Influence of the target front-surface curvature on proton acceleration in laser-foilinteractionJ. H. Bin, A. L. Lei, L. H. Cao, X. Q. Yang, L. G. Huang, M. Y. Yu, and Wei Yu Citation: Physics of Plasmas (1994-present) 16, 043109 (2009); doi: 10.1063/1.3116639 View online: http://dx.doi.org/10.1063/1.3116639 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/16/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Preplasma effects on the generation of high-energy protons in ultraintense laser interaction with foil targets Phys. Plasmas 20, 123105 (2013); 10.1063/1.4843975 Self-proton/ion radiography of laser-produced proton/ion beam from thin foil targets Phys. Plasmas 19, 123101 (2012); 10.1063/1.4769380 Stabilized radiation pressure dominated ion acceleration from surface modulated thin-foil targets Phys. Plasmas 18, 073106 (2011); 10.1063/1.3606562 A double-foil target for improving beam quality in laser ion acceleration with thin foilsa) Phys. Plasmas 18, 056707 (2011); 10.1063/1.3574388 Lateral hot electron transport and ion acceleration in femtosecond laser pulse interaction with thin foils Phys. Plasmas 17, 013102 (2010); 10.1063/1.3276524

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Influence of the target front-surface curvature on protonacceleration in laser-foil interaction

J. H. Bin,1 A. L. Lei,1,a� L. H. Cao,2 X. Q. Yang,1 L. G. Huang,1 M. Y. Yu,3 and Wei Yu1

1Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800,China2Institute of Applied Physics and Computational Mathematics, Beijing 100088, China3Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027, China

�Received 6 November 2008; accepted 19 March 2009; published online 20 April 2009�

Energetic proton generation from thin foil targets by ultraintense laser pulse is investigated usingtwo-dimensional particle-in-cell simulation. Foil targets with concave, flat, and convex frontsurfaces are considered. The maximum energy of the accelerated protons depends on thefront-surface curvature, and the highest-energy protons are from the concave foil. The result can beattributed to an enhancement of the generation as well as concentration of the laser-driven hotelectrons by the concave surface. © 2009 American Institute of Physics. �DOI: 10.1063/1.3116639�

I. INTRODUCTION

The acceleration of protons by the interaction of intenseshort laser pulse with matter is of interest because the energyrange, spatial quality, and duration of the laser-generatedprotons are suitable for proton radiography and theraphy,1,2

isochoric heating of solid matter,3 fast ignition in inertialconfinement fusion,4 etc. Several mechanisms for proton ac-celeration in laser-target interaction have been proposed.5–16

In most existing proposals, the process is initiated by expul-sion of the electrons near the front target surface by the pon-deromotive force of the laser pulse and appearance of anintense electrostatic charge-separation field which then accel-erates the target protons. A mechanism which has attractedmuch recent attention is target-normal sheath acceleration�TNSA�.5–9 As an intense laser pulse irradiates a solid foil,hot electrons are produced at the target front and are trans-ported through the target to the back side vacuum, forming astrong electrostatic space-charge sheath field there. Thestrong electrostatic field is normal to the target surface andcan efficiently accelerate some of the protons in the latter toenergies up to 58 MeV.6 Similarly, protons on the target frontsurface can be accelerated by TNSA since target electronsare also expelled to the front vacuum region by the laserponderomotive force.

The number and energy of the TNSA protons depend onthe electrostatic sheath field E at the target rear side. Thelatter is proportional to the temperature and density of thehot electrons in the rear vacuum, or E� �nhTh�1/2, where nh

and Th are the hot electron density and temperature,respectively.17 The density nh can be increased by enhancingthe laser-light absorption and spatial concentration of theelectrons in the target. Recently, Psikal et al.18 found that theproton energy can be increased by using a cylindrical target.The increase is attributed to an enhancement of light absorp-tion by the curved front surface of the latter. However, thefront-surface curvature can also affect the hot electron trans-port inside the target, which can in turn affect the electron

density at the rear vacuum region, and thus the back sidesheath field and proton energy. For example, Adam et al.19

showed that the hot electron beam created at the front surfaceof a planar target is divergent.

In order to investigate the effect of the front-surface cur-vature on TNSA protons, in this paper, we perform two-dimensional �2D� particle-in-cell �PIC� simulations of the in-teraction of ultrashort laser pulses with thin foils for threedifferent �concave, flat, and convex� front-surface curvatures.It is found that more hot electrons are generated with thecurved foils and that the maximum energy of the protons isstrongly influenced by the concentration of the hot electrons.In particular, the hot electrons are concentrated by the con-cave foil target and the highest proton energy is achieved.With the convex foil target, although laser absorption isnearly the same as that with the concave foil, the hot electrontransport inside the target is divergent, so that the target-back-side space-charge field is weaker.

II. SIMULATION PARAMETERS

We use the 2D PIC code LAPINE to simulate energeticproton generation in the interaction of intense laser pulseswith foil targets. The simulation box is 60��20�, where �=1 �m is the laser wavelength. A p-polarized laser pulsewith spatially Gaussian envelope exp�−��y−10� /y0�2� andpeak intensity I0=1.38�1020 W /cm2, which corresponds toa normalized vector potential a=eA /mec

2=10, where A isthe vector potential, is normally incident along the x axisfrom the left side. The laser polarization is in the y directionand its focal-spot diameter is 10� �or y0=5��. The laserpulse has a sine-and-flattop temporal profile, so that the timescales of the rising front and the pulse period can be con-trolled separately. In the following, we shall present resultsfor a pulse which rises in two light-wave periods � with asine profile, maintains its peak intensity for 18�, and thenvertically drops to zero, as shown in Fig. 1.

The target consists of electrons and protons. The initialelectron and proton temperatures are 1 keV, and their densityis 10ncr, where ncr is the critical density. Thin targets witha�Electronic mail: lal@siom.ac.cn.

PHYSICS OF PLASMAS 16, 043109 �2009�

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three different front surfaces are considered: �i� a target ofsize 10��10� with a concave hemisphere of radius 5� atthe front side, �ii� a flat target of size 5��10�, and �iii� atarget with a convex hemisphere of radius 5� on the frontside. All targets have a thickness of 5� at the center, alongthe laser axis. The profiles of these three targets and theirinitial positions in the simulation box are shown in Fig. 1.

III. SIMULATION RESULTS AND DISCUSSION

Simulations of laser-target interaction are carried out forthe three target profiles. The proton and electron energyspectra, the electromagnetic fields, the light reflection andabsorption, as well as the particle distributions are monitoredand compared.

The proton energy spectra for the three targets at t=150� are shown in Fig. 2. Each energy spectrum showsexponential decay at high energies until a maximum isreached. In general, the concave target produces higher en-ergy protons. The maximum energies for the concave, flat,and convex foil are 66.5, 52.5, and 57.5 MeV, respectively.This can also be seen in Fig. 3 for the proton phase space�x ,vx� at t=150�. There we see that for all the three targetsthe protons from the target front and rear surfaces are wellseparated. Furthermore, the highest-energy protons are fromthe rear surface, indicating that TNSA is responsible for thehigh-energy protons. One can also see that the concave foiltarget produces protons with the highest velocity �from thetarget rear�.

The intense light is absorbed via the vacuum and j�Bheating processes.20,21 For the flat-foil target, the laser pulseis normal to the front surface everywhere and the main ab-sorption mechanism is j�B heating. For the concave andconvex foil targets, parts of the laser light is oblique to thefront surface, so that both j�B and vacuum heating are ac-tive. Laser absorption is 18.5%, 18.7% for the concave and

convex foil targets, and 11.3% for the flat-foil target. In Fig.4 for the hot electron energy spectra, we see that more hotelectrons are generated by the concave and convex targetfronts, consistent to the corresponding higher laser absorp-tion by these targets. This results in more electrons and largerspace-charge field on the target back side, therefore alsohigher proton energies.

The front surfaces of the concave and convex foil targetsare radially symmetric with respect to the incident laserpulse, so that one might expect that light absorption �viavacuum and j�B heating� should be the same for these twotargets. On the other hand, the concave front surface mightpartially focus the incident laser light to the propagation axisand the intensified light can enhance the light absorption,like in the case of a fast ignition hollow-cone target.22,23

Figure 5 shows the total electromagnetic field amplitude�square root of the instantaneous electromagnetic energy� forthe concave and flat foils at t=27�. One sees that light re-

FIG. 1. �Color online� The targets and their positions in the simulation box.The initial density of the targets is 10ncr. The width of the targets is 10�,located at 5��y�15�, and the thickness is 5� at y=0. The space coordi-nates are normalized by the laser wavelength �. The lower-right panel showsthe temporal profile of the laser pulse, the peak intensity is 1.38�1020 W /cm2, which corresponds to a��eA /mec

2�=10. � is a laser cycle.

FIG. 2. �Color online� Proton energy spectra at 150� for the concave, flat,and convex foil targets.

FIG. 3. �Color online� Phase spaces �x ,vx� of protons at time 150�. Thetarget rear surface is now located at x=30� due to the plasma movement.

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flection does not lead to focusing or intensification of laserenergy in front of the concave target. This result is also con-sistent with that from simple optical ray tracing, whichshows that a hemispherical concave mirror does not reflectlight such that the resulting light will concentrate and/orpropagate forward. Thus, the concave target used here cannotfocus the laser pulse. In fact, the degree of light absorption isalmost identical for the concave and convex targets, as canalso be seen from the energy spectra of the hot electrons,shown in Fig. 4. Therefore, the difference in the maximumproton energy for the concave and convex foils is not due toa difference in the laser-light absorption.

However, a concave surface favors concentration of thehot electrons, a process that increases the electron densityand enhances the proton acceleration. To verify the concen-tration of the hot electrons in the case of the concave target,Fig. 6 shows the electron energy density distributions ��−1�ne �normalized by the initial electron density 10ncr� forelectrons with �= �1−�2 /c2�−1/21.98 �corresponding to hot

electrons with energies higher than 500 keV� at t=18� andt=33�. At t=18�, when the laser pulse is on, one sees thatthe maximum electron energy density is 100 for both theconcave and convex targets, and only 45 for the flat target.That is, the laser absorption efficiency is almost the same forthe concave and convex targets and is higher than that for theflat target. At t=33�, when the laser pulse has vanished, onesees that the hot electrons are much better concentrated in theconcave foil target compared to that in the other two targets.Similar concentration of hot electrons in a concave foil wasobserved earlier by Ruhl et al.24 The concentration can alsobe seen in Fig. 7, which shows the hot �500 keV� electronenergy density in the transverse direction at x=12.5� and att=33�. For the concave target, one sees that there is a needle-shaped electron bunch with the peak value reaching 24.7. Forthe flat target one finds a broader energy distribution and apeak value of only 12, and for the convex target one finds a

FIG. 4. �Color online� Energy spectra of hot electrons with px0 at time18� for the concave, flat, and convex targets.

FIG. 5. �Color online� Spatial distribution of the square root �normalized bythe laser electric field E0� of the instantaneous electromagnetic energy at t=27�.

FIG. 6. �Color online� The electron energy density distributions ��−1�ne

normalized by the initial electron density 10ncr for electrons with �= �1−�2 /c2�−1/21.98 �corresponding to the hot electrons with Te500 keV� att=18� �left� and t=33� �right�. The maximum electron energy density is 100for both the concave and convex targets and 45 for the flat target.

FIG. 7. �Color online� The profiles of the electron energy density distribu-tions ��−1�ne at x=12.5� and at t=33�.

043109-3 Influence of the target front-surface curvature… Phys. Plasmas 16, 043109 �2009�

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much broader energy distribution. Thus, with the concavefoil the hot electrons are much better concentrated, so thatthe maximum energy of the TNSA protons is higher.

The mechanism for the hot electron concentration in theconcave and convex foil targets is as follows. When an in-tense laser pulse is irradiated obliquely on the target, hotelectrons are generated by vacuum and j�B heating andpenetrate into the target surface region. The resulting elec-tron current along the laser axis induces in the latter regionan intense magnetic field, which drives a part of the hotelectrons backward into the front vacuum. These electronsare driven back again by the negative space charge in thevacuum.25 That is, some of the accelerated electrons are con-fined in the front-surface region. When the surface is con-cave, they converge to the target center and become concen-trated. When the surface is convex, the electrons becomedivergent �move away from the laser axis�. Therefore the hotelectron energy density is higher for the concave foil thanthat for the convex foil, as shown in Figs. 6 and 7. Thisresults in the higher proton energy with the concave foiltarget.

Figure 8 shows the cycle-averaged magnetic field�Bz /B0� distribution at t=18� �left� and t=33� �right�. At t=18�, the location and direction of the magnetic field indi-cates that the hot electron motion in the concave and convextargets is still only near the front surface, as discussed above.The electron motion in the magnetic �and electrostatic� fieldalong the concave surface causes the electrons to move to-ward the axis, thus collimating them. Similarly, the motion ofthe electrons in the convex target surface leads to their di-vergence, as can be inferred from the magnetic field configu-ration at the later time t=33�, which indicates that there aretwo strong concentrated electron jets inside the concave foiland several divergent electron jets inside the convex foil tar-get. The acceleration of electrons on the front target surfaceby the self electric and magnetic fields there has been ob-served experimentally by Li et al.26 and Habara et al.,27 andthe divergence or concentration of hot electrons by the mag-netic field has also been discussed by Adam et al.19

In this paper we are interested in intense laser pulses

with a steep �2�� rising time. Because of the latter, the regionin front of the target is almost free of plasma before the peakof the pulse arrives. For lasers with prepulse or long risingtime, the existence of a large preplasma can reflect and ab-sorb the later part of the pulse as well as affect the hot elec-tron generation and transport,28 and hence also the protongeneration process. To see the effect of a smoother laserpulse, we have also carried out simulations with a pulsewhich rises in 10� with a sine profile and then drops in 10�with a cosine profile, with the other parameters unchanged.The resulting proton energy spectra �not shown� are qualita-tively similar to that in Fig. 2. However, the maximum pro-ton energies for the flat, convex, and concave foils are now40, 50, and 50 MeV, corresponding to laser absorption of9.6%, 15.3%, and 14.2%, respectively. That is, the advantageof the concave foil disappears since the latter now enhancesthe preplasma instead of concentrating the hot electrons in-side the target. In the experiments, a preplasma-free surfacecan be realized by doubling the laser frequency and/or usinga plasma mirror.29

IV. CONCLUSION

We have used 2D PIC simulations to study the effect ofthe target front-surface curvature on energetic proton genera-tion in intense laser interactions with thin foil targets. Thefront-surface curvature not only affects laser-light absorptionbut also the motion of the hot electrons from both vacuumand j�B heating in the cases of the concave and convextargets, but mainly from j�B heating in the case of the flattarget. More hot electrons can be generated with the concaveand convex foil targets. The front-surface curvature can af-fect the concentration of the hot electrons through the self-generated magnetic field, which for the concave target canconcentrate the electrons to the center and collimate them,and for the convex target will diffract them outward. As ex-pected, the highest proton energy is obtained from the con-cave target, since there are more hot electrons and they arewell concentrated, producing a stronger space-charge fieldthat enhances the generation and maximum energy of theprotons. Thus, such a target configuration presents an alter-native approach for more efficient production of energeticprotons useful for fast ignition in inertial confinement fusion4

and proton therapy,1,2 etc. It may also be of interest to pointout that electron acceleration along target surfaces is by itselfa topic of recent interest since collimated hot electrons areproduced.26,27,30,31

ACKNOWLEDGMENTS

We are grateful to the anonymous referee for helpfulcomments to improve this manuscript. This work was sup-ported by the Natural Science Foundation of China underGrant Nos. 10675024, 10734130, 10775165, 10835003, and10875158, the NSAF under Grant Nos. 10876011 and10676010, and the Science and Technology Commission ofShanghai Municipality under Grant No. 08PJ14102.

FIG. 8. �Color online� The cycle-averaged magnetic field Bz /B0 at t=18��left� and t=33� �right�.

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