aa r X i v : . [ phy s i c s . p l a s m - ph ] J un High-quality proton bunch from laser interaction with a gas-filledcone target
H.Y.Wang,
1, 2
F.L.Zheng, Y.R.Lu, Z.Y.Guo, X.T.He, J.E.Chen, and X. Q. Yan
1, 2, ∗ State Key Laboratory of Nuclear Physics and Technology,Peking University, Beijing 100871, China Key Lab of High Energy Density Physics Simulation,CAPT, Peking University, Beijing 100871, China (Dated: October 15, 2018)
Abstract
Generation of high-energy proton bunch from interaction of an intense short circularly polar-ized(CP) laser pulse with a gas-filled cone target(GCT) is investigated using two-dimensionalparticle-in-cell simulation. The GCT target consists of a hollow cone filled with near-critical gas-plasma and a thin foil attached to the tip of the cone. It is observed that as the laser pulsepropagates in the gas-plasma, the nonlinear focusing will result in an enhancement of the laserpulse intensity. It is shown that a large number of energetic electrons are generated from thegas-plasma and accelerated by the self-focused laser pulse. The energetic electrons then transportsthrough the foil, forming a backside sheath field which is stronger than that produced by a simpleplanar target. A quasi-monoenergetic proton beam with maximum energy of 181 MeV is producedfrom this GCT target irradiated by a CP laser pulse at an intensity of 2 . × W/cm , which isnearly three times higher compared to simple planar target(67MeV). PACS numbers: 52.38.Kd, 41.75.Jv, 52.35.Mw, 52.59.-f ∗ [email protected] . INTRODUCTION With the rapid development of the chirped pulse amplification technique, generation ofenergetic ion beam by interactions of an ultra intense laser pulse with a solid target hasbecome realizable. Such energetic ions can be promising for many scientific or societalapplications, such as proton radiography[1], fast ignition for inertial confined fusion[2–4], orhadron-therapy[5]. For most of these applications, ion beams with high energy, low energyspread and high collimation are required.Depending on the target paraments and laser intensity, ions can be accelerated by severaldifferent mechanisms, such as shock acceleration[6, 7],light-pressure acceleration[8, 10–12],Coulomb explosion[13], target-normal sheath acceleration (TNSA)[14–16], etc., as well astheir combinations. In TNSA, the energetic electrons produced at the front of a target bythe laser ponderomotive force propagate through the target into the backside vacuum cangenerate a sheath electrostatic field. The sheath field, of order 10 V/m, can accelerate theions on the target back surface to high energies. However, the proton beams obtained in thisway are typically characterized by low particle density, large divergence, and almost 100%energy spread. An improved TNSA scheme, using a microstructured double-layer (DL)target, can decrease the energy spread. The possibility to generate 1.3 MeV proton beamswith energy dispersion ∼
25% and 3 MeV carbon beams with energy dispersion ∼
17% usinga microstructured DL target has already been demonstrated experimentally by Schwoereret al.[17] and Hegelich et al.[18], respectively.A tiny hollow metal cone was first introduced in fast ignition experiments to shield theigniting laser pulse from the underdense region of the precompressed fuel plasma[19], anda remarkable increase in the thermal fusion-neutron yield was observed. Since then thecone target was intensively examined both in experiments and simulations[20–32]. PICsimulations showed that a cone target could nonlinearly guide and focus a laser beam, andimprove the efficiency of the coupling and transport of the energy into dense plasma[33, 34].Accelerating proton beams using a cone target with open tip was also studied by Cao etal.[35], and energetic ion bunches of high density were observed. In this paper, we report thatquasi-monoenergetic proton beam with peak energy of 130MeV and maximum energy of 181MeV can be generated from a gas-filled cone target irradiated by a CP Gaussian laser pulseat an intensity of 2 . × W/cm . The gas-filled cone target, as shown in Fig.1, consists2 IG. 1: (color online).Schematic view of the interaction of a laser pulse with a GCT target. Theleft trapezoid represents the laser pulse (red), the trapezoid irradiated by the laser pulse representsthe gas-plasma (blue), the two parallelograms besides the gas-plasma represent the cone (orange),the rectangle on the tip of the cone represents the foil (dark). of a hollow cone filled with near-critical heavy-ion gas-plasma and a thin foil attached tothe tip of the cone. Our results indicate that, comparing with that from a simple protontarget, energetic protons with smaller energy spread and higher energy can be obtained.This result can be attributed to the much higher electron density and temperature behindthe foil and the small transverse size of the foil. The energetic electrons are generated fromthe gas-plasma and accelerated by the enhanced laser pulse, which undergoes self-focusingin gas-plasma and is even focused by the tip of the cone. These energetic electrons caneasily propagate through the thin foil to form a stronger sheath field behind the foil (thanthat behind a planar target). Since the foil has a small transverse size, the protons inthe foil are accelerated in the homogenous sheath field, so that the protons are acceleratedlongitudinally forward with smaller energy spread. In contrary to TNSA acceleration, hereenergetic electrons originate mainly from the gas rather than the solid target.3
I. SIMULATION PARAMETERS
We carried out simulation using a fully relativistic particle-in-cell code (KLAP2D) [8, 9].Insimulations, the simulation box is 80 λ × λ , where λ = 1 µm is the laser wavelength, andcontains 3200 ×
800 cells. A CP laser pulse with a peak laser intensity of I L = 2 . × W/cm is normally incident from the left side, The pulse has a Gaussian radial profilewith 2 σ = 10 λ full width at half maximum and a trapezoidal shape longitudinally with40 T flat top and 1 T ramps on both sides, where T is the laser period. The correspondingpeak dimensionless laser amplitude a = eE/ ( m e ωc ) is 9.8, where E, ω , c, m e , and e arethe laser electric field, frequency, speed of light in the vacuum, electron mass, and charge,respectively. The GCT target, as shown in Fig.1, consists of electrons, protons, and heavycarbon ions. The initial temperature of electrons, protons, and carbon ions is 10 eV. Thecone has a width of 1 µm , and is located in 10 < z [ µm ] <
45 with the diameters of the leftand right cone openings of 16 µm and 2 µm , respectively. For simplicity, the cone consists ofcarbon plasma with an electron density n e = 10 n c , where n c = πm e c / ( eλ ) is the criticaldensity. The carbon gas-plasma is full in the cone with density n e = 0 . n c . The foil with2 µm wide and 0 . µm thick is placed at z = 45 µm . It consists of a proton-carbon mixedplasma with an electron density n e = 40 n c , and the ratio of C:H=1:1. III. SIMULATION RESULTS
A laser beam propagating in underdense plasma with a frequency ω p smaller than thelaser frequency ω undergoes relativistic self-focusing[36–40] as soon as its total power Pexceeds the critical value P cr ≈ ω/ω p ) GW ; (1)The self-focusing is due to the relativistic mass increase of plasma electrons and theponderomotive expulsion of electrons from the pulse region. Both effects lead to a localdecrease of plasma frequency and an increase in refractive index. The strong non-linearself-focusing of the laser pulse propagating in the near-critical gas-plasma at t = 56 T isshown in Fig.2(a). For clarity, only a part of the simulation box is shown. The spot size ofthe laser is focused to be smallest at z = 35 µm , and the transverse electric field is enhancedto 17 there, which is 1.7 times higher than the initial laser electric field. The pulse retains4 IG. 2: (color online). Left: Transverse electric field (in units of m e cω/e ) at (a) t = 56 T , (c) t = 64 T . Right: (b) electron density (in units of critical density n c ), and (d) the longitudinalelectron current J ze (in units of en c c ) at t = 44 T . its Gaussian radial profile, however, its spot size varies with the distance of propagation ina periodic manner. The smallest spot size at z = 35 µm is about 3 µm , while it varies toabout 4 µm at z = 40 µm . This result is due to dynamic balance between diffraction andnon-linear self-focusing, which is also in good agreement with the analysis of the paraxial rayapproximation[41]. When the laser propagates to the tip of the cone, it is even focused orsqueezed by the tip of the cone for the small radius there, as is shown in Fig.2(b). The spotsize is focused to about 1 µm at the tip of the cone( z = 45 µm ), with the transverse electricfield as high as 20 there. The electrons that are initially at the front of the pulse are moreefficiently accelerated as the pulse undergoes intensity enhancement due to self-focusing.Strong flows of relativistic electrons, axially comoving with the laser pulse, are observed5
50 100 150 20000.511.522.53 x 10 energy (MeV) A r b . U n i t (a) Planar targetGCT target 0 20 40 60 80 100 120020406080100120140160180200 t(T) m ax i m u m p r o t on e n e r g y ( M e V ) (b) Planar targetGCT target
FIG. 3: (color online).(a) the proton energy spectrum of the protons behind the targets for differentcases at t=120T.and (b) Evolution of the maximum proton energy for different cases. in the simulation, as shown in Fig.2(b)and Fig.2(d). The maximum electron density nearthe axis is as high as 17 n c , and the longitudinal electron current J ze = − en e v ze is about − en c c (negative J ze due to negative electron charge). These energetic electrons thentransport through the thin foil and form a strong backside sheath field there.Fig.3(a) shows the energy spectrum of the proton bunches behind the targets in the twocases at t = 120 T . For the case shown, the maximum energy for the GCT target is about181 MeV, which is nearly three times higher than that of the planar target(65MeV)underthe same conditions. The energy conversion efficiencies from laser to protons are 2 .
5% and0 .
7% for GCT and planar targets at t = 120 T , respectively. For the GCT target, dueto the small transverse size of the foil where the sheath field is homogenous, the energyspectrum of the proton bunch has a quasi-monoenergetic peak with energy dispersion ofabout 36%. In contrast, the energy spectrum from the planar target is much broadened dueto multidimensional effects such as hole boring and other instabilities. The evolution of themaximum proton energy is shown in Fig.3(b). For the planar target, as the laser impinges6
20 40 60 80 100 12005101520 t(T) E z ( m e c ω / e ) (a) −1 energy (MeV) A r b . U n i t (b) Planar targetGCT targetPlanar targetGCT target
FIG. 4: (color online).(a)Evolution of the electrostatic fields at the place of the proton layer for thetwo cases of planar and GCT target and (b)the electron energy spectrum of the protons behindthe targets at t=50T for planar target and t=80T for GCT target. on the target at t = 10 T (the planar target is initially located at z = 10 µm ), the maximumproton energy increases earlier than the GCT target(for which the laser impinges on the foilat t = 60 T ). However, as the electrostatic field at the place of the proton layer is muchweaker for the planar target(see in Fig.4(a)), the increase of proton energy is much slowerthan the GCT target. For the GCT target, the maximum proton energy increases rapidlyfrom 3.3MeV to 120MeV in only 20T(from t = 60 T to t = 80 T ), which is attributed to thestrong electrostatic field during that time. At later time, the maximum proton energies inboth cases remain almost constant.Evolutions of the electrostatic fields at the place of the proton layer for the planar andGCT targets are shown in Fig.4(a), which explains the energy enhancement of GCT targetin Fig.3(b). The electrostatic fields straight up quickly at t = 60 T for the GCT target whenthe laser impinges on the target, because the energetic electrons generated from the gas-plasma reach the back side of the foil at t = 60 T and establish a strong sheath field there(see7n Fig.5(a)). The maximum electrostatic field is about 20 for GCT target at t = 60 T , whichis about 3.3 times higher than the planar target(6 at t = 44 T ). Since the energetic electronsexpand away quickly, the electric fields decrease quickly after reaching the maximum forboth cases. The electron energy spectrums behind the targets at t=50T for planar targetand t=80T for GCT target are shown in Fig.4(b), at both times when the maximum energyof the electrons behind the targets is highest . We can see that the electron temperatureand density are higher for the GCT target , which will result in a higher longitudinal fieldand eventually higher proton energy, as shown in Fig.4(a) and Fig.3(a). t(T) A r b . U n i t (b) t(T) A r b . U n i t (a) Planar targetGCT target ConeGasFoil
FIG. 5: (color online).(a) Time evolution of the number of electrons behind the planar and GCTtargets. (b)Time evolution of the number of electrons behind the planar originated from differentplaces.
Since the TNSA mechanism depends strongly on the charge seperation field establishedby the energetic electrons, it is of interest to investigate the electron number behind thetarget. Fig.5(a) shows the time evolution of electron number behind the planar and GCTtargets. For both cases, the electron numbers initially increase after the laser irradiates onthe targets, and then flatten out. For GCT target, the electron number is nearly 5 times8igher than the planar target at t = 120 T . From Fig.5(b) we can see the energetic electronsare almost generated from the gas-plasma (97% of the total number), while only a smallnumber of the electrons are from the cone (3% of the total number). This result indicatesthat with the GCT target the efficiency of proton acceleration is determined by the electronsgenerated from the gas, which is quite different from the planar target(the electrons are fromthe target itself). density(n c ) m ax i m u m p r o t on e n e r g y ( M e V ) (a) thickness( µ m) m ax i m u m p r o t on e n e r g y ( M e V ) (b) FIG. 6: (color online).(a) Maximum proton energy for different gas-plasma density. (b) Maximumproton energy for different foil thickness.
The effects of the gas-plasma density and the foil thickness of the GCT target are shown inFig.6. It is found that the maximum proton energy remains almost the same(near 180MeV)while the gas-plasma density is between 0 . n c and 0 . n c , and the foil thickness is between0 . µm and 0 . µm . These simulation results demonstrate that our acceleration scheme isrobust. On the other hand, for the gas-plasma density, over-high gas-plasma density willresult in much depletion of laser pulse, while over-low gas-plasma density will leads fewerenegertic electrons behind the foil, both will result in a decrease of the maximum protonenergy. For the foil thickness, thin foils proved to be more efficient for ion acceleration inTNSA by hot-Electron recirculation[42], but over-thin foil will result in a quick expandingof the electrons, which will also result in a lower proton energy.9e have also stimulated the interaction of a Linear polarized(LP) laser pulse with aGCT target at the same intensity, while the other parameters are the same as in Fig.1. Oursimulations results verify that similar phenomenon can also be observed with the LP laserpulse. A quasi-monoenergetic proton beam with peak energy of 139 MeV and maximumenergy of 185 MeV can be generated. This indicates that our acceleration scheme can bealso efficient for the LP laser pulse. IV. CONCLUSION
In conclusion, proton acceleration from a GCT target is proposed to enhance the ionenergy. A quasi-monoenergetic proton bunch with peak energy of 130MeV and maximumenergy of 181MeV is achieved by using the GCT target at laser intensity of 2 . × W/cm .It is nearly three times higher than that from the planar target. This result is attributedto a stronger electrostatic field behind the foil, which is formed by the energetic electronsgenerated and accelerated by the enhanced laser pulse in the gas-plasma. The effects of thegas-plasma density and the foil thickness have been investigated. The results demonstratethat our acceleration scheme is robust. Such GCT target may be difficult to make at present,however, with the rapid advance in nanofabrication technology such a small conical channelfilled with gas-plasma should be realizable[43]. Accordingly, the GCT target can remarkablyreduce the cost of a laser driven ion accelerator in the applications such as cancer therapy. Acknowledgments
This work was supported by National Nature Science Foundation of China (Grant Nos.10935002,10835003,11025523) and National Basic Research Program of China (Grant No.2011CB808104). XQY would like to thank the support from the Alexander von HumboldtFoundation. [1] M. Borghesi, D. H. Campbell, A. Schiavi, M. G. Haines, O. Willi, A. J. MacKinnon, P. Patel,L. A. Gizzi, M. Galimberti, R. J. Clarke, F. Pegoraro, H. Ruhl, and S. Bulanov , Phys. Plasmas , 2214 (2002).
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