Transverse Characteristics of Short-Pulse Laser-Produced Ion Beams:
A Study of the Acceleration Dynamics
E. Brambrink,1,2,3,*J. Schreiber,4T. Schlegel,2,3P. Audebert,1J. Cobble,5J. Fuchs,1,6M. Hegelich,5and M. Roth2,3
1Laboratoire pour l’Utilisation des Lasers Intenses (LULI) Unite ´ Mixte n?7605 CNRS - CEA - Ecole Polytechnique -
Universite ´ Pierre et Marie Curie, Ecole polytechnique, Palaiseau, France
2Institute for Nuclear Physics, Darmstadt University of Technology, Darmstadt, Germany
3Gesellschaft fu ¨r Schwerionenforschung, Darmstadt, Germany
4LMU, Mu ¨nchen, Germany
5Los Alamos National Laboratories, Los Alamos, New Mexico, USA
6Nevada Terawatt Facility, University of Nevada, Reno, Nevada, USA
(Received 19 January 2006; published 21 April 2006)
We report on first measurements of the transverse characteristics of laser-produced energetic ion beams
in direct comparison to results for laser accelerated proton beams. The experiments show the same low
emittance for ion beams as already found for protons. Additionally, we demonstrate that the divergence is
influenced by the charge over mass ratio of the accelerated species. From these observations we deduced
scaling laws for the divergence of ions as well as the temporal evolution of the ion source size.
DOI: 10.1103/PhysRevLett.96.154801PACS numbers: 29.27.Fh, 52.38.Kd, 52.40.Kh
Introduction.—Energetic ions, emitted from solid den-
sity targets during the interaction with ultraintense lasers,
are an interesting area of research per se, but also exciting
because of the various possibilities of applications [1–3].
Intense proton beams, observed in several laboratories [4–
6], are collimated (divergence angle <20?), carry high
currents (MA), and reach energies up to 50 MeV. Many
experiments have been performed to investigate the influ-
ence of target [7–9] and laser parameters [10,11] on the
proton beam characteristics to understand the acceleration
The acceleration of ions with lasers is complementary to
that of energetic protons. Because of their specific inter-
action characteristics (higher stopping power, different
nuclear reaction), ion beams may be in favor for several
applications, e.g., isochoric heating, isotope production, or
the injection into a conventional accelerator. Moreover, the
latter applications will strongly profit from the high bright-
ness and low emittance of these beams. To make such
applications work, it is important to study the character-
istics ofion beams in detail and to develop practical scaling
laws. Since ions with different masses and charge states
will appear at the same time in the space charge volume,
the complex acceleration process itself can be analyzed,
measuring, for example, the maximum electric field
strength [12,13]. In this Letter, we investigated the trans-
verse characteristics of laser-produced light ion beams,
from which we concluded on the acceleration dynamics.
For our experimental conditions, the acceleration from
the nonirradiated rear surface, so-called target normal
sheath acceleration (TNSA) [14,15], is the dominant
mechanism . In this model, a beam of energetic elec-
trons is generated during the interaction of the laser with
the front surface of the target, propagates through the
target, and sets up an electrostatic field (typ. 1012V=m)
on the rear surface. This field ionizes all atoms in a surface
layer due to field ionization and subsequently accelerates
them. Usually, there is a thin layer of impurities present on
the target surface containing hydrogen (water, hydrocar-
bons), thus providing protons for the acceleration. Since
the charge over mass ratio for the protons is higher than for
all other ion species, the protons undergo the strongest
acceleration, ranging out the other species and shielding
them from the space charge field, suppressing their accel-
eration. Removing these contaminants [12,17], the proton
generation will be inhibited but the acceleration of ions can
be enhanced remarkably. The acceleration of light ions,
such as carbon, beryllium, oxygen, or fluorine, as well as
heavier species like palladium to high energies has been
demonstrated recently .
An important discovery for the exploration of the trans-
verse beam parameters of laser generated protons was the
possibility of beam intensity profiling by means of spatial
structures on the rear surface of the target. With this
technique, the source size on the rear surface of the target
as well as the beam emittance were determined. The latter
result pointed at an extremely laminar expansion . For
this Letter, we have extended this technique to light ions
studying the corresponding beam parameters.
Experimental setup.—The experiments were performed
with the 100 TW laser system of the Laboratoire pour
l’Utilisation des Lasers Intenses (LULI). A laser beam
with 20 J in 350 fs was focused with an f=4 off-axis
parabola onto a thin foil providing focal intensities of
2–5 ? 1019W=cm2.
We irradiated 25 ?m thick gold and tungsten foils with
engraved linear structures of 10 ?m spacing on the rear
surface. The tungsten foils were heated by a high current
up to 1300?C to remove hydrogen and carbon impurities
from the target surface. In this case, we observed that only
the stable oxides remained, providing a beam of oxygen
PRL 96, 154801 (2006)
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© 2006 The American Physical Society
Figure 1 shows the setup for the ion diagnostics used in
this experiment. The ions were detected with a Thomson
parabola, a spectrometer with parallel magnetic and elec-
tric fields, which disperses ions with different q=m values
on separate parabolas. The distance between the spec-
trometer and the target was about 70 cm; the entrance
pinhole had a diameter of 200 ?m, which corresponds to
a solid angle of approximately 3 ? 10?8sr.
The spectrally dispersed ions were detected with a CR-
39 plastic detector , where the ions cause a local
destruction of the polymer structure, which leaves later a
small crater (pit) after etching in NaOH. These pits were
then counted under a microscope to obtain an energy
For the angular distribution measurement of the ions,
radiochromic film (RCF)  was placed in a distance of
63 mm in front of the entrance pinhole of the Thomson
parabola. This film is sensitive to the deposition of energy
by ionizing radiation. As the energy deposition of the ions
is very high in comparison to electrons and x rays, the
imprint in this detector is mainly caused by ions.
Experimental results.—Figure 2 shows a spectrum ob-
tained with the Thomson parabola for the charge state Z ?
6? of oxygen, which was the highest charge state mea-
sured in this experiment. Only the ions of this charge state
are energetic enough to be compared with protons; the
lower charge states are therefore disregarded. The spec-
trum shows an exponential energy distribution with a mean
energy (temperature) of 5 MeV, which was also deduced
from the RCF stack for a proton beam from an unheated
target under the same experimental conditions. The spec-
trum obtained from the Thomson parabola ensured also the
absence of protons which could have falsified the results
obtained with RCF. The resemblance between ions and
protons concerning laser parameters and spectral charac-
teristics allows us to assume the same accelerating field
and to compare the transverse parameters directly.
From the beam profiles obtained with the RCFdetectors,
we deduced the divergence of the beam and the size of the
ion sourceonthe rear surface ofthe target. Since each layer
of the RCF stack detects a different group of ions with an
energy, at which those ions are stopped (highest deposition
in the Bragg peak), these parameters can be measured for
several particle energies in the case of protons. However,
for heavy ions due to their low penetration depth, this is
possible only for one distinct energy, which is determined
by the protective aluminum layer (13 ?m thick) in front of
the RCF. In our case, this total energy was ?16:5 MeV,
which corresponds to an acceleration potential (equivalent
proton energy) of 2.75 MeV for the measured charge state
O6 ? . The ions with lower charge states are stopped in the
In Fig. 3, the source size and the divergence for protons
and ions are plotted over the accelerating potential. For the
proton beam, we see a linear dependence of the source size
on the potential and a divergence, which is proportional to
the source size. These findings correspond well to the
results in Ref.  and have also been observed system-
atically over a wide range of experimental conditions and
FIG. 1 (color online).
Experimental setup. Ions are character-
Thomson parabola (spectrally)a and with
Thomson parabola spectrometer.
Energy spectrum for the O6? ions obtained with the
FIG. 3 (color online).
foot) measured for different accelerating potentials. While the
source size has comparable values for ions and protons, the
divergence for ions is significantly lower.
Source size and divergence (foot-to-
PRL 96, 154801 (2006)
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proton energies . The source size obtained for the
heavy ions fits well into the linear dependence found for
the protons, while the divergence is significantly lower,
about a factor of 1.6. Also the magnification of the struc-
ture on the rear surface of the target is decreased by the
same factor; the beam divergence is therefore changing
globally and not only at the edge of the beam.
Furthermore, the intensity modulation of the beam al-
lows us to measure the transverse beam emittance.
Following the approach of Ref. , we obtain a normal-
ized emittance of 0:09 mmmrad, which is close to that for
protons and much lower than for conventional ion sources
[e.g., 2:5 mmmrad for the GSI UNILAC accelerator ].
Discussion.—The measurement of the transverse beam
parameters of heavy ions reveals many similarities be-
tween the acceleration of protons and heavy ions. Ions as
well as protons are emitted from the cold rear surface,
resulting in a low-emittance, laminar beam. The spatial
distribution of the acceleration potential is independent of
the accelerated ion species, as suggested by the measure-
ments of the source size. This is consistent with the TNSA
model, which considers an electric field determined by the
(spatial) electron distribution.
However, the divergence of the heavy ion beam is sig-
nificantly lower than the proton beam divergence, which
can be explained by the lower velocity of ions compared to
that of protons after passing the same acceleration poten-
tial. The divergence is directly related to the shape of the
ion front in the beginning of the free propagation, which
can be well approximated by an inverse parabola , and
is only determined by the diameter and the maximum of
this parabola, e.g., the maximum distance of the ion front
from the initial surface (see Fig. 4). Since the parabola is
defined by the source size and the divergence, we can
estimate a corresponding distance of ?12 ?m for the ion
front, which is 1.6 times smaller than for protons under
equivalent experimental conditions.
Since the ions detected in a distinct layer of the RCF
have all the same energy, the final velocity of these ions is
the same. Therefore, the curvature of the ion front cannot
be explained bydifferent ionvelocities atthe central part of
the beam and on its edge. We attribute this curvature to a
temporal effect in the ion acceleration, where the ions at
the edge start later in time than in the middle of the
acceleration field. So, the distance between the ion front
in the center of the beam and the initial target surface
should scale with the ion sound velocity cs, which can be
described analytically in an isothermal one-dimensional
expansion approximation :
Here T is the electron temperature, Z the charge state of the
ion, mithe ion mass, and kBthe Boltzmann constant. For
the oxygen ions we calculate an ion sound velocity, which
? 1:63 times smaller than for protons. This value
matches very well the measured one.
From the model we can estimate the time delay in the
beam propagation between the beam edge and at its center.
With an electron temperature of 2 MeV , the sound
velocity csis 8:5 ? 106m=s and the delay becomes 1.4 ps,
which is in agreement with radiography experiments ,
showing the expansion of the whole ion front within the
first two ps.
Finally, it is possible to evaluate the temporal evolution
of the ion source size. With the parabolic shape for the ion
fronty ? yf?t? ? x2(see Fig.4),wefindforthe source size
on the target r2?t? ? yf?t? / hcsit and arrive at the follow-
ing expressions for the temporal evolution and the growth
rate of the source size:
where r0and t0are fit parameters, which can be calculated
from a measured source size and divergence. In our ex-
periment we obtained the values r0? 83 ?m and t0?
1:4 ps. Figure 5 shows the growth rate of the ion source.
The initial source size radius, defined by the focal spot and
the divergence of the electron beam inside the target ,
is ? 20 ?m; therefore, this model is only valid for times
t > 120 fs. Measurements of the rear side reflectivity 
show qualitatively the same temporal dependence (hyper-
bolic) but different values for the maximum velocity,
which can be attributed to the different laser intensity in
The initial growth rate can be well explained if one
suggests that the electrons gain a transverse momentum
ina self-generated field onthe rear surface (fountain effect)
. We estimated the transversevelocity predicted by this
model. An electron, traveling at the speed of light with the
momentum p, gains the transverse velocity,
r?t? ? r0
_ r?t? ?r0
while traveling through a magnetic field B of length l. With
FIG. 4 (color online).
beam divergence and the curvature of the ion front, which
depends on the expansion velocity in the center of the beam.
Illustration of the correlation between
PRL 96, 154801 (2006)
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B ? 1000 T , l ? 2 ?m (Debye length) and an elec- Download full-text
tron energy of 2 MeV we obtain a vtof approximately 8 ?
107m=s, which is close to the values shown in Fig. 5.
Summary.—We have measured for the first time the
transverse characteristics of laser-produced ion beams
and compared those to results for protons obtained under
similar experimental conditions. We demonstrated an ex-
cellent ion beam quality (e.g., low emittance) similar to
laser generated proton beams. This is an important result
for future applications, where a good focusability and/or
beam quality is essential. Especially for the future accel-
erator development aiming for ultrabright beams, short-
pulse laser based ion sources can be a key component.
The size of the emitting area on the rear surface as well
as the electric field distribution is comparable to values
obtained for protons. The significantly lower divergence
can be explained by the influence of the higher ion mass on
the acceleration dynamics resulting in an emission angle
scaling with the ion sound velocity.
Thus for the design of post acceleration and beam guid-
ing, the results obtained for protons, which afford less
sophisticated experiments, can be scaled to various ion
species. In addition, we got some insight into the dynamics
of the beam generation, examining the temporal evolution
of the ion emitting zone on the rear surface.
We thank the staff of the LULI laser for their ongoing
help during the experiment and the ‘‘Institut fu ¨r
Halbleitertechnik’’ at Darmstadt for target preparation.
This work was supported by the Grant No. E1127 from
Re ´gion Ile-de-France and by BMBF.
*Electronic address: firstname.lastname@example.org
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size and divergence measurements for heavy ions.
Growth rate of the ion source deduced from the source
PRL 96, 154801 (2006)
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