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Intense laser-driven energetic proton beams from solid density targets C. T. Zhou1,2,* and X. T. He1,2 1 Center for Applied Physics and Technology, Peking University, Beijing 100871, China Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China *Corresponding author:
[email protected]
2
Received April 26, 2007; revised June 25, 2007; accepted July 9, 2007; posted July 12, 2007 (Doc. ID 82233); published August 9, 2007 The effects of target density on proton acceleration driven by an intense sub-ps laser pulse are investigated using two-dimensional hybrid particle-in-cell simulations. Results show that at higher density the targetnormal-sheath acceleration (TNSA) is more effective than shock acceleration for protons from a plastic target. Furthermore a lower-density target is favorable to higher energy of the TNSA protons. Moreover, the longitudinal electric fields at the target surfaces may reveal typical inhomogeneous structures for a long acceleration time. The conversion efficiency of laser energy into particle (electron, proton, and C+ ion) energy is found to increase with decreasing target density. © 2007 Optical Society of America OCIS codes: 350.5400, 350.4990, 320.2250.
Recent advances in laser technology have pushed the frontier of maximum intensity reached about 1022 W / cm2 [1]. This has stimulated considerable progress in the development of intense laser interactions with matter. The rapidly growing physical interest includes laser–plasma interactions [2], inertial confinement fusion [3], astrophysical plasmas [4], laser nuclear physics [5], and fast ignition physics [6], etc. In recent years, one of the most important results obtained in laser–plasma interaction experiments is the observation of very energetic beams of electrons and ions (including protons) produced from short pulse laser-irradiated solid foils [7,8]. In experiments, proton generation and acceleration from contaminant water vapor and hydrocarbons at both the front and rear surfaces of thin solid targets [9], or foils, have often been observed by intense laser pulses. Plastic targets have often been used because of their considerably higher hydrogen content compared to that (due to contamination) of metal targets. Since the protons are accelerated by the electron sheath on the target surface, their spatial and angular characteristics are determined by the electron sheath spatial distribution. Therefore the emission characteristic of proton beams will depend on the target material, the target surface roughness, the target shape, and the laser focal distribution on the target. Although acceleration of protons in low-density thin foils has been intensively simulated [10–13] using short-pulse ultrahigh-intensity lasers, it is still not clear if the acceleration processes and results would remain applicable for high-density foils driven by a longer-duration laser pulse. In this Letter, we consider the dependence of proton acceleration on the plastic targets at sub-ps pulse duration. When the plasma electron density is only a few times of the relativistic critical density particle-incell (PIC) electromagnetic codes can provide a fundamental, first principles description of laser–plasma interactions for moderately dense plasma. In the absorption and hole-boring process, strong nonlinearities and kinetic effects are essential features. For 0146-9592/07/162444-3/$15.00
solid-density plasmas, the numerical results based on hybrid-PIC simulations [14] for the generation, transport, and acceleration of electrons and protons are also in very good agreement with experimental evidence. We start with a brief illustration of our numerical model and physical parameters. In order to enhance the density effect, we will consider a plastic target foil [Fig. 1(a)], represented by a fully dissociated C+H2+ plasma at 5 eV. The plasma thus contains electrons, protons, and carbon ions. The plasma density considered is = 3 g / cm3, corresponding to the electron, proton, and carbon-ion number densities 关n0,e , n0,H+ , n0,C+兴 = 关15.12, 2.16, 10.8兴 ⫻ 1022 cm−3, re2 spectively. Traditional PIC techniques are impractical for studying such overdense plasmas. The twodimensional 共x , z兲 simulation box is 50 m ⫻ 50 m. The thin plasma slab, initially uniform in the transverse direction, is located in 19⬍ z 关m兴 ⬍ 26 and
Fig. 1. (Color online) (a) Simulation setup of CH target irradiated by intense laser pulses. Inset (b) shows the electron-density profile investigated, and (c) gives trajectories of several typical electrons (from t = 50 to 500 fs) initially at 共x , z兲 = 共0 , 19兲 m. © 2007 Optical Society of America
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bounded by two vacuum regions. On both sides of the slab there is a 1 m linear rise to the uniform density 共n0兲 region at the center. The initial densities at z = 19 and 26 m are taken to be n0 / 100, as shown in Fig. 1(b). There are 1000 uniform grids in the laserpolarization direction 共x兲. The grid in the laserpropagation direction 共z兲 is variable according to need. The grid step ␦z in the two vacuum regions is 0.05 m; enough to resolve the laser wavelength. To include the details of the laser–plasma interaction at the relativistic critical density, we use much smaller grid steps in the plasma slab. In our simulations, there are 16 particles of each species (C+, H+, PIC, and fluid electrons) per cell. The temporal resolution is ␦t = 0.01 fs. Outgoing-particle boundary conditions are used. The electromagnetic fields are periodic in the transverse direction. The incoming laser is launched from the left boundary of the simulation box with its electric field in the simulation plane, as shown in Fig. 1(a). The Gaussian p-polarized laser pulse has a peak intensity I0 ⬇ 3.3⫻ 1020 W / cm2 and wavelength 0 = 1 m, with a rise time of 63 fs, corresponding to the time for the light to cross the 20 m of vacuum to the front surface of the plasma foil. It has a transverse spot size (Gaussian radial profile) on the target of x = 6 m full width at halfmaximum. At the very beginning of the interaction, electrons driven by the laser pulse out of the target front (laser) side by the ponderomotive force [15,16] set up electrostatic fields that accelerate protons backward against the laser direction. On the other hand, the accelerated front-side electrons traverse the plasma slab and exit into the rear vacuum region. Huge (several times 1010 V / cm) space-charge electrostatic fields at the front and back sides of the slab are generated, as shown in Fig. 2(a). These fields create across the plasma slab an electrostatic potential well, as given in Fig. 2(b). Thus, before their eventual exit into the front or back vacuum regions, the laserdriven electrons can experience multiple reflections over hundreds of femtoseconds time, since their mean free path is much larger than the slab thickness. Furthermore, in conjunction with the large selfgenerated magnetic field, the energized electrons spread along and heat the slab surfaces. These phenomena are illustrated in Fig. 1(c) by the several trajectories of electrons initially at rest at 共x , z兲 = 共0,19兲 m. It is noted from Fig. 2(a) that the longitudinal averaged (over 0 艋 兩x 兩 艋 2x) electric field 具Ez共z , t兲典 reveals an inhomogeneous structure at both surfaces of the target. Such oscillations could also be seen from the hydrodynamic results [17,18]. To further analyze the effect of target density, we also consider = 1 / 3 g / cm3. Figure 3 shows the distributions of the proton energy at t = 400 fs. The effects of the acceleration mechanisms operating at the front and back target surfaces can be observed. By comparing Fig. 3(d) with Fig. 3(a), it is found that at lower density shock acceleration and TNSA are more effective than at higher density. Moreover the efficiency of both mechanisms decreases with increasing plasma
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Fig. 2. (Color online) (a) Spatial-averaged longitudinal electric field Ez共z , t兲 (in V/cm). The dashed lines indicate the initial target surfaces in the simulation box, and the solid lines indicate the initial surfaces of the 5-m-thick homogeneous section of the plasma at density n0. Inset (b) gives a comparison of Ez共z , t = 200 fs兲 (in units of the transverse E0 field of the laser) for densities = 3 and 1 / 3 g / cm3.
density. For our low- and high-density targets, at the backside of the target the surface protons experiencing TNSA can reach ⑀p ⬎ 25 MeV and ⑀p ⬃ 6 MeV, respectively. The accelerated proton energy is consistent with that of the maximum value of the electric field at the rear surface, as shown in Fig. 2(b), in =1/3 =3 兩 / 兩Emax 兩 ⬃ 4. Figure 3 also shows the anwhich 兩Emax gular distribution of proton energy. From Figs. 3(b) and 3(e), we see that the forward propagating Bragg peak energy proton beam has a rather small emission cone. The bright center spots 共⬍5 ° 兲 are well collimated. However the low energy protons accelerated from shock-induced density compression have a larger emission cone. In the case of = 3 g / cm3, the angle of the emission cone is measured by 兩共⑀p ⬍ 2兲兩 ⬎ 40°. However in the case of = 1 / 3 g / cm3, we have
Fig. 3. (Color online) Proton energy and angular distribution at t = 400 fs. (a)–(c) and (d)–(f) correspond to = 3 and 1 / 3 g / cm3, respectively. (a) and (d) give the proton energy ⑀p (MeV), (b),(e), and (c),(f) represent the forward [ → (deg) for vz ⬎ 0] and backward 共 ←兲 propagating proton angular distribution, respectively.
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兩共5 ⬍ ⑀p ⬍ 20兲兩 ⬍ 22°. Comparing Fig. 3(e) with Fig. 3(d), we note that some of these energetic protons 共⑀p ⬍ 20兲 are driven by the shock-accelerated process. Furthermore, we observe that the backward propagating proton beam at high density has a sharp Bragg peak, but at low density a flat beam with ⬃ ± 20° is observed. Obviously, this behavior is associated with the ponderomotive potential of the laser [2]. At lower density plasmas, electrons on the target front side are more easily expelled from highintensity regions of the laser pulse, setting up a wider electric field profile that will accelerate ions in the backward direction. An important question to be addressed for energetic proton beams driven by sub-ps ultraintense laser pulses is the conversion efficiency of laser energy into particle energy. We found that the conversion process is quite dependent on target density. For = 1 / 3 g / cm3, about 26% laser is converted into energetic particle population, but only 4.6% conversion efficiency is observed for = 3 g / cm3. Obviously, both conversion efficiencies are much lower than the known scaling law [7] of energetic electrons. Moreover, our simulations show that the corresponding rates of electron energy transfer to the high-energy 共⬎3 MeV兲 proton and C+ ion beams for = 1 / 3 g / cm3 are about 9.6% and 4.7%, respectively, but only 5.7% and 1% rates are observed for = 3 g / cm3. In conclusion, we have used a two-dimensional hybrid PIC code to investigate the influence of the effects of target density on proton acceleration driven by an intense sub-ps laser pulse. By comparing the longitudinal electric field structures at the target surfaces, energetic proton angular distributions and energy conversion efficiencies for two density cases, we show that at higher density the TNSA is more effective than shock acceleration for protons, but at lower density both acceleration processes are comparable. Furthermore a lower-density target is favorable to higher energy of the TNSA protons. These results are clearly essential in realizing plasma proton accelerators. Finally it is mentioned that the longitudinal field oscillation could also be relevant to the laser polarization. Whether an ion bunch [13] can be generated from the rear surface due to the oscillation behavior needs further investigation. This work is supported by the National Natural Science Foundation of China, Grant Nos. 10575013, 10576007, and 10335020, and the National HighTech ICF Committee in China and partially by the National Basic Research Project “HEDP in China.”
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