Self-Organizing GeV, Nanocoulomb, Collimated Proton Beam from Laser Foil Interaction at 7×1021W/cm2

Abstract

We report on a self-organizing, quasi-stable regime of laser proton
acceleration, producing 1 GeV nano-Coulomb proton bunches from laser foil
interaction at an intensity of 7*10^21 W/cm2. The results are obtained from 2D
PIC simulations, using circular polarized light normally incident on a planar,
500 nm thick hydrogen foil with Gaussian transverse profile. While foil plasma
driven in the wings of the driving pulse is dispersed, a stable central clump
with 1 - 2 lamda diameter is forming on the axis. The stabilisation is related
to laser light having passed the transparent parts of the foil in the wing
region and encompassing the still opaque central clump. This feature is
observed consistently in 2D and 3D simulations. It depends on a laser pulse
shape with high contrast ratio.

Full text

Self-organizing GeV nano-Coulomb collimated proton beam
from laser foil interaction at 7 × 1021 W/cm2
X.Q. Yan1,2,4*, H.C. Wu1, Z.M. Sheng3, J.E. Chen2, J. Meyer-ter-Vehn1
1 Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Straße 1,
D-85748 Garching, Germany
2 State Key Laboratory of Nuclear Physics and Technology, Peking University,
Beijing 100871, China
3Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, CAS,
Beijing 100190, China, and Department of Physics, Shanghai Jiao Tong University,
Shanghai 200240, China.
4Center for Applied Physics and Technology, Peking University, Beijing 100871, China
Abstract:
We report on a self-organizing, quasi-stable regime of laser proton acceleration,
producing 1 GeV nano-Coulomb proton bunches from laser foil interaction at an intensity of 7
× 1021 W/cm2. The results are obtained from 2D PIC simulations, using circular polarized
laser pulse with Gaussian transverse profile, normally incident on a planar, 500 nm thick
hydrogen foil. While foil plasma driven in the wings of the driving pulse is dispersed, a stable
central clump with 1 - 2 λ diameter is forming on the axis. The stabilisation is related to laser
light having passed the transparent parts of the foil in the wing region and encompassing the
still opaque central clump. This feature is observed consistently in 2D and 3D simulations. It
depends on a laser pulse shape with high contrast ratio.
PACS numbers: 52.59.-f, 52.38.Kd, 52.35.Mw
* Email: xyan@mpq.mpg.de

With the development of chirped pulse amplification technique [1], ultra-intense short
laser pulses with peak intensity as high as 21 2
10 W/cmI> and contrast ratios in excess of
1010 are now available, allowing for studies of laser interaction with ultrathin targets [2].
Energetic ions can be produced by means of intense laser light interacting with thin foils.
These ion beams are attracting much attention due to a wide range of potential applications
covering radiograph transient processes [3], ion beam tumor therapy [4], and fast ignition of
fusion cores [5]. As a rule, these applications require ion beams with low energy spread and
high collimation.
Usually a linear polarized (LP) laser pulse is used which generates hot electrons due to
J×B heating [6]. Ion acceleration mechanisms [7–11] are electrostatic shock acceleration at
the front and target normal sheath acceleration (TNSA) at the rear side. However, the proton
pulses obtained in this way are far from monochromatic. Often the energy spread is 100%,
and ions with the highest energy represent only a small fraction of the total flux [12]. Certain
techniques can be used to decrease the energy spread [13-15], and the best results to date have
yielded an energy spread of about 20% FWHM at relatively low energy (few MeV).
In the present paper, we consider circular polarized (CP) light. As pointed out recently in
a number of papers [16-20], CP laser pulses can accelerate ions very efficiently and produce
sharply peaked spectra. When normally incident on plane foils, the light pressure is quasi-
stationary, following only the time dependence of the pulse envelope. Electrons are then
smoothly pushed into the high-density material without strong heating and ions are taken
along by means of the charge separation field. This is in contrast to linear polarization which
triggers fast longitudinal electron oscillations and excessive heating.
For appropriate parameters, CP pulses may accelerate foils as a whole with most of the
transferred energy carried by ions. The basic dynamics are well described by a one-
dimensional (1D) piston model [18, 20]. Acceleration terminates due to multi-dimensional
effects such as transverse expansion of the accelerated ion bunch and transverse instabilities.
In particular, instabilities grow in the wings of the indented foil, where light is obliquely
incident and strong electron heating sets in. Eventually, this part of the foil is diluted and
becomes transparent to the driving laser light. The central new observation in the present
paper is that this process of foil dispersion may stop before reaching the centre of the focal
spot and that a relatively stable ion clump forms near the laser axis which is efficiently
accelerated. The dense clump is about 1 - 2 laser wavelengths in diameter. The stabilization is

Fig. 1 (color online): Foil density evolution. Left: electrons, right: ions, at times (a,d) 16t
=
,
(b,e) 36t=, (c,f) 46t=, in units of laser period. The laser pulse is incident from the left and
hits the plasma at 10t=.
related to the driving laser pulse that has passed the dispersed foil in the transparent wing
region and starts to encompass the opaque clump, keeping it together. Acceleration is then
similar to that studied for so-called reduced mass targets [21], where small droplets or
clusters are used as targets. In what is described below, the new configuration is self-
organizing with small pieces of matter punched out of a plane foil. In this Letter, we exhibit
this new regime in terms of two-dimensional particle-in-cell (2D-PIC) simulations.

In the simulations, we have taken a CP laser pulse with wavelength 1 m
λ
μ
= and
maximum normalized vector potential 2
/50aeAmc
=
=, corresponding to an intensity of
18 2 2 2
1.37 10 W/cm 2 /Ia
λ
=× ⋅ . The pulse has a Gaussian radial profile with 20
λ
full width at
half maximum and a trapezoidal shape longitudinally with 20
λ
flat top and 1
λ
ramps on both
sides. It is normally incident from the left on a uniform, fully ionized hydrogen foil of
thickness 0.5D
λ
= and normalized density / 80
e crit
Nnn
=
=, where the electron density e
n
is given in units of the critical density 22
/
crit e
nmc
π
λ
= and c is the velocity of light. Proton
to electron mass ratio is / 1836
pe
mm=. The size of the simulation box is 60 40
λ
λ
× in (x,y)
directions, respectively. We take 40 particles per cell per species and a cell size of /80
λ
. The
flat plasma foil is located at 10x
λ
= initially. Periodic boundary conditions are used for
particle and fields in transverse direction, and fields are absorbed at the boundaries in
longitudinal direction.
The temporal evolution of the foil is shown in Fig. 1, separately for electron and ion
density. One observes that electrons and ions move closely together. At 16t=(in unit of laser
period), about 6 laser cycles after the pulse front has reached the plasma, the foil is slightly
curved, following the transverse Gaussian profile of the laser pulse. At 36t=, a periodic
structure having approximately 1 λ scale is seen, very prominently in the electron distribution,
but also already imprinted in the ion distribution. Such surface rippling has been identified
before in a number of numerical studies [6, 18, 19, 21-23] and has been described as a
Rayleigh-Taylor-type instability (RTI) occurring in thin foils when driven by strong radiation
pressure [24-26]. Here we depict it when the foil is already strongly deformed. At this time,
the laser light is reflected from the indented walls and creates an intense standing-wave
pattern at the bottom of the crater (see Fig. 2a).
We attribute the foil rippling to this λ-period seed pattern, at least in part. A second
source is a fast current instability, setting in at early times when the foil is still plane. It has
been described in [23]. Inspecting the longitudinal jx current at time 36t= in Fig. 2c, a
periodic structure of current cells can be recognized, also with λ period. It indicates a pattern
of forward and backward currents typical for Weibel instability, which is known to grow fast
on the time-scale of the inverse plasma frequency
ω
p-1, which is shorter than the light period
for solid density. These current patterns contribute to the unstable foil dynamics in the wing
region.

Fig.2 (color online) (a) laser field 22
yz
EE+ at 46t
=
, the dashed line marks the concave
pulse front pushing the ion clump; (b) charge density distribution ( )
ie
nn
−
at 46t=; (c)
current density at 36t= (normalized by e
en c); (d) current density at 46t
=
. The black
arrows in the clump region indicate the direction of electron motion.
Another important aspect is that the foil is strongly accelerated as a whole, and RTI
depending on ion motion will add to perforate and break the foil. This is clearly seen in Figs.
1c and 1f, both for electrons and ions. Using the RTI growth rates derived in [25], we find e-
folding within 6 laser cycles for the wing region which is consistent with the present
simulation. The actual dynamics are very complicated, combining RTI and Weibel
instabilities in the phase of nonlinear evolution. This is not yet understood in detail and needs
separate investigation. As a result, the foil becomes transparent in the wing region, where then
light starts to pass the foil and to overtake the dense clump located near the laser axis (see Fig.
2a).
Let us now describe the evolution of the central clump in more detail. From Figs. 1c and
1f we see that the transverse extension of the clump is about 2
λ
at 46t
=
. It is driven by a
laser field distribution having the form of a concave bowl which encompasses the clump and

tends to keep it together. Plotting charge density ( )
ie
nn
−
in Fig. 2b, one recognizes how
electrons (blue) are running ahead dragging ions (red).
The current cells, seen with
λ
-period at time 36t
=
in Fig.2c, have almost been dissolved
at time 46t= in Fig.2d, except for the central cell on the laser axis which is stabilised by the
local laser field. The black arrows in Fig.2d indicate the electron motion around the clump.
Electrons move in laser direction on the axis and return on the side of the clump. This kind of
current dipole may add to the stabilization of the clump by magnetic compression.
Unfortunately, we did not succeed to show this B-field separately, because of the strong laser
field superimposed.
0 102030405060
0
1
2
3(a)
Number of proton (1010)
t/T
10 20 30 40 50 60
0.0
0.2
0.4
0.6
0.8
1.0 (b)
RPDA model
simulations
γ-1
t/T
0.00.40.81.2
0
20
40
60 (c)
t=40
t=50
t=54
t=58
Arb.Unit
γ-1
Fig.3 (color online) (a) Number of protons in the center of the foil ( /2r
λ
≤
) versus time in
units of laser cycles; (b) proton energy; (c) evolution of energy spectrum for beam ions
located inside the central clump ( /2r
λ
≤); (d) energy distribution of protons at 58t= (the
colour bar gives ion energy in MeV).
(
d
)

Figure 3 highlights the central results concerning clump evolution. The total number of
protons, comprised within a /2
λ
distance from the laser axis and shown in Fig. 3a, drops
after time 26t= from an initial value of 10
2.5 10×due to transverse expansion, but this trend
is interrupted at about 35t=, when the foil becomes transparent in the wing region and the
new regime of quasi-stable acceleration sets in. In the present 2D-PIC simulation, about
1.7×1010 protons (1 nano-Coulomb) are trapped in the central clump and are accelerated to an
ion energy of approximately 1 GeV, as it is seen in Fig. 3b. An enhanced acceleration mode
sets in at t=35 after clump formation, exceeding the predictions of the Radiation Pressure
Driven Acceleration (RPDA) [27] by a factor 2. At the same time, the ion energy spectra start
to exhibit sharp peaks, as it is seen in Fig. 3c. The perspective view in Fig. 3d then shows ion
density in the ( , )
x
yplane with colour marking ion energy. One observes the high-density
region of the unperturbed foil at the boundaries, the low-density plasma remains of the foil in
the wing region (dark blue), and the accelerated ion clump sticking out as a conspicuous red
spike in the centre. Results similar to those presented here have been obtained with other
independent 2D-PIC codes [28]. Also 3D-PIC simulations reveal the existence of the new
regime [29].
The present results depend on the high-contrast laser pulse (1 cycle rise time). More
extended rise times tend to disperse the foil plasma not only in the wing region, but also to
prevent ion trapping in the central dense clump. Although much progress has been made
recently in generating laser pulses with ultra-high contrast [30], there may be other ways by
modifications of the irradiation geometry to improve ion trapping. More systematic
investigations based on 2D- and 3D-PIC simulation are now under way to map out the
parameter space in which the new regime of central clump acceleration can be achieved.
In summary, we have identified a new regime of laser ion acceleration and have
described the essential dynamics, self-organizing a mass-limited ion clump which is
accelerated in a quasi-stable manner over many laser cycles without dispersion. This leads to
sharply peaked proton spectra with energies of 1 GeV and more. These findings, obtained on
the basis of multi-dimensional PIC simulations, go beyond previous results on phase stable
acceleration published so far. An important point is that the nonlinear physics itself select the
amount of accelerated ions (about 1 nano-Coulomb of protons in the present simulations),
rather than relying on complicated target structures. This opens an option to use simple targets
adequate for high-repetition rates by means of plane foils. This is attractive for applications.

Acknowledgements
One of the authors (XQY) would like to thank the Alexander von Humboldt Foundation
for a scholarship. This work is partially supported by NSFC (10855001), by the Munich
Centre for Advanced Photonics (MAP), and by the Association EURATOM – Max-Planck-
Institute for Plasma Physics. ZMS is supported in part by the National Nature Science
Foundation of China (Grants No. 10674175, 60621063). The authors acknowledge
stimulating discussions with Prof. H. Ruhl and also with Dr. M. Chen and Prof. A. Pukhov.
• On leave Peking University
References
[1] G. A. Mourou, T. Tajima, and S. V. Bulanov, Rev. Mod. Phys. 78, 309 (2006).
[2] A. J. Mackinnon, Y. Sentoku, P. K. Patel, D. W. Price, S. P. Hatchett, M.H. Key, C.
Andersen, R. A. Snavely, and R. R. Freeman, Phys. Rev. Lett. 88, 215006 (2002).
[3] M. Borghesi et al., Phys. Plasmas 9, 2214 (2002).
[4] S. V. Bulanov, T. Zh. Esirkepov, V. S. Khoroshkov, A. V. Kuznetsov, F. Pegoraro, Phys.
Lett. A 299, 240 (2002).
[5] M. Roth et al., Phys. Rev. Lett. 86, 436 (2001); N. Naumova et al., Phys. Rev. Lett. 102,
025002 (2009).
[6] S. C. Wilks, W. L. Kruer, M. Tabak, and A. B. Langdon, Phys. Rev. Lett. 69, 1383 (1992).
[7] E. L. Clark et al., Phys. Rev. Lett. 85, 1654 (2000); A. Zhidkov et al., Phys. Rev. E 60,
3273 (1999).
[8] J. Denavit, Phys. Rev. Lett. 69, 3052 (1992).
[9] A. Zhidkov, M. Uesaka, A. Sasaki, H. Daido, Phys. Rev. Lett. 89, 215002 (2002); L. O.
Silva, M.Marti, J.R.Davies, R.A.Fonseca, C.Ren, F.Tsung, W.B. Mori, Phys. Rev. Lett. 92,
015002 (2004); A. Maksimchuk, S. Gu, K. Flippo, D. Umstadter, V.Y. Bychenkov, Phys. Rev.
Lett. 84, 4108 (2000).
[10] P. Mora, Phys. Rev. Lett. 90, 185002 (2003); T. Esirkepov, M.Yamagiwa, and T.Tajima
Phys. Rev. Lett. 96, 105001 (2006).
[11]Y. T. Li, Z. M. Sheng et al, Phy. Rev. E 72, 066404 (2005).
[12]V. Malka et al., Med. Phys. 31, 1587 (2004).
[13] H. Schwoerer et al., Nature 439, 445 (2006).

[14] T. Toncian et al., Science 312, 410 (2006).
[15] M.Hegelich et al, Nature 439, 441 (2006).
[16] A. Macchi, F. Cattani, T.V. Liseykina, F. Cornolti, Phys. Rev. Lett. 94, 165003 (2005).
[17] S.G. Rykovanov, J. Schreiber, J. Meyer-ter-Vehn, C Bellei, A. Henig, H.C. Wu and M.
Geissler, New J. Phys. 10, 113005 (2008) ; X. Zhang, et al., Phys. Plasmas 14, 123108 (2007);
C.S. Liu, V.K. Tripathi and X. Shao, Frontiers in Modern Plasma Physics 246-254 (2008).
[18] O. Klimo, J. Psikal, and J. Limpouch, and V. T. Tikhonchuk, Phys. Rev. Special Topics
- Accelerators and Beams 11, 031301 (2008).
[19] A. P. L. Robinson, M. Zepf, S. Kar, R.G. Evans, and C. Bellei, New J. Phys. 10, 013021
(2008).
[20] X.Yan et al., Phys. Rev. Lett. 100, 135003 (2008).
[21] A. Henig, D. Kiefer, M. Geissler, S.G. Rykovanov, R. Ramis, R. Hörlein, J. Osterhoff,
Zs. Major, L. Veisz, S. Karsch, F. Krausz, D. Habs,and J. Schreiber, Phys. Rev. Lett. 102,
095002 (2009).
[22] A. Macchi, F. Cornolti, F. Pegoraro, T.V. Liseikina, H. Ruhl, and V. A. Vshivkov, Phys.
Rev. Lett. 87, 205004 (2001).
[23] M. Chen, A. Pukhov, Z.M. Sheng, X.Q.Yan, Physics of Plasma, 15, 113103 (2008).
[24] E. G. Gamaly, Phys. Rev. E 48, 2924 (1993).
[25] F. Pegoraro and S.V. Bulanov, Phys. Rev. Lett. 99, 065002 (2007).
[26] Y. Yin, W. Yu, M. Y. Yu, A. Lei, X.Yang, H. Xu and V.K. Senecha, Phys. Plasmas 15,
093106 (2008).
[27] T. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phys. Rev. Lett.
92, 175003 (2004).
[28] H.C. Wu, Z.M. Sheng, J. Zhang, Phys. Rev. E 77, 046405 (2008).
[29] The formation of a central clump and proton acceleration to GeV energies is also
observed in 3D PIC simulations, when using similar parameters as in the present paper. M.
Chen, private communication.
[30] R. Hoerlein, et al, New Journal of Physics 10, 083002 (2008).