. This result was also suggested by several theoretical
studies . This is effective when the target surface area
is also reduced below ?3–4 ? 104?m2.
of laser target interactions were performed with the code
described in Ref.  to help us identify that lateral
refluxing of the hot electrons is the key process here.
Because of computational limitations the laser and target
parameters were rescaled, however the ratio of Dsto ?L
was kept the same as in the experiment. As ?t=?L¼
reflux laterally during or shortly after ?L. We thus used in
the simulations ratios ?t=?Lof 0.85 and 3.4 as for ‘‘small’’
(50 ? 80 ?m2) and ‘‘medium’’ (200 ? 300 ?m2) foils
used in the experiment, respectively. The simulations use
?L¼ 80 fs, a laser beam with the same polarization as in
the experiment, a wavelength of ? ¼ 600 nm and a super-
Gaussian profile (n ¼ 3) with a FWHM of 7?. The inci-
dence angle is 45?, and the maximum intensity is I ¼
2:4 ? 1019W=cm2. Targets are 2? thick and composed
of protons and electrons with a steplike density profile of
ne¼ 20ncand an initial temperature of 2 keV. Simulation
boxes are 76? ? 76?, 2? thick absorption layers are added
behind each side of the box and the cell size is set to 12 nm.
The electrons that reach the simulation box boundaries are
frozen there. The simulations were run up to 3:5?Lafter the
laser hits the foil when ion acceleration starts to saturate. In
both cases, the observed laser pulse absorption is the same.
The mechanism of refluxing, as observed in the simula-
tions,is as follows:because of their highvelocity,electrons
trajectories can be considered as ballistic. As electrons
enter the target with an angle close to the laser incident
angle (45?), their average transverse (with respect to the
target normal) velocity in the target is vt
cosð45Þ ¼ 0:7 c, as shown in Fig. 4(a). After several re-
flections off the sheath fields on the front and back surfaces
with that same angle, the electrons will have traveled
transversely to the edge of the target to be again reflected
back . Note that electrons could be also generated
along the surface in thin current sheets, but this happens
only for larger (>60?) laser incidence angles . The
hot? is key in determining whether the electrons
hot? c ?
FIG. 3 (color online).
give (a) maximum proton energies for
2 ?m thick Au targets of various surface
area and (b) laser-to-proton energy con-
version efficiencies (for protons with en-
ergy >1:5 MeV) for the same targets.
Data from RCF
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expansion velocity of 0:2 ?m=fs predicted theoretically
 and with previous measurement of the sheath lateral
Such refluxing takes place obviously more quickly for
smaller targets. As a result, we observe in the simulations
that the hot electron spectra, measured at the target center,
display time-averaged higher Thotand nhot, by, respec-
tively, factors 1.2 and 2.3, for the small foil case when
compared to the medium one. Figure 4(b) illustrates the
temporal evolution of Thotfor both foil dimensions in good
agreement with the measurements shown in Fig. 1. For the
small foil, due to the constant refluxing of hot electrons
from the foil edges, Thotdecreases slowly. On the contrary,
for the medium foil, Thotdrops dramatically after the laser
pulse ends but later reincreases due to electrons refluxing
after 2:5?L(corresponding to ?tfor this target dimension).
As the electrons sustain the sheath fields, lateral refluxing
goes along with an energy loss for the electrons (there is a
?10% energy loss in each bounce for the electrons ).
This explains why refluxing produces a lesser increase of
Thotthan of nhot, in agreement with the results of Figs. 1(b)
Regarding proton acceleration, the simulation results
also agree well with the variation of the experimental
proton cutoff energies. However, the enhancement of the
laser-to-ion conversion efficiency found in the simulations
(6% for small vs 4% for medium foil) is smaller than in the
experiments. This can be explained by the fact that the
electrons cannot spread in the third spatial dimension in
our 2D simulations. The conversion efficiency is propor-
tional to the product Thotnhot and therefore very sensi-
tive to the electron density. On the contrary, the maximum
ion energy depends on Thotand only weakly on nhot.
Preliminary 3D simulations show that the 2D ones can
hotobserved here agrees well with the electric field
predict well the maximum ion energy, but overestimate
the conversion efficiency for large targets.
The enhancement in ion acceleration can take place only
if the electrons can come back to the target center within
the ion acceleration time ?acc, i.e., if Ds? Ds? , where
Ds? ¼ ?accvt
observe indeed an increase in the proton beam parameters
(see Fig. 3) when Ds? Ds? ¼ 170–200 ?m. From this,
we can deduce an experimental proton acceleration time
?acc? 800–950 fs. This is consistent with theoretical es-
timates. For this, we note that ?accis the duration it takes
the proton leading front to leave the target and to travel far
enough so that it is no longer affected by the initial electron
pressure. Obviously, ?accis proportional to the character-
istic time of initial ion motion !?1
ðnhote2=mi"0Þ1=2is the ion plasma frequency. Knowing
ðThot=miÞ1=2, the hot sound speed, and that the ions in the
leading edge of the beam eventually reach a constant
velocity vi, we have: ?acc¼ !?1
after which the ions stabilize their velocity. Combining
experimental results  and simulation data over a large
range of parameters , we found a simple linear relation
vi? 6cshleading to ?acc? 6!?1
with previous numerical estimates . From the simula-
tions, we estimate nhot? 5 ? 1019cm?3, yielding a con-
sistent ?acc? 900 fs.
Also in good agreement with the experimental result of
Fig. 2, Figs. 4(c) and 4(d) show that refluxing produces in
the simulations a more uniform sheath in small targets as
the hot electrons are forced to recirculate in the small foil.
Use of the lateral electron recirculation mechanism is of
interest for future experiments at higher intensity laser
facilities , but will impose high temporal contrast laser
hot. As mentioned above, we experimentally
piðvi=cshÞ, i.e., the time
pi, which is in agreement
FIG. 4 (color online).
phase space of hot electrons (with energy
>100 keV) for the medium foil at time
?L(the x axis is along the foil, the y axis
is perpendicular) demonstrating trans-
(b) Temporal evolution of hot electron
temperature component in the y direction
for small and medium foils. Only elec-
trons in a central strip 10? wide around
the target center are considered. The
schematic drawings inset represent, for
each target (to scale) at 1:5?Lafter hav-
ing being launched at the target center,
the path of an electron traveling at vt
(c) Spatial distributions of electrons for
the (c) small and (d) medium foils at
2:5?L. The color bar shows electron den-
sity normalized to nc.
hot? 0:7 c.
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2 JULY 2010
In addition, progress in target fabrication will offer targets
that are not only of reduced lateral size, but also thinner as
it is now found favorable for ion acceleration .
We acknowledge the support of the LULI laser team and
discussions with M. Bussmann, T. Kluge, L. Gremillet, E.
Lefebvre, P. Mora, A. He ´ron J.C. Adam, J.C. Kieffer, and
R. Kodama. This work was supported by DAAD, British
Council/Alliance, Grant No. E1127 from Re ´gion Ile-de-
France, ANR-06-BLAN-0392 from ANR-France, EPSRC
Grants No. EP/C003586/1 and No. EP/E035728/1 (LIBRA
consortium), the EU program HPRI-CT-1999-0052, TR18
and GK1203 funding, and EU Grant (Marie Curie)
(No. PIIF-GA-2008-221727). M.N. received support
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