Investigation of longitudinal proton acceleration in exploded targets irradiated by intense short-pulse laser M. Gauthier, A. Lévy, E. d'Humières, M. Glesser, B. Albertazzi, C. Beaucourt, J. Breil, S. N. Chen, V. Dervieux, J. L. Feugeas, P. Nicolaï, V. Tikhonchuk, H. Pépin, P. Antici, and J. Fuchs Citation: Physics of Plasmas (1994-present) 21, 013102 (2014); doi: 10.1063/1.4853475 View online: http://dx.doi.org/10.1063/1.4853475 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/21/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Three dimensional effects on proton acceleration by intense laser solid target interaction Phys. Plasmas 20, 063107 (2013); 10.1063/1.4812458 Direct laser acceleration of electron by an ultra intense and short-pulsed laser in under-dense plasma Phys. Plasmas 18, 053104 (2011); 10.1063/1.3581062 Investigation of laser ion acceleration inside irradiated solid targets by neutron spectroscopy Phys. Plasmas 13, 030701 (2006); 10.1063/1.2177230 Spectral and dynamical features of the electron bunch accelerated by a short-pulse high intensity laser in an underdense plasma Phys. Plasmas 12, 073103 (2005); 10.1063/1.1948347 Proton acceleration mechanisms in high-intensity laser interaction with thin foils Phys. Plasmas 12, 062704 (2005); 10.1063/1.1927097 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 207.162.24.136 On: Mon, 16 Feb 2015 16:15:03
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Investigation of longitudinal proton acceleration in exploded targets irradiated byintense short-pulse laserM. Gauthier, A. Lévy, E. d'Humières, M. Glesser, B. Albertazzi, C. Beaucourt, J. Breil, S. N. Chen, V. Dervieux,J. L. Feugeas, P. Nicolaï, V. Tikhonchuk, H. Pépin, P. Antici, and J. Fuchs Citation: Physics of Plasmas (1994-present) 21, 013102 (2014); doi: 10.1063/1.4853475 View online: http://dx.doi.org/10.1063/1.4853475 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/21/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Three dimensional effects on proton acceleration by intense laser solid target interaction Phys. Plasmas 20, 063107 (2013); 10.1063/1.4812458 Direct laser acceleration of electron by an ultra intense and short-pulsed laser in under-dense plasma Phys. Plasmas 18, 053104 (2011); 10.1063/1.3581062 Investigation of laser ion acceleration inside irradiated solid targets by neutron spectroscopy Phys. Plasmas 13, 030701 (2006); 10.1063/1.2177230 Spectral and dynamical features of the electron bunch accelerated by a short-pulse high intensity laser in anunderdense plasma Phys. Plasmas 12, 073103 (2005); 10.1063/1.1948347 Proton acceleration mechanisms in high-intensity laser interaction with thin foils Phys. Plasmas 12, 062704 (2005); 10.1063/1.1927097
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accelerated in the volume by an electric field generated by hot
electrons. This field is composed of both an inductive compo-
nent induced by the variation of a long living quasistatic mag-
netic field at the rear plasma-vacuum interface28–30 and an
electrostatic component located in the expanded sheath front
formed by the hot electrons. Due to the smooth density gradi-
ent at the rear side, the electric field monotonously decreases
with the distance from the high-density zone. Ions in the low-
density region therefore experience an electric field lower
than ions from the higher density region. As a result, ions
from the low-density region are caught by the ions coming
from the higher density region leading to the formation of an
electrostatic shock front, i.e., a peak of ion density propagat-
ing inside the decreasing (low) density ramp. The ions located
upstream are then reflected by the shock structure and acceler-
ated at velocities up to twice the shock velocity. The reflected
ions can then be accelerated again by the expansion electro-
static field which is inhomogeneous in the longitudinal and
transverse directions, leading to a broad energy spectrum.
In this paper, we investigate experimentally and numeri-
cally longitudinal ion acceleration in exploded targets irradi-
ated by an intense short (ps duration) laser pulse (SP). We use
thin solid foil targets partially exploded by a long (ns duration)
laser pulse (LP). Controlling the irradiation of the solid foil by
the LP, or varying the delay between the LP and the SP, we
are able to produce different density gradients for the plasma
targets. This way, we can study different laser ion acceleration
mechanisms and the transition between them. In particular, we
demonstrate that energetic protons can be accelerated to high
energy and high number with targets having rear gradient
characteristic length up to 8 lm. Indeed, we produce with a
good reproducibility few to several 1010 protons/sr energetic
(>1.4 MeV) protons of energies up to �8 MeV. These charac-
teristics are comparable to what we measured in the same laser
conditions and during the same experiment, in the well-known
target normal sheath acceleration regime using 10 lm gold
solid foils. We show as well that the protons accelerated using
exploded targets are emitted on a broader angle than when
using solid foils. All of these observations are found in fair
agreement with results from Particle-In-Cell (PIC) simula-
tions. The latter may allow finding the path for future optimi-
zation of ion acceleration in exploded foils as they show that,
using a longer plasma gradient and higher laser energy, CSA
would then produced higher energy protons than TNSA.
The paper is organized as follows. In Sec. II, we detail
the experimental set-up and the laser and target conditions.
Section III describes the experimental results, comparing the
proton spectra obtained when irradiating with a SP thick
solid-density planar foils (having negligible density gra-
dients) and thin targets exploded by a LP (having short to
moderate density gradients). In Sec. IV, we present simula-
tions and numerical calculations and discuss the experimen-
tal findings. Section V concludes the paper.
II. EXPERIMENTAL SET-UP
The experiment was carried out on the Etablissement
Laser de Forte Intensit�e et Energie (ELFIE) 100 TW laser fa-
cility (Laboratoire pour l’Utilisation des Lasers Intenses,
(LULI)). The experimental set-up is shown in Figure 1. A first
laser pulse, i.e., LP, s-polarized, with nominal energy E¼ 30-
40 J, Gaussian pulse duration s¼ 580 ps full width at half
maximum (FWHM), 20 lm focal spot diameter, producing
on-target intensity of �3� 1015 W/cm2 (see Figure 2) was
used to irradiate a target of variable thickness under an inci-
dent angle of 45�. As targets, we used commercially available
solid 10 lm Au and custom made plastic (Mylar) 500 nm
foils. The intensity of the LP was varied either by putting
neutral optical densities, or by defocusing it. A second laser
pulse, i.e., SP, linearly polarized, with energy of 5–8 J, 400 fs
pulse duration, 6 lm focal spot diameter (FWHM), and inten-
sity of �5� 1018 W/cm2 interacted with the exploded target,
accelerating protons in the laser-forward direction. For the
SP, the Amplified Spontaneous Emission (ASE) has been
measured to be <10�6 in intensity contrast compared to the
temporal peak of the SP and so is well below the LP intensity.
The influence of such ASE light irradiating the target prior to
the peak of the SP is therefore negligible except for the cases
where the LP intensity is strongly reduced. The SP hits the
target at normal incidence. Due to the geometry of the experi-
ment (see Figure 1), since the LP induces an asymmetric
expansion, we expect the main ion acceleration axis to be
angularly tilted with respect to the target normal axis as al-
ready observed in Ref. 26.
FIG. 1. Experimental set-up.
FIG. 2. LP temporal profile measured with an optical streak camera.
013102-2 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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As diagnostics, we used two calibrated Thomson parabo-
las (TPs) located at 0� (TP A) and 15� (TP B) with respect to
the SP laser axis (see Figure 1) to measure the forward gener-
ated proton spectrum. Proton spectra measured by the TPs
were readout in an absolute manner31,32 using ImagePlates
(BAS-TR 2025 from Fuji Photo Film Co., Ltd.) that we ana-
lyzed using a FUJIFILM FLA-7000 reader. Due to technical
constraints, the detection range of TP A was limited: it could
not measure particles with energy below 1.35 MeV. Transverse
interferometry was performed using a low-energy, short (400
fs FWHM), frequency doubled (2x), optical probe beam, a
pick-off of the SP, and a Nomarski interferometer. It could
diagnose the plasma conditions and the exploded foils density
gradients. Concerning the delay between the LP and the SP, we
choose as convention that a zero delay between both pulses
corresponds to their temporal peaks hitting the target simulta-
neously whereas negative delays indicate that the peak of
the SP arrives on the target before the peak of the LP (see
Figure 3). Delays were varied from�500 to 300 ps.
III. EXPERIMENTAL RESULTS
A. Ion acceleration from planar solid foils
We first present the results of reference shots, i.e., with-
out LP (no target preformation by LP), measuring the maxi-
mum energy that can be achieved in the TNSA regime using
solid targets and these experimental conditions. We found in
the experiment that Au 10 lm foils yielded the highest pro-
ton energies for our laser conditions.33 Figure 4(a) shows
typical spectra measured at 0� (TP A) and 15� (TP B). At
normal incidence, the maximum proton energy cut-off is
around 8 MeV whereas at 15�, the cut-off is around 1.5 MeV.
Comparing the particle numbers at �1.4 MeV, we find more
than one order of magnitude difference between the 0� and
15� proton spectra confirming that the acceleration process
produces a beam that is strongly peaked in the target normal
direction.31
Thinner and lower-Z targets lead to less energetic pro-
tons.19 For example, Figure 4(b) shows spectra obtained
when irradiating 500 nm Mylar targets using the SP only.
We also observed that the acceleration process is, in this
case, less sensitive to the shot-to-shot fluctuations. However
it produces lower energy protons with cut-offs around
3-4 MeV for both TPs. Moreover, one observes that the
beam is angularly broadened compared to the thick solid tar-
get case: the cut-off energies recorded at 0� and 15� are close
to each other. This can be interpreted as follows. If one
assumes that a shock wave is launched into the plastic target
by the ablation pressure induced on the front surface by the
ASE pedestal, when it reaches the back side, it gives rise to a
dynamic expansion of the rear surface, which becomes con-
vex with a time-dependent curvature. It results in an increase
of the beam divergence. This phenomenon has already been
observed in Ref. 34 with an ASE intensity and duration simi-
lar to ours (I� 1012 W/cm2, s¼ 1 ns) using a much thicker
Al target (6 lm). We expect the effect to be even more sig-
nificant in our case since the thinner the target is, the more
sensitive it is to the prepulse.19 In addition, the time required
for the shock to pass through the target (83 ps), estimated
using the shock velocity derived in Ref. 32 (6 lm/ns), is
much shorter than our ASE duration (ns scale).
B. Ion acceleration in exploded targets
1. Plasma gradients characterization
We will first discuss the target conditions induced by
irradiating the targets by the LP. For this, we have performedFIG. 3. Intensity temporal profile of the SP and LP with a delay of Dt
between them.
FIG. 4. Proton spectra obtained at 0� (TP A) and 15� (TP B) with respect to
the target normal axis when the short pulse (I� 5� 1018 W/cm2) is interact-
ing with, respectively, a 10 lm thick gold foil (a) and a 500 nm plastic foil
(b). The spectra are all averaged over 3 different laser shots. The vertical
error bars are related to shot-to-shot variations while the horizontal ones are
both due to shot-to-shot variations and the resolution of the diagnostic (<5%
of the proton energy).
013102-3 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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simulations using the two-dimensional (2D) axially symmet-
perimental conditions (e.g., using the temporal profile shown
in Figure 2 which is within the range I¼ 3� 1013–3� 1014
W/cm2, and a 45� irradiation angle). In Figure 5 are shown
2D density maps of the expanding plasma resulting from the
LP irradiation at times corresponding to a Dt of, respectively,
�350, 0, and 400 ps with respect to our convention (see Sec.
II). In Figure 5(a), one can see that for negative delays, the
target is still overdense: the laser deposits a part of its energy
in the expanding underdense front plasma and is reflected
from the target at 45� with respect to the target normal axis.
The rear density gradient starts developing and the expansion
is almost symmetric with respect to the normal target surface.
After a longer time of irradiation, one can see in Figure 5(b)
that the plasma density becomes undercritical: the LP is no
longer reflected and passes through the target. Contrary to the
front expanding plasma, the expansion of the rear plasma is
found asymmetric. The expanded plasma in the laser pulse
direction is indeed observed to be less dense and the gradient
smoother than in any other direction. At longer times (see
Figure 5(c)), the target density is well below the critical den-
sity (nc) and completely transparent for the LP that passes
though the plasma gradient.
In order to validate the density profiles obtained by the
simulations, we will now compare the front density plasma
expansions simulated with CHIC to those measured experi-
mentally by the interferometry diagnostic. In Figure 6 are
presented two different experimental electron density maps,
deduced using Abel inversion,36 at, respectively, 400 and
0 ps prior to the LP peak, with the LP intensity of, respec-
tively, 3� 1014 and 3� 1013 W/cm2. In agreement with the
Abel inversion hypothesis, the electron density map has been
symmetrized around the expansion axis. The observation
zone of our diagnostic was limited to low-density zones of
the plasma profile since at higher density the gradients are ei-
ther too strong and induce strong refraction of the probe, or
the zone is inaccessible due to the strong 2x emission. When
comparing both density maps in Figure 6, one can see that
the expanding plasma is less dense in Figure 6(b). It corre-
sponds to a longer delay and therefore to a more expanded
plasma.
Regarding the rear side plasma expansion of the target,
we were not able to detect any expanding plasma. Indeed the
non-irradiated side of the target was not sufficiently
expanded so that the plasma could be detected by our
interferometer.
In Figure 7, we compare the density profile deduced
from the interferometry images shown in Figure 6 and those
extracted from CHIC simulations for the same interaction
conditions. Although the longitudinal density range detected
by our diagnostic is very narrow, we can assess that the ex-
perimental gradient characteristic length xgl, defined by n(x)
/ exp(x/xgl), is comprised, respectively, between 15 and
45 lm in Figure 7(a) and between 30 and 48 lm in Figure
7(b). These experimental profiles are found in reasonable
agreement with the results obtained by CHIC.
Figure 8 summarizes the characteristics front-side, back-
side plasma gradient scale length and peak density of each
simulated plasma, as obtained by CHIC for the different
delays and LP intensities explored in the experiment. First,
one can see that all gradient characteristic lengths strongly
increase with the delay and laser intensity. The target front
FIG. 5. Superposed electron density (in logarithmic scale) and LP absorption
maps obtained using CHIC 2D for LP intensity of 3� 1013 W/cm2 and
delays of, respectively, �350 (a), 0 (b), and þ400 ps (c). The LP propaga-
tion direction is indicated by the white arrows.
FIG. 6. Density maps obtained by Abel inversion from interferometry
images. These density profiles correspond to a 500 nm Mylar target irradi-
ated by a LP of, respectively, (a) I� 3� 1014 W/cm2 with Dt¼�400 ps and
(b) I� 3� 1013 W/cm2 with Dt¼ 0 ps. The maps correspond to the
low-density zone accessible to the optical probe. Absolute positions along
x-axis are consistent with the CHIC simulations shown in Figure 7.
013102-4 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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surface, i.e., the surface facing the laser, is heated earlier in
time and to higher temperature compared to the rear surface.
Thus, it is obviously more expanded and exhibits a longer
gradient characteristic length. Second, we observe that the
maximum density of the exploded target drops with the delay
and intensity reaching sub-critical densities at delays from
Dt�þ100 ps (corresponding to the LP highest intensity) to
þ500 ps, (corresponding to the LP lowest intensity). It
FIG. 7. Density profiles corresponding to a 500 nm Mylar target irradiated by a LP of, respectively, (a) I� 3� 1014 W/cm2 with Dt¼�400 ps and (b)
I� 3� 1013 W/cm2 with Dt¼ 0 ps. Blue dots indicate the density profiles obtained by the interferometry diagnostic; red lines by CHIC simulations.
FIG. 8. Evolution of, respectively, the
front gradient characteristic length
(length to reach a decrease of the
density by a factor exp (1)), the rear
gradient characteristic length, and
the maximum electron density of the
exploded foil in the CHIC simulations
as a function of the delay for LP inten-
sities of I¼ 3� 1013 (blue plain curve),
I¼ 1014 (green dashed curve), and
I¼ 3� 1014 W/cm2 (red dotted curve).
013102-5 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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should be noted that CHIC simulations do not take into
account the ASE of the SP. This is justified since the expan-
sion induced by the ASE is negligible compared to the
expansion caused by the LP in the delays covered by our
experiment.
2. Proton spectra
Using two different LP intensities and various Dt, we
have measured the proton spectra accelerated by the SP
(I� 5� 1018 W/cm2) irradiating exploded targets having rear
plasma gradients with characteristic length up to 8 lm
according to CHIC simulations. As can be seen in Figure 9,
an increase of the density gradient does not decrease signifi-
cantly the maximum proton energy (or energy cut-off). We
notably observed that such targets lead to similar proton
energies than the best maximum proton energy obtained
without any target preformation and this for both observation
angles (0� and 15�).In the TNSA regime, we would expect that, with such
density gradients, the energy cut-off decreases notably.37,38
In addition, we observed that for certain gradient characteris-
tic lengths such as 0.4 or 2.4 lm, the most energetic protons
are found at 15� from the target normal, rather than at 0�.For example, as shown in Figure 10, we measured at 0� and
15� for a LP intensity I¼ 3� 1013 W/cm2 and Dt¼�400 ps
(corresponding to a gradient characteristics length of 0.4 lm)
a higher proton energy cutoff on the TP positioned at 15�
(�7–8 MeV); however, on the TP located at 0� we only
measured 2.8–3.7 MeV. This indicates that the acceleration
mechanism is affected by the asymmetric expansion caused
by the LP. While the maximum proton energy is dependent
on the electrostatic field, the angle with which the protons
stem out of the target strongly depends on the geometry of
the sheath field since ions are accelerated normally to the
isopotential.1 We also observed that the most energetic pro-
tons generated using exploded targets have energies that are
similar—if not better—to those obtained in the best TNSA
conditions using solid targets. In addition, when comparing
the different spectra, we observe that the number of high
energy protons (>1.4 MeV) is also comparable to the one
measured in the case of a 10 lm solid-density target. For
example, we calculated from the spectra that we produced
�6.2� 1010 protons/sr above 1.4 MeV at 15� with a 500 nm
thick plastic foil exploded by a ns laser pulse. These numbers
are close to the proton beams we produced with a 10 lm
gold foil where we recorded �2� 1011 protons/sr above
1.4 MeV at 0� (see Figure 4(a)).
In order to further investigate the beam angular charac-
teristics, we tilted the target at 7�, 15�, 22�, and 30� with
respect to the initial target surface as shown in Figure 11 in
which the rotation angle is noted h. We kept the other param-
eters fixed (LP intensity I¼ 3� 1013 W/cm2 and
Dt¼�400 ps), since in this configuration we had experimen-
tally obtained the highest proton energies. Note that due to
geometrical effects, the rotation of the target changes the LP
intensity by a factor cos(45�-h), inducing an intensity varia-
tion �26%, and thus an electron temperature variation �9%
according to the scaling in Ref. 39. We assume this effect to
be negligible with respect to the shot-to-shot fluctuations of
the laser beam.
A comparison of the proton energy cut-offs measured for
different target angles is presented in Figure 12. It should be
noted that no protons were detected at 0� (TP A) when the
target was tilted at 15�, 22�, and 30� with respect to the initial
target surface. It means that for these shots, the maximum
FIG. 10. Proton spectra measured at 0� and 15� when irradiating 500 nm
plastic foils by the LP of intensity I¼ 3� 1013 W/cm2 with Dt¼�400 ps.
FIG. 11. Angle of the target compared to the SP axis.
FIG. 9. Proton energy cut-off obtained using 500 nm Mylar exploded foil as
a function of the characteristic length of the target rear density gradient. The
proton energy cut-offs measured without LP, i.e., with negligible target pre-
formation either with a 500 nm Mylar foils or a 10 lm Au (hashed zones
delimited by, respectively, plain and dashed lines) are added for
comparison.
013102-6 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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proton energy did not reach more than 1.35 MeV. The most
energetic protons are clearly produced close to the target nor-
mal axis, but energetic protons are still found with angles up
to 15�. The accelerated ion beam is therefore not isotropic,
but less collimated than the one produced from solid targets.
This decrease of the beam collimation could be explained by
the geometry of the SP. Indeed, according to Ref. 27, the pro-
tons are expected to be preferentially emitted at an angle
lying in between the direction of the plasma expansion gener-
ated by the LP and the direction of the SP propagation: the
long living magnetic field induced by the hot electron current
generated by the SP slightly deflects the beam from the direc-
tion of the plasma expansion. In our experiment, the direction
of the plasma expansion is given by the axis normal to the tar-
get, w direction in Figure 11 while the SP remains collinear
to x. The proton beams direction is therefore tilted from w to
x. This effect is not visible when both the SP and the plasma
expansion are pointing in the same direction (w and x are col-
linear, h¼ 0), but becomes perceptible when the angle
between the two axis increases. Nevertheless, the fact that we
clearly observe an energy cut-off decrease when increasing
the angle h means that the effect of the long living magnetic
fields is not strong enough to overcome the direction induced
by the plasma expansion generated by the LP. It could be the
case with a higher intensity or a more energetic SP producing
a higher number of hot electrons and thus generating a stron-
ger magnetic field.
It should also be noted that the highest energy is found
in TP B at 15� in the case where the target is positioned at
0�, i.e., when the target surface is normal to the SP. This cor-
responds to an asymmetric expansion of the rear plasma: the
plasma expansion direction is slightly modified in the direc-
tion of the LP propagation axis, tilting the proton beam in
the direction given by TP B.
IV. SIMULATIONS AND DISCUSSION
To study the transition between the sharp and the long
gradient regime and to understand the possibility of
obtaining high energy protons for various gradient condi-
tions, we have performed 2D PIC simulations with the
PICLS code.40 Depending on the gradient characteristic
length, several regimes, already studied theoretically, can be
obtained. (1) For sharp density gradients, classical TNSA is
dominant even when irradiating lower-than-solid density tar-
gets.41 (2) For longer gradients, on both sides of the target, a
trade-off takes place between the laser absorption increase
on the interaction side and the decrease of the TNSA electric
field on the rear side due to the lengthening of the density
gradient. The acceleration regime is similar to the gradient
regime studied by Ref. 19 in which the maximum proton
energy decreases with increasing plasma gradient length. (3)
When the target starts to become transparent during the inter-
action, the laser-to-target coupling is significantly improved.
The increase of the hot electron temperature can counterbal-
ance the effect of the characteristic scale length in the peak
electric field formula E ¼ kbTh
eklss
ffiffiffiffiffiffiffiffiffiffi2
expð1Þ
q(where Th is the hot
electrons temperature, kb the Boltzmann constant, e the
charge of an electron, and klss the density gradient scale
length) and lead to higher energy protons.23 In this regime,
for long rear side density gradients, a secondary accelerating
mechanism can occur through a strong electrostatic
shock15,19 and enhance the maximum proton energy. This
rear-side shock is different from front-side collisionless
shocks already observed when the laser is reflected at the
front of a dense target15 and from the BOA, observed when
using a higher contrast SP laser, coupled to very thin tar-
gets.13 (4) For too long gradients, obtained with a strongly
expanded target, the laser-to-target coupling decreases since
the target becomes too low density and thus too transparent
to the laser light for producing energetic electrons.
The PIC simulations illustrating these regimes were per-
formed using a 1.057 lm wavelength, 350 fs (FWHM) dura-
tion, p-polarized laser pulse focused on a 10 lm diameter
spot. The spatial and temporal profiles are truncated
Gaussians. The laser intensity of 8� 1018 W/cm2 is similar
to the intensity of the SP in our experiment. The pulse is
injected from the left side of the simulation box.
The density profile in the first simulation corresponds to
a long negative delay between the two pulses reproducing
the case of the SP interacting almost directly with the thin
foil used in the experiments. We used the truncated (as can
be seen in Figure 13(a)) CHIC density profile obtained for a
delay of �500 ps and a LP intensity of 3� 1013 W/cm2: the
gradient characteristic length of the rear plasma profile is
below 1 lm. Since the laser energy and the small target
thickness lead to a quick heating of the target, collisions
inside the plasma can be neglected. The target is composed
of C6þ ions, protons, and electrons with a 300 nc maximum
electron density. The initial electron, proton, and carbon ion
temperatures are set to zero. The plasma is located 70 lm
away from the left side in the 176 by 160 lm simulations
box. The spatial and temporal steps are respectively
Dx¼Dy¼ 15 nm and Dt¼ 0.05 fs. The boundary conditions
we used are absorbing in x and y. The density profile we
used and the obtained proton phase space on axis are shown
respectively in Figures 13(a) and 13(b).
FIG. 12. Proton energy cut-off recorded at 0� (TP A) and 15� (TP B) to the
SP axis as a function of the angle between the normal of the irradiated target
and the SP propagation axis.
013102-7 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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This simulation exhibits a standard TNSA acceleration
process with the maximum energy protons coming from the
back surface and a strong laser absorption leading to high
energy protons. The maximum proton energy is here
15.6 MeV. This is higher than our best measurement per-
formed in the TNSA regime, i.e., obtained using 500 nm
Mylar target and the sole SP (see Sec. III A). However, this
was expected since 2D simulations are known to overesti-
mate the final proton energy. These observations indicate
that we are in the regime (1) described before.
In a second simulation, we used (as initial density pro-
file) for the PIC simulation the CHIC density profile obtained
with a LP intensity of 1014 W/cm2 and Dt¼þ100 ps. In this
case, the density profile corresponds to a lower density, with
a 2.53 nc maximum electron density, and larger plasma with
smoother gradients (see Figure 14(a)): the gradient charac-
teristic length of the rear plasma profile is around 28 lm. We
are dealing here with a plasma gradient that is much longer
that those we investigated experimentally. The simulation
parameters are the same as above except for the following
parameters. The target has a maximum electron density
slightly higher than the critical density. The plasma is
located 100 lm away from the left side in the 800 by 128 lm
simulation box. The spatial and temporal steps are, respec-
tively, Dx¼Dy¼ 100 nm and Dt¼ 0.33 fs.
The obtained proton phase space along the x-axis is
shown in Figure 14(b). In this simulation, the maximum
energy protons are also accelerated by a strong electrostatic
field in the decreasing density gradient, but a secondary
acceleration process occurs. The first step is not as efficient
as in the case described in Figure 13. The long density gradi-
ent at the back side of the target will lead to a lower acceler-
ating electric field, but the strong laser-to-target coupling can
compensate this decrease and still leads to high energy pro-
tons. In our case, this first step leads to a maximum proton
velocity of around 0.1 c. In a second step, protons are accel-
erated further in the gradient by an electrostatic shock over a
short distance which leads to a distinct feature in the proton
phase space that is clearly visible at x¼ 660 lm in Figure
14(b). In this case the maximum proton energy at saturation
is 13.2 MeV, which is very close to the maximum energy
obtained in the case described above in Figure 13. This case
corresponds to the regime (3) described before.
Depending on the density gradient at the back side of
the target, it is therefore possible to accelerate ions to similar
energies than when using sharp rear gradients target (com-
pare Figures 13 and 14) but through different processes.
Figures 15(a) and 15(b), respectively, show the forward
proton energy spectrum obtained in the second simulation
(regime (3)) and the associated divergence distribution for
protons with energy higher than 1 MeV. Overlaid are the
same plots obtained with a 500 nm thick (non-exploded)
solid foil (i.e., in the TNSA regime (1)). The divergence dis-
tribution in regime (3) is more complex than in regime (1).
The divergence is broader, and additional features are
observed at �35� and for angles higher than 60�. This latest
feature is even observed for protons with energy higher than
1 MeV corresponding to protons that are accelerated almost
FIG. 14. (a) Density profile obtained
with the CHIC code for a 500 nm
Mylar foil exploded with a 1014 W/cm2
intensity and aþ 100 ps delay. (b)
Normalized proton phase space lineout
in the longitudinal direction 7.42 ps af-
ter the interaction of the maximum of
the SP. The laser comes from the left.
FIG. 13. (a) Density profile obtained
with the CHIC code for an exploding
foil with a 3� 1013 W/cm2 intensity
(LP) and Dt¼�500 ps. (b) Normalized
proton phase space lineout in the longi-
tudinal direction (along the x-axis) 0.6
and 1 ps after the interaction of the
maximum of the SP (m is the proton
mass and c the speed of light). The
laser comes from the left.
013102-8 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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perpendicular to the laser axis in the channel created by the
laser through the Coulomb explosion mechanism.42
To study the transition between these two efficient laser
proton acceleration regimes (regimes (1) and (3)) and to
compare with our experimental results, we have simulated
intermediate density gradients. Here, we decreased the
plasma length used for the case illustrated in Figure 14 by
changing the rear surface profile characteristics, starting
from the CHIC profile obtained for a LP intensity of
1014 W/cm2 and a delay of þ100 ps. In Figure 16, we show
the proton phase spaces obtained at two simulation times for
characteristic gradient lengths of 5 and 10 lm, i.e., at the
frontier between regimes (2) and (3). When decreasing the
gradient scale length to 10 lm, the laser coupling with the
target is still high, but the electrostatic field in the density
gradient is decreased. This leads to moderately high energy
protons (5.2 MeV) as evidenced by the lower maximum
velocities reached and shown in Figure 16(a). In this case,
the coupling efficiency is not enough to compare to either
TNSA with thin targets (regime (1), Figure 13) or shock
acceleration with exploded foils (regime (3), Figure 14).
Figure 16(b) corresponds to the case of a 5 lm scale
length for which the laser coupling is even more decreased
and will lead to lower energy protons (2.8 MeV). The higher
coupling efficiency in the 10 lm scale length case is also evi-
denced by the enhanced backward (towards the laser) accel-
eration visible in Figure 16(a) compared to Figure 16(b).
When comparing the evolution from a steep back sur-
face density gradient in Figure 13 to a longer and smoother
one in Figures 14 and 16, it is clear that it is possible to
accelerate high energy protons on a wide range of target pa-
rameters in the near-critical laser ion acceleration regime.
This is very similar to our experimental observation that
MeV protons can be generated with various delays and vari-
ous LP intensities.
In addition, these simulations indicate that there are two
optimum regimes for laser proton acceleration: the thin tar-
get TNSA and the exploded foil CSA, generating similar
maximum proton energies. For thin target TNSA, high laser
contrast is necessary. One drawback of this regime is that the
various techniques to improve the laser contrast also
decrease the total laser energy in the focal spot (it is the case
using plasma mirrors43 or non-linear systems laser frequency
doubling). For exploded foil shock acceleration, a small
range of density gradient scale length can lead to this regime.
According to simulations, in between, a large range of target
parameters will lead to moderately high energy protons
through degraded TNSA.
V. CONCLUSION/PERSPECTIVES
We have studied the longitudinal acceleration of protons
using a high intensity picosecond laser pulse irradiating a
500 nm thick plastic foil exploded by a nanosecond pulse.
We varied the nanosecond pulse intensity and the delay
between the picosecond and the nanosecond pulses to study
the acceleration mechanism in various target conditions hav-
ing short to moderate plasma density gradients, i.e., with
FIG. 15. Comparison of (a) the proton
energy spectra in the forward direction
for all angles, and (b) the divergence
distribution for protons with energy
>1 MeV in the forward direction in the
case of the SP interaction with a
500 nm plastic foil non-exploded and
one exploded with a 1014 W/cm2 inten-
sity and aþ 100 ps delay.
FIG. 16. Proton phase space on axis at
3.96 ps (blue) and at 5.28 ps (red) after
the beginning of the PIC simulation in
the case of the SP interacting with an
exploded foil with a rear surface gradi-
ent with characteristic lengths of
10 lm (a) and 5 lm (b).
013102-9 Gauthier et al. Phys. Plasmas 21, 013102 (2014)
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207.162.24.136 On: Mon, 16 Feb 2015 16:15:03
gradient characteristic lengths from 0 to 8 lm. We have
shown, in agreement with PIC simulations, that, in these gra-
dient density ranges, protons can be accelerated in number
and energy similar to the one recorded when using thin solid
planar foils in the TNSA regime. In addition, we highlighted
that the use of exploded targets generates a broader angular
proton distribution compared to solid targets and accelera-
tion anisotropy. The requirements for such acceleration
mechanism to occur are (1) high laser intensity to initiate a
strong expansion in the decreasing density gradient, as well
as (2) a density profile tailored so the plasma at the back is
long enough for ions to be reflected, and (3) a high laser
energy to be able to propagate in a near-critical target so that
energetic electrons reach the back gradient to initiate a
strong expansion that is also necessary to reach ion reflec-
tion. We expect that at higher SP energies we would be able
to achieve higher electric fields in longer gradients. This
should improve underdense laser ion acceleration and enable
to observe clearer the CSA acceleration process.27,44 As a
consequence, this should allow obtaining higher energy pro-
tons than with the conventional TNSA regime.
ACKNOWLEDGMENTS
We acknowledge support from the LULI technical teams.
We thank Professor Yasuhiko Sentoku for usage of the code
PICLS and Dr. T. Vinci for usage of the code neutrino to ana-
lyze the interferometry measurements. This work was sup-
ported by the European Commission (CRISP FP-7 Contract
(P. Antici), CRSNG decouverte (Grant No. 435416) and FP-7
Laserlab-Europe (Grant Agreement No. 602 284464 and
Grant No. 001528) (M. Gauthier, A. L�evy, M. Glesser, B.
Albertazzi, S. N. Chen, V. Dervieux, P. Antici, J. Fuchs),
National Science Foundation (Grant No. 600 1064468) (S. N.
Chen), HPC resources of CINES under allocations 2011-604
056129, 2012-056129, and 2013-056129 made by GENCI
(Grand Equipement National de Calcul Intensif) (E.
d’Humieres, C. Beaucourt, J. Breil, J. L. Feugeas, P. Nicolai,
V. Tikhonchuk). Support from the Aquitaine Regional
Council is also acknowledged.
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