Laser Acceleration of Highly Energetic Carbon Ions Using a Double-Layer Target
Composed of Slightly Underdense Plasma and Ultrathin Foil
W. J. Ma,1,3,* I Jong Kim,2,4,† J. Q. Yu,1 Il Woo Choi,2,4 P. K. Singh,2 Hwang Woon Lee,2 Jae Hee Sung,2,4
Seong Ku Lee,2,4 C. Lin,1 Q. Liao,1 J. G. Zhu,1 H. Y. Lu,1 B. Liu,5 H. Y. Wang,6 R. F. Xu,1 X. T. He,1
J. E. Chen,1 M. Zepf,7,8 J. Schreiber,3,5 X. Q. Yan,1,9,‡ and Chang Hee Nam2,10,§
1State Key Laboratory of Nuclear Physics and Technology, and Key Laboratory of HEDP of the Ministry of Education,
CAPT, Peking University, Beijing 100871, China
2Center for Relativistic Laser Science, Institute for Basic Science, Gwangju 61005, Korea
3Fakultät für Physik, Ludwig-Maximilians-Universität München, D-85748 Garching, Germany
4Advanced Photonics Research Institute, Gwangju Institute of Science and Technology (GIST), Gwangju 61005, Korea
5Max-Planck-Institute für Quantenoptik, D-85748 Garching, Germany
6School of Environment and Chemical Engineering, Shanghai University, Shanghai 200444, China
7Helmholtz-Institut-Jena, Fröbelstieg 3, 07743 Jena, Germany
8Department of Physics and Astronomy, Centre for Plasma Physics, Queens University, Belfast BT7 1NN, United Kingdom
9Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
10Department of Physics and Photon Science, GIST, Gwangju 61005, Korea
(Received 20 November 2017; published 10 January 2019)
We report the experimental generation of highly energetic carbon ions up to 48 MeV per nucleon by
shooting double-layer targets composed of well-controlled slightly underdense plasma and ultrathin foils
with ultraintense femtosecond laser pulses. Particle-in-cell simulations reveal that carbon ions are ejected
from the ultrathin foils due to radiation pressure and then accelerated in an enhanced sheath field
established by the superponderomotive electron flow. Such a cascaded acceleration is especially suited for
heavy ion acceleration with femtosecond laser pulses. The breakthrough of heavy ion energy up to many
tens of MeV=u at a high repetition rate would be able to trigger significant advances in nuclear physics,
high energy density physics, and medical physics.
DOI: 10.1103/PhysRevLett.122.014803
Dense, energetic heavy ion bunches with an ultrashort
duration are in high demand for high- energy-density
physics and nuclear astrophysics [1,2]. Near the source,
laser-driven ion acceleration can deliver exceptional ion
bunches 1010 times denser than classically accelerated ion
bunches [3,4], which highlights its application prospect in
related fields. So far, energetic heavy ions up to 80 MeV=u
have been generated through breakout afterburner [5,6] and
relativistic transparency [7,8] acceleration schemes. But
both of these schemes require expensive 100s J level long-
pulse lasers which are still unable to operate at a high
repetition rate. Femtosecond laser pulses have been suc-
cessfully applied in proton acceleration with the advantages
of lower request on laser energy and Hertz-level repetition
rate [9]. However, heavy ion acceleration with femtosecond
pulses has not achieved the same success. The maximum
energy per nucleon is still no more than 25 MeV=u, mostly
only a few MeV=u [9–14], inefficient to overcome the
Coulomb barrier to excite nuclear reactions or isochorically
heat bulk matters to a warm dense state.
For femtosecond pulses, target normal sheath acceler-
ation (TNSA) [15] and radiation pressure acceleration
(RPA) [16,17] are the most widely employed schemes.
In the TNSA scheme, the acceleration field (sheath field),
established by laser-produced dilute thermal electrons, is
easily diminished by contaminated protons and poorly
ionized heavy ions which appear at the beginning of the
interaction. Thus the acceleration of highly ionized heavy
ions is strongly suppressed [18–21]. By completely remov-
ing the protons in the contamination layer, the energy of
the heavy ions can be improved to, in the best cases, a few
MeV=u [18,19,21], which is still much lower than the
maximum proton energy of 85 MeVachieved in the TNSA
scheme [22]. Compared to TNSA, RPA using nanometer-
thin foils as targets has been proven more beneficial to
accelerating heavy ions due to the fact that the majority
of the bulk electrons in the targets are displaced by the
radiation pressure. In particular, quasimonoenergetic ions
can be obtained by entering the light-sail RPA regime when
circular polarized pulses and matching ultrathin foils are
used. Experimental results show that carbon ions up to
25 MeV=u can be generated in the light-sail RPA regime
[23]. Simulations predict that highly energetic heavy ions
can be generated by using compound targets at an intensity
above 1021 W=cm2 [24,25]. The major problem at the
current intensity for RPA is the fast decline of the
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0031-9007=19=122(1)=014803(6) 014803-1 © 2019 American Physical Society
acceleration field after laser reflection and unwanted early
termination of acceleration due to plasma instability
[26,27]. To generate highly energetic heavy ions, increas-
ing the on-target laser intensity, or prolonging the accel-
eration time, is essential. Recently, a plasma-lens-enhanced
RPA (PLE RPA) scheme has been realized [28,29] by
enhancing the on-target intensity using a few-μm-thick and
slightly overdense plasma (SOP) slab as a plasma lens.
Significant enhancement of carbon energy is observed. But
30%–50% of the pulse energy was lost in the SOP without
significant contribution to the ion acceleration process.
In this work, we demonstrate the realization of a
cascaded acceleration (CA) scheme especially suited for
heavy ions. It happens when a laser pulse is focused on a
target composed of a homogeneous, tens-of-μm-thick,
slightly underdense plasma (SUP) slab in front of an
ultrathin foil. Figure 1(a) schematically illustrates the
scheme. The density of the SUP is in the range of 0.1 to
1nc to ensure that direct laser acceleration, instead of
wakefield acceleration, happens [30–32], where nc ¼
meω2ε0=e2 is the critical density of the plasma. In the
SUP, the electrons are trapped in the plasma channel by
an electrostatic field and a self-generated magnetic field,
and in-phase accelerated by the laser field to an energy
far beyond the ponderomotive limit [33]. As the forward
velocities of these “superponderomotive electrons” are
lower than the group velocity of the laser pulse, they form
a dense and energetic electron flow behind the pulse. Once
the laser pulse, self-steepened in SUP and followed by the
electron flow, arrives at the ultrathin solid foil, ions residing
in the foil undergo radiation pressure acceleration at first,
then cascaded acceleration in a long-lifetime sheath field
dominated by the superponderomotive electron flow. The
superiority of CA is that the initial RPA stage gives rise to
an efficient ionization and ejection of highly ionized ions,
and the enhanced TNSA stage thereafter ensures a suffi-
ciently long acceleration time. Experimental results show
that carbon ions with energy up to 48 MeV=u can be
generated by using double-layer targets, which is, to our
knowledge, about 2 times that of the previous record
obtained by using femtosecond lasers.
The experiments were performed using the petawatt Ti:
sapphire laser facility at Center for Relativistic Laser
Science (CoReLS) of the Institute for Basic Science
(IBS) in Korea. After a recollimating double plasma mirror
(DPM) system, 33-fs s-polarized laser pulses with energy
of 9.2 J were focused to spots of 4.5 μm diameter (FWHM)
using a f=3 off-axis parabolic mirror, resulting in a peak
intensity of 5.5 × 1020 W=cm2, corresponding to a relativ-
istic normalized vector potential of a0 ¼ eE=mecω ≈ 16.
After the DPM, the contrast of the laser pulses was about
3 × 10−11 at 6 ps before the main pulse, which is good
enough to avoid the premature expansion of the nanotargets
before the arrival of the main pulse. The incident angle was
2.4°, and the ion energy spectra were measured with a
Thomson parabola (TP) placed in the direction of the laser
axis. The TP was equipped with a microchannel plate
(MCP) with a phosphor screen to convert the ion signal to
an optical signal imaged by a 16-bit CCD. The absolute
response of the MCP was calibrated following the literature
[34]. A 6-mm-thick tungsten plate with a 375-μm iris was
used as the ion collimator in front of the TP, corresponding
to the acceptance angle of 3.5 × 10−8 sr. Bright and stable
zero points, on top of halos that resulted from secondary
radiation from the collimator, were observed on the CCD as
shown in Fig. 1(b). The energy measurement error of the
TP, estimated by considering the linewidth of the ion trace
and the spatial resolutions of the MCP and CCD, was about
2.2 MeV for 60-MeV protons and 3.3 MeV=u for
50 MeV=u C6þ.
The SUP layer of the double-layer targets was made of
carbon nanotube foam (CNF) [35]. Behind the CNF, a
nanometer-thin diamondlike carbon (DLC) [36] foil was
attached, in which only a minute amount of protons or
FIG. 1. (a) Schematic drawing of the cascaded acceleration
process. (b),(c) Raw data and ion spectra obtained from a 20-nm
DLC target [upper image in (b), red lines in (c)] and a double-
layer target with 80 μm CNF [lower image in (b), black lines in
(c)]. The dashed lines in (c) show the detection threshold. (d) The
dependence of the maximum proton or carbon energy on the
thickness of the CNF layer.
PHYSICAL REVIEW LETTERS 122, 014803 (2019)
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oxygen lie in the contamination layer (for details about
the targets, see Supplemental Material [37]). The targets
were not treated by laser heating or other proton-removal
methods. In the experimental campaign, the bulk density of
the employed CNF was 3 1.5 mg=cm3, corresponding to
an electron density of 0.4 0.2nc if carbon atoms were
fully ionized. The thickness of CNF was varied from 0 to
120 μm in the experiments, while the DLC was fixed to
20 nm for all the targets. The raw data and ion spectra of
2 shots, obtained from a single-layer 20-nm DLC target and
from a double-layer target with 80 μm CNF are shown in
Figs. 1(b) and 1(c), respectively. Two features are obvious:
(1) the energy and the number of carbon and proton ions
obtained from the double-layer target are remarkably
higher than those from the single-layer target and (2) 6þ
is the only dominant charge state of carbon ions for the
double-layer target, while multiple charge states were
observed in the case of the single-layer target. For further
confirmation, an additional 53 shots by varying the thick-
ness of the CNF were made in the campaign. It turned out
that the above features were repeatedly observed. The
missing low charge states of carbon ions for the double-
layer targets implies that the ionization processes were not
evolving but abrupt and complete. The maximum energies
of protons and of C6þ are plotted as a function of CNF
thickness in Fig. 1(d), where the error bars reflect the shot-
to-shot fluctuation and the dots are the arithmetic means.
A strong dependency of ion energy on the CNF thickness
is observed. The optimal thickness is 80 μm for carbon
acceleration, resulting in a maximum 48 MeV=u. The solid
lines in Fig. 1(d) depict the numerical simulation results
(for simulation parameters, see below), which fit to the
experimental results very well.
To illustrate the physics, 2D particle-in-cell simulations
were performed using the EPOCH2D [38] code. The simu-
lation window wasWx ×Wz ¼ 160 × 40 μm2 with the cell
size of dx ¼ dz ¼ 10 nm. The laser pulse traveled along x
from the left side with a central wavelength of 800 nm and
sin2 temporal profiles. Its peak laser intensity, focused spot,
and duration is 5.5 × 1020 W=cm2, 4.5 μm, and 33 fs,
respectively, the same as in experiments. The electron
density of the CNF/DLC layer was 0.2nc=50nc. The
thickness of the DLC layer in simulation was set to
200 nm to ensure its areal density was the same as that
of the 20-nm unionized DLC. The thickness of the CNF
varied from 0 to 120 μm.
Snapshots of Ey, Ex, and ðγ − 1Þne at four different times
obtained from simulations for targets with 60 μm CNF are
shown in Fig. 2(a), where Ey and Ex are the electric fields
and γ and ne are the Lorentz factor and the density of
FIG. 2. (a) Snapshots of transverse electric field (Ey), longitudinal electric field (Ex), and the energy density [ðγ − 1Þne] of electrons
from CNF at different times. (b) Snapshots of the density of C6þ. (c) Energy spectra of electrons in CNF (red line) and in DLC (black
line) at T ¼ 480 fs, and the C6þ spectra at different times.
PHYSICAL REVIEW LETTERS 122, 014803 (2019)
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electrons from the CNF, respectively. At T ¼ 430 fs, the
laser pulse has not arrived at the solid foil (the blue dash-
dotted line at 122 μm). After propagating ∼55 μm in CNF,
the pulse duration (FWHM) is reduced from 33 to 15 fs
with a steep rising edge due to relativistic nonlinearity in
the SUP. The intensity is moderately enhanced by 50%, in
contrast to the case of PLE RPA, where the pulse is strongly
self-focused. A major portion of the laser energy is coupled
to superponderomotive electrons in the near-critical-density
channel through direct laser acceleration [33,39], forming
a high-energy-density electron flow behind the pulse. At
T ¼ 450 fs, the pulse has been at the solid foil for 5 fs.
Electrons in the foil are piled up by the radiation pressure,
resulting in a strong and localized charge separation field,
which piles up ions as well and accelerates them forward.
Figure 2(b) shows the density of C6þ at different times. It
can be seen that ions in the foil are piled up at 450 fs with a
density rise of a factor of 2, and then a large portion of them
were ejected from the foil at 460 fs. At T ¼ 480 and 500 fs,
the laser pulse has been completely reflected away, but
the accelerating field is still very strong. The dominant ion
acceleration process is TNSA. The sheath field is estab-
lished by the superponderomotive electron flow from the
SUP and the thermal electrons from the DLC. The energy
spectra of the two kinds of electrons are shown in Fig. 2(c).
It can be seen that both the number and the energy of the
superponderomotive electrons are much higher than those
of the thermal electrons. Thus, the sheath acceleration stage
is dominated by the superponderomotive electrons, which
is remarkably different from the hybrid-RPA scheme where
the sheath acceleration is purely due to thermal electrons
[11,40]. Simulation results show that such a sheath field is
very strong and can last over 200 fs, which is crucial for
achieving efficient acceleration of heavy ions with low
charge-to-mass ratio. The energy spectra shown in Fig. 2(c)
indicate that carbon ions gain most of their energy in the
TNSA stage. From the energy conversion point of view,
the TNSA stage plays the dominant role in CA (see
Supplemental Material [37]). Nevertheless, the RPA stage
is still important because it leads to an efficient ionization
and injection of heavy ions at the beginning of the
acceleration process.
As demonstrated in the experiments, there is an optimal
thickness of the SUP layer for ion acceleration. Around this
thickness, a significant amount of pulse energy is converted
into electron flow and eventually contributes to the sheath
field acceleration. Meanwhile, the remaining pulse is strong
enough to displace the bulk electrons and eject ions. This is
confirmed by simulations in Fig. 3(a) by tracking the
energy gain rate (EGR) of the most energetic carbon ions.
In the case of a single foil target without SUP, the EGR
starts to rise after the laser pulse arrives at 425 fs, then
peaks at about 480 fs when the pulse is reflected away,
and quickly declines afterwards. In contrast, for the double-
layer target with 60 μm CNF, the steepened laser pulse
arrives at the foil at 445 fs. The corresponding EGR rises
with a higher speed and reaches a similar value when the
pulse is reflected. After that, the EGR continuously grows
up until 500 fs, when the majority of the superponder-
omotive electron flow passes through the foil. If the CNF
layer is too thick, for example, 120 μm, the laser pulse is
seriously depleted and filamented [41] before it reaches the
DLC. The ions are accelerated merely by the sheath field
without the RPA stage. For a comparison to the PLE-PRA
regime, a simulation by setting the electron density of
CNF to 2nc and thickness to 6 μm was performed as well
and presented in Fig. 3(a). The tenfold increment of the
CNF density to slightly overdense results in stronger self-
focusing but without a long superponderomotive electron
flow. As a result, although the EGR in the RPA stage
(before 480 fs) is higher, the final ion energy is lower
compared to 0.2nc.
Besides the length and density of the SUP layer,
simulations reveal that the thickness of the DLC foil
imposes significant influence on the ion acceleration as
well. Figure 3(b) shows the dependence of the maximum
C6þ energy on the thickness of the DLC foils. In the case of
0.2nc SUP, the optimal DLC thickness is 5 nm, and the
maximum carbon energy varies little for 10–100 nm DLCs
and eventually drops to 27 MeV=u for 1 μm DLC. Such a
dependency is different from the case of 2nc, where the
optimal thickness is 10 nm and the maximum C6þ energy
quickly drops to 12 MeV=u. The simulation results clearly
demonstrate the importance of using an ultrathin foil
behind the foam, so that the RPA stage can efficiently
eject and preaccelerate heavy ions. This has been proved by
previous experimental studies where foam-coated microm-
eter-thick metal foils were shot at laser intensity close to
ours, where the energy of the heavy ions was no more than
11 MeV=u [42,43]. As a comparison, the results from
FIG. 3. (a) Energy gain rate (MeV=fs) of C6þ ions as a function
of time for targets with different CNF layers obtained from
simulations. The arrows show the arrival instant of the laser
pulses for different cases. (b) The dependence of maximum C6þ
energy on the thickness of DLC for single DLC targets and
double-layer targets obtained from simulations.
PHYSICAL REVIEW LETTERS 122, 014803 (2019)
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single-layer DLC foils irradiated by linearly polarized laser
pulses are also shown in Fig. 3(b). One can see that their
maximum C6þ energies are significantly lower than those
using double-layer targets for all the cases.
To reveal the dependency of the ion energy on laser
intensity, simulations were performed by varying the laser
intensity. The maximum carbon energies obtained from the
simulations are shown in Fig. 4 as the solid and dashed
lines, where the laser energy is calculated as εlaserðJÞ ¼
1.69 × I0ðW=cm2Þ=1020 according to the relationship
between intensity and laser energy in our experiments.
The solid line is obtained at the optimal thickness of the
CNF for different intensities with a fixed CNF density of
0.2nc. The dashed line is obtained by scaling up the density
of the CNF with laser intensity as well. It can be seen that
the carbon energy is higher in the latter case, following
Emax ∝ I0.6. This scaling is superior to TNSA but inferior to
RPA. By comparing with existing RPA and TNSA results,
one can speculate that for the laser intensity available now
and in the near future, the cascaded acceleration would be
a realistic optimal scheme for the generation of highly
energetic heavy ions. It should be noted that the scaling
obtained from carbon ions may not be directly applied to
very heavy ions like Cu and Au, since the detailed
ionization dynamics is not taken into account here. But
the advantages of cascaded acceleration will be sustained.
In addition to the study performed here, the dependence of
ion spectra on the polarization of laser pulses needs to be
explored further.
In summary, we demonstrate that cascaded laser accel-
eration of carbon ions can be achieved by combining a tens-
of-micrometer-thick, slightly underdense plasma layer with
a nanometer-thin foil. The subsequent interplay of RPA and
sheath acceleration leads to substantially higher maximum
ion energy. This scheme is especially suited for heavy
ion acceleration at realistic laser parameters currently
accessible.
The work has been supported by the Institute for Basic
Science of Korea under IBS-R012-D1, the National Basic
Research Program of China (Grants No. 2013CBA01502
and No. 11475010), NSFC (Grants No. 11535001,
No. 11775010, No. 61631001, and No. 11605111), and
National Grand Instrument Project (No. 2012YQ030142).
J. Q. Y. acknowledges the Projects No. 2016M600007 and
No. 2017T100009 funded by China Postdoctoral Science
Foundation. The particle-in-cell code EPOCH was in part
funded by the UK EPSRC Grant No. EP/G054950/1. Our
simulations were carried out at the Max Planck Computing
and Data Facility and Shanghai Super Computation Center.
J. S. and W. J. M. acknowledge support by the DFG-funded
MAP cluster and the LMU target factory.
W. J. M. and I. J. K. contributed equally to the experi-
ments in this work.
*Corresponding author.
wenjun.ma@pku.edu.cn
†Present address: Division of Scientific Instrumentation,
Korea Basic Science Institute (KBSI), Daejeon 34133,
Korea.
‡Corresponding author.
x.yan@pku.edu.cn
§Corresponding author.
chnam@gist.ac.kr
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