focusing dynamics of high-energy density, laser-driven ion beams · direction of plasma ﬂow since...

Focusing Dynamics of High-Energy Density, Laser-Driven Ion Beams

Chen, S. N., D'Humieres, E., Lefebvre, E., Romagnani, L., Toncian, T., Antici, P., Audebert, P., Brambrink, E.,Cecchetti, C. A., Kudyakov, T., Pipahl, A., Sentoku, Y., Borghesi, M., Willi, O., & Fuchs, J. (2012). FocusingDynamics of High-Energy Density, Laser-Driven Ion Beams. Physical Review Letters, 108(5), [055001].https://doi.org/10.1103/PhysRevLett.108.055001

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Focusing Dynamics of High-Energy Density, Laser-Driven Ion Beams

S.N. Chen,1 E. d’Humières,2,3 E. Lefebvre,4 L. Romagnani,1 T. Toncian,5 P. Antici,6 P. Audebert,1 E. Brambrink,1

C. A. Cecchetti,7 T. Kudyakov,5 A. Pipahl,5 Y. Sentoku,2 M. Borghesi,7 O. Willi,5 and J. Fuchs1,*1LULI, École Polytechnique, CNRS, CEA, UPMC, route de Saclay, 91128 Palaiseau, France

2Nevada Terawatt Facility, MS-372, University of Nevada, Reno, Nevada 89557, USA3Université de Bordeaux, CNRS, CEA, Centre Lasers Intenses et Applications, 33400, Talence, France

4CEA, DAM, DIF, 91297 Arpajon, France5Heinrich Heine Universität Düsseldorf, D-40225 Düsseldorf, Germany

6Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma, Italy7School of Mathematics and Physics, The Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, United Kingdom

(Received 19 May 2011; published 30 January 2012)

The dynamics of the focusing of laser-driven ion beams produced from concave solid targets was

studied. Most of the ion beam energy is observed to converge at the center of the cylindrical targets with a

spot diameter of 30 �m, which can be very beneficial for applications requiring high beam energy

densities. Also, unbalanced laser irradiation does not compromise the focusability of the beam. However,

significant filamentation occurs during the focusing, potentially limiting the localization of the energy

deposition region by these beams at focus. These effects could impact the applicability of such high-

energy density beams for applications, e.g., in proton-driven fast ignition.

DOI: 10.1103/PhysRevLett.108.055001 PACS numbers: 52.38.Kd, 52.57.Kk, 52.59.Hq, 52.65.Rr

The ability to tightly focus, i.e., over tens of microns,dense (> 1010 particles), short (with duration �ps)bunches of positively charged particles is far beyond thepossibility of present particle accelerators. The increase ofthe particle density of these beams would significantlyimprove the efficiency and prospects of a number of im-portant applications. High-energy density proton beamswould allow, for example, igniting preassembled inertialconfinement fusion (ICF) targets, also known as proton fastignition (PFI) [1], or enable ultrafast heating, above keV, ofdense materials to explore their properties [2]. High-energydensity positron beams would allow enhancing the rate ofantimatter creation in the laboratory [3], opening up inves-tigations of many fundamental laws of nature.

These positively charged beams, broadband or monoen-ergetic, can nowadays be produced with a high particlenumber and over a short duration using ultraintense, shortpulse lasers interacting with solids targets [4,5]. Protonbeams are electrostatically accelerated by MeV hot elec-trons. These electrons are generated at the laser-solid in-teraction surface. After crossing the target, they induce aDebye sheath on the target rear surface. The quasielectro-static fields in the sheath then accelerate surface ions [6,7].Acceleration of positrons, which are produced in the bulkthrough nuclear processes, when they exit the solid targethave also been reported [5]. When using flat targets assources, the ion beam is divergent, 0�–25� depending onproton energy [8–10], since the expanding sheath fieldfront on the target rearside is Gaussian in shape [11,12].Such divergence can, however, be compensated by curvingthe back surface of the target, so that the accelerated protonbeam will converge [4,13–15]. This points to the necessity

of understanding and optimizing the dynamics of the fo-cusing sheath in order to achieve tight focusing, as neces-sary for the above-mentioned applications.In this Letter, we study the ion beam focusing dynamics

through temporally and spatially resolved measurements,with picosecond and micrometer resolution, of the shape ofthe sheath field from a curved target, irradiated by a high-intensity short pulse laser. These are coupled to numericalsimulations performed using the 2D particle-in-cell (PIC)codes CALDER [16] and PICLS [17], and a particle transportcode, CMC [18]. The main results are as follows: (i) aconvergence of the ion beam accelerated from the innersurface of a 800 �m diameter cylinder is observed to�30 �m diameter, (ii) significant filamentation, however,occurs in the converging plasma, (iii) the location of thefocus is a function of proton energy, although most ofthe protons focus at the geometric target center, and(iv) the exact location of laser illumination on the curvedtarget does not adversely affect the ability to focus thesheath-accelerated ion beam, although it modifies the di-rectionality of the ion beam.The experiment was carried out using the 100 TW laser

at the Laboratoire pour l’Utilisation des Lasers Intenses(LULI) operating in the chirped pulse amplification (CPA)mode. To diagnose the sheath field structure, we used thenow established technique of transverse proton radiogra-phy, which can uniquely resolve, in space and time, quasi-static fields in dense plasmas [19]. Radiography usinglaser-driven proton beam is unique in that it is able toprobe both electric and magnetic fields in dense plasmaswith high temporal and spatial resolution, thanks to the lowemittance of the beam and the short emission duration [20].

PRL 108, 055001 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

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0031-9007=12=108(5)=055001(5) 055001-1 � 2012 American Physical Society

http://dx.doi.org/10.1103/PhysRevLett.108.055001

Studying the field structures in a 3D curved target, such asa hemisphere, is very difficult, if not impossible. Therefore,by using a simpler curved geometry, such as a half cylin-der, we can study the fields in 2D. The experimental setupis shown in Fig. 1. The wavelength of the laser light was1:057 �m and the pulse duration was � ¼ 320 fs, as mea-sured after compression and before focusing. Two shortpulse beams were used. The first short pulse beam (B1),with 1 J in energy, 11 �m spot diameter, and intensity of2:5� 1018 W=cm2 on target, was used to irradiate alumi-num half cylinders, 670 �m long, having 50 �m thickwalls and 800 �m diameter, producing protons with en-ergy up to 1 MeV. The second independently compressedshort pulse beam (B2), with 7 J in energy, 7 �m spotdiameter, and intensity of 4:4� 1019 W=cm2, irradiated a10 �m thick gold foil to produce protons with energy up to15 MeV, which were used for proton radiography. Thistechnique inherently takes advantage of proton time-of-flight [21] such that the highest energy protons will probethe cylinder at the beginning of the interaction and theslower protons will probe later in time. Therefore, multi-frame snapshots of the fields’ evolution can be captured ona single shot.

The detector was a stack of radiochromic film (RCF)where the deflected protons will deposit most of their

energy at a depth within the stack according to theirBragg curve. The stack was composed of four pieces ofGafchromic HD-810 film followed by MD-55 films with a13 �m Al foil filter at the very front to block unwantedradiation. The distance from the Au foil to the B1 irradia-tion point on the cylinder is 3 mm and from the cylinder tothe RCF is 25 mm. On some shots, a copper mesh wasplaced 2 mm from the Au foil, i.e., before the half-cylindertarget, to imprint a grid pattern onto the proton probe beamto explicitly show the magnitude and direction of thefields [20].Side-on experimental radiographs of the inner surface of

the half-cylinder target are shown in Figs. 2(a)–2(d) and alltimes are normalized to tarrival at which the highest energyprotons arrive at the focus point. The dark regions, indica-tive of proton pileup, outline the expanding sheath fieldcreated by the hot electrons [11]. The first radiograph of theseries is taken at 2 ps after irradiation of the cylinder, a timeat which the cloud of hot electrons produced during thelaser interaction has already surrounded the entire halfcylinder uniformly (not shown). In Fig. 2(a), at t ¼ 4 ps,we can see that in addition to this general sheath front, atthe center of the half cylinder, there is another sphericallyshaped front which is expanding faster. As observed inprevious experiments, this front is produced by the�MeVhot electrons that accelerate the highest energy ions [7,11],with the lower energy protons being accelerated behind thefront by lower amplitude fields [4,6]. At t ¼ 11 ps, thespherical expansion front disappears and short filamentsappear inside the expanding plasma, which is consistentwith what has been simulated by PIC codes [22]. This canbe attributed to either electromagnetic or electrothermalinstabilities [23]. As time progresses, the filaments growand elongate. We have previously observed [8] that such afilamented sheath will give rise to a filamented protonbeam. Therefore, this will impair the homogeneity of thefinal produced beam. However, in our observations, we canalso use these filaments as a fiducial which indicates the

FIG. 1 (color online). Experimental setup (see text).

FIG. 2 (color online). (a)–(d) Selected proton deflectograms of only the interior of the half-cylinder target in time up to 48 ps. (e),(f) Proton deflectograms of the interior of bent foils later in time. The contrast of the images was optimized to show the structures inthe radiograph. The laser irradiates the half cylinder from the left side (the interaction side of the target is not shown). All times arenormalized to tarrival ¼ 27 ps.


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direction of plasma flow since the filaments are producedin the direction of the hot electron flow. Thus, despite thefilamentation, we can witness that the plasma begins toconverge after 10 ps.

At t ¼ 27 ps, the filaments reach a crossing point whichdefines tarrival. The convergence is clearest at t=tarrival ¼1:77 and the image is shown in Fig. 2(c). It should benoted that in the radiographs at t=tarrival ¼ 1:77, Figs. 2(c)and 2(d), there appear to be two sets of filaments: a shorterset close to the cylinder wall and a longer set within theexpansion region. The shorter set is likely due to filamen-tation in the general sheath field, which extends over theentire target, but remains close to the target surface. Thelonger set is only produced close to the laser interactionarea and is associated with the progressing proton cloudand its localized focusing. Since the radiographs integrateover the 670 �m length of the target, both sets are capturedon the radiograph. Note that filamentation could not beobserved in the first experiment reporting proton focusing[13], due to limited spatial resolution and because thefocusing was observed indirectly by measuring the heatingof a secondary target placed at the ion beam focus. Thefocus of the central filaments and of the overall beamenvelope is 370 �m away from the inner surface of the

cylinder, which is consistent with the radius of curvature ofthe cylinder, and has a spot size of�30 �m diameter. Thisgives a D=r ¼ 0:93 with D being the location of focusrelative to the target back surface and r the radius ofcurvature of the target. In projecting the shorter filaments,corresponding to lower energy protons accelerated far fromthe laser irradiation location, they too come to a crosspoint, but this time at 400 �m from the back surface andthe projections make a much larger spot size of 100 �m,which is consistent with previous data showing that lowerenergy protons have a larger divergence [9,10]. We canestimate the proton current density at focus. For this, wetake our laser parameters, a spread of proton energies from500 keV to 1 MeV, a proton conversion efficiency of 1% ofthe laser energy [24], and a spot area of 9� 10�6 cm2. Thedifference in time of arrival at focus is 11 ps which gives acurrent density of 1� 108 A:cm�2.The radiographs of the half cylinders shown in Figs. 2(c)

and 2(d) are for early times. The radiographs in Figs. 2(e)and 2(f) are shown using curved targets, made from a largefoil moulded onto a rod. They show the sheath field struc-ture later in time. Both the filaments and caustic featuresalso come to a crossing point near the radius of curvatureand then diverge after the focus point as is predicted in thesimulation shown in Fig. 3(c) (detailed below). Note thatthe structures appearing in Figs. 2(e) and 2(f) are notnecessarily in a one-to-one correspondence to the filamentswithin the converging ion beam since they represent mod-ulations induced on the probing proton beam passingthrough the plasma and projected far away on the film.Nevertheless, the fact that such structures appear in theprobing proton beam implies that the converging protonbeam is indeed inhomogeneous.We used CALDER and CMC codes to simulate, in 2D

geometry, laser-cylinder interaction, proton acceleration,and focusing. Here, the CALDER code is used to calculatethe laser-target interaction, electromagnetic fields, and

FIG. 3 (color online). CMC simulation results showing protonposition in the interior of the half-cylinder target at(a) t=tarrival ¼ 0:47, (b) t=tarrival ¼ 1, (c) t=tarrival ¼ 2. All timesare normalized to tarrival ¼ 5:7 ps.

FIG. 4. Simulation results from CALDER and CMC. (a),(b) Proton beam waist and focusing location as a function of proton energywhen laser intensity is 1018 W=cm2. (c),(d) Same, but using laser intensity of 8� 1018 W=cm2.


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particle positions up to 1.2 ps after the interaction; theninformation on protons velocity and direction is used inCMC to trace particle trajectories for longer times than what

can reasonably be done in standard PIC codes, until andafter the ion beam reaches its focus.

In the simulation, the half cylinder has a radius of curva-ture of 80 �m (5 times smaller than the experimentaltarget) and the laser intensity is 1018 W=cm2, acceleratingprotons to a maximum energy of several MeVs, as we seeexperimentally. The convergence time is tarrival ¼ 5:7 ps,i.e., 5 times smaller than the experimental tarrival, which isconsistent with the experimental results of a reduced scaletarget. The evolution of the proton beam in the simulation isconsistent with the measured data, such that early in time,the protons, accelerated off the back surface of the target,also exhibit a convex shape in the central region [seeFig. 2(b)] and later on transformed into a focused beam[see Fig. 3(a) compared to 3(b)]. Once protons travel be-yond the focus point, they tend to diverge again as shown inFig. 3(c). Furthermore, we found that the focus is chromaticsuch that the higher energy protons focus farther than thelower energy protons. Hence, the location of the protonfocus changes in time and extends over 110 �m as shownin Fig. 4(b). The highest energy protons originate only nearthe laser interaction region and converge at a distance110 �m farther than the geometrical focus, giving a ratioD=r ¼ 2:4, which is consistent with previous findings [25].However, the bulk of the protons are lower in energy(� 1 MeV) and they originate from the entire surface ofthe sheath and converge at its geometrical center, giving aratio D=r ¼ 1, which is consistent with the behavior of theshort filaments in the experimental images.

Finally, we performed simulations with higher laserintensity in order to produce protons which have higherenergy than in the experiments discussed in this Letter, butcloser to fast ignition requirements [1]. The proton beamcharacteristics for laser intensity of 8� 1018 W=cm2 areshown in Figs. 4(c) and 4(d). The higher intensity increasedthe proton spectrum up to 25 MeV, reduced the beam waistat the focus location for lower energy protons, and reducedthe spread of distances that the protons focus to as afunction of energy, as is beneficial for fast ignition. Italso suggests that with even higher laser intensities, focus-ing of the proton beam will improve even more.

Beyond determining the dynamics of the focusing, wealso tested the effect of unbalanced irradiation onto thehalf-cylinder target. Indeed, in future large-scale ICF fa-cilities (HiPER [26], NIF-ARC [27]), short pulse beamswill use several ‘‘beamlets’’ to construct the overall laserbeam that will impinge onto the target. In view of PFIapplications, where these beamlets will irradiate a hemi-spherical shell to produce the igniting proton beam [28],there is a clear interest in testing how ion beam focusabilitycan be affected by an unbalanced distribution of intensityon the shell.

Here we tested this by taking one shot where the shortpulse laser B1 was aimed slightly beneath the axis of thehalf cylinder. In Figs. 5(a) and 5(b), proton radiographs attwo different times for the same shot are shown. It isobvious that off-axis irradiation prevents formation of auniform sheath field, with a larger field observed at theedge of the cylinder closest to where the laser impacted.We simulated this scenario using a half cylinder with a

radius of 42 �m (10 times smaller than the experimentaltarget) and thickness of 5 �m using the code PICLS. Thesimulation box was 92� 92 �m2, the laser intensity of3� 1018 W=cm2 with a pulse duration of 175 fs andFWHM of 6 �m. Figures 5(c) and 5(d) show the spatialposition of the hot electrons with energy of 100 to 500 keVat different times (normalized to tarrival ¼ 1:5 ps). As ex-pected, the edge closest to where the laser hit the target hasa higher concentration of hot electrons than the ends of thetarget. This asymmetry is maintained even later in time asthe sheath expands into vacuum due to the fact thatelectrons take more time to transit to the far distant edge

FIG. 5 (color online). The B1 short pulse laser was aimed off-center on the half cylinder. Deflectograms of the sheath field att=tarrival ¼ 0:08 (a) and 0.27 (b). PICLS simulation results plottinghot electron positions are shown in (c) and (d). Simulated protonpositions are shown in (e) and (f) that also show the location ofthe focus.


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and to come back to their initial location than they dorelative to the closer edge. The influence of such transverseelectron refluxing dynamics [29] leads to an uneven devel-opment of the sheath field. However, when looking at theaccelerated protons as shown in Figs. 5(e) and 5(f), this isnot detrimental to proton beam focusing, but only changesthe directionality of the focused beam itself. It is clear fromthe contours in the proton beam that they do still convergeto a point. In more general terms, balancing of the laserbeamlets that would compose the single laser beam ontarget used for PFI would thus not be important in termsof the ability to focus the ion beam.

In conclusion, we diagnosed converging filaments in thesheath field at the back of a curved, laser-irradiated solidfoil. The coupling of experimental data and simulationsuggests that protons with intermediate energies, whichcarry most of the beam energy, consistently focus closeto the center of the cylinder, even for off-axis laser impacton the half cylinder. Filamentation in the plasma, however,implies that the proton beam transverse size at focus willbe enlarged since filamentation is a manifestation of anemittance degraded beam [30]. All this, resulting here inthe observed beam size of 30 �m, is detrimental to theproton fast ignition scheme which would require10–20 �m beam to minimize the required igniter energy[1]. However, simulations shown in Figs. 4(c) and 4(d)suggest that focusing could improve for conditions closerto fast ignition than tested here. The next step will be to testthis in future experiments.

We acknowledge the support of the LULI technicalteams. This work was supported by DAAD, BritishCouncil/Alliance, Grant No. E1127 from Région Ile-de-France, the ’’ULIMAC’’ junior chair program ofRTRATriangle de la Physique, ANR-06-BLAN-0392from ANR-France, EPSRC, Grants No. EP/C003586/1and No. EP/E035728/1 (LIBRA consortium), the EU pro-gram HPRI-CT-1999-0052, and TR18 and GK1203 fund-ing. E. L. acknowledges HPC resources at CINES providedby GENCI under Grant No. 2011-056304, and access to theCURIE supercomputer at CEA/TGCC provided byPRACE. E. d’H. acknowledges EURATOM within the’’Keep-in-Touch’’ activities and was granted access to theHPC resources of CINES under the allocation 2011-

056129 made by GENCI (Grand Equipement National deCalcul Intensif).

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