1. INTRODUCTION
The application of laser-accelerated ions in high energy-density physics and for fast ignition (FI) of fusion targets require collimated ion beams of relatively low ion energies (≤10 MeV) but of very high power P i and intensity I i (for instance, FI requires MeV proton beams of Ii~1020 W/cm2 and P i~1 PW (Temporal et al., Reference Temporal, Honrubia and Atzeni2002; Badziak et al., Reference Badziak, Jabłoński and Wołowski2007)). Potentially, the ion beams of such extreme parameters can be produced by currently known laser methods of ion acceleration such as target normal sheath acceleration (TNSA) (Wilks et al., Reference Wilks, Langdon, Cowan, Roth, Singh, Hatchett, Key, Pennington, MacKinnon and Snavely2001; Borghesi et al., Reference Borghesi, Fuchs, Bulanov, Mackinnon, Patel and Roth2006; Badziak Reference Badziak2007; Yang et al., Reference Yang, Ma, Shao, Xu, Yu, Gu, Yu, Yin, Tian and Kawata2010) or skin-layer ponderomotive acceleration (SLPA) (Badziak et al., Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2004, Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2005, Reference Badziak, Jabłoński and Głowacz2006, Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008; Badziak Reference Badziak2007; Hora et al., Reference Hora, Badziak, Boody, Hopfel, Jungwirth, Kralikova, Krasa, Laska, Parys, Perina, Pfejfer and Rohlena2002; Sadighi-Bonabi et al., Reference Sadighi-Bonabi, Hora, Riazi, Yazdani and Sadighi2010) (also referred to as radiation pressure acceleration (RPA) (Liseykina & Macchi, Reference Liseykina and Macchi2007; Robinson et al., Reference Robinson, Zepf, Kar, Evans and Bellei2008; Liseykina et al., Reference Liseykina, Borghesi, Macchi and Tuveri2008). In TNSA, ions are accelerated at the rear surface of the foil target by a virtual cathode (Debye sheath) created by hot electrons produced by a laser pulse at the target front and penetrating through the target. Though at relativistic laser intensities IL (i.e., at ILλ2 > 1018 Wcm−2µm2, where λ is the laser wavelength) TNSA can produce collimated ion beams of fairly high ion energies (of tens of MeV for protons (Borghesi et al., Reference Borghesi, Fuchs, Bulanov, Mackinnon, Patel and Roth2006; Badziak, Reference Badziak2007; Snavely et al., Reference Snavely, Key, Hatchett, Cowan, Roth, Phillips, Stoyer, Henry, Sangster, Singh, Wilks, MacKinnon, Offenberger, Pennington, Yasuike, Langdon, Lasinski, Johnson, Perry and Campbell2000; Robson et al., Reference Robson, Simpson, Clarke, Ledingham, Lindau, Lundh, McCanny, Mora, Neely, Wahlstrom, Zepf and McKenna2007)) or of several MeV/amu for heavier ions (Badziak, Reference Badziak2007; Hegelich et al., Reference Hegelich, Albright, Audebert, Blazevic, Brambrink, Cobble, Cowan, Fuchs, Gauthier, Gautier, Geissel, Habs, Johnson, Karsch, Kemp, Letzring, Roth, Schramm, Schroeiber, Witte and Fernandez2005; McKenna et al., Reference McKenna, Lindau, Lundh, Carroll, Clarke, Ledingham, McCanny, Nelly, Robinson, Robson, Simpson, Wahistrom and Zepf2007), the ion density of TNSA beams is relatively low (≤1019cm−3 at the source) and, as a result, the ion beam intensity Ii = niυiE i or current density ji = zeniυi are usually moderate (z is ion charge state, e is the elementary charge, ni, υi, Ei are ion density, velocity and energy, respectively). In turn, SLPA employs the ponderomotive pressure induced by a laser pulse near the critical plasmas surface, which drives forward a dense plasma (ion) bunch of density ni higher than the plasma critical density nc. As for relativistic laser intensities usually ni ≥1022 cm−3, the intensities and current densities of SLPA-driven ion beams can be much higher than in the case of TNSA beams, in spite of the fact that SLPA-driven ions are usually a few times slower than those generated by TNSA (Badziak et al., Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2004, Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2005, Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008; Badziak, Reference Badziak2007). Moreover, SLPA-driven ions can be extracted from a fairly thick solid-density layer (of the thickness of several μm or even thicker at multi-ps driving pulses), thus a large number of ions can be generated from the source of a small area (Ss), much smaller than in the case of TNSA (or the methods using ultrathin targets like e.g., the laser break-out after burner (Yin et al., Reference Yin, Albright, Hegelich and Fernandez2006; Fernandez et al., Reference Fernandez, Honrubia, Albright, Flippo, Gautier, Hegelich, Schmitt, Temporal and Yin2009), where the ions are efficiently extracted from the layer of only several to tens nm (Roth et al., Reference Roth, Blazevic, Geissel, Schlegel, Cowan, Allen, Gauthier, Audebert, Fuchs, Meyerter-Vehn, Hegelich, Karsch and Pukhov2002; Allen et al., Reference Allen, Patel, Mackinnon, Price, Wilks and Morse2004; Foord et al., Reference Foord, Patel, Mackinnon, Hatchett, Key, Lasinski, Town, Tabak and Wilks2007). The last feature of SLPA is especially important for application of ion beams for FI research, where a huge number of high-energy ions are required to ignite a Deuterium-Tritium fuel. For instance, (2–3) × 1016 protons of mean energy Ēp ≈ 3–5 MeV necessary for the fuel ignition (Temporal et al., Reference Temporal, Honrubia and Atzeni2002; Badziak et al., Reference Badziak, Jabłoński and Wołowski2007) can be produced by SLPA from a hydrogen-rich target of Ss ≤ 0.05 mm2, while it needs Ss at about a few mm2 when using TNSA (Badziak et al., Reference Badziak, Jabłoński and Wołowski2007). As a result, the laser power PL required for the ignition (P L ∝ I LS s) and the proton source-fuel distance d sf~S s1/2 can be significantly smaller when using SLPA-driven ion beams (the last feature benefits, in particular, in the permissibility of using non-monoenergetic proton beams for the ignition (Badziak et al., Reference Badziak, Jabłoński and Wołowski2007)). One of the questions is the laser-SLPA protons energy conversion efficiency that is still open.
At relativistic laser intensities and experimental conditions currently attainable, both TNSA and SLPA can contribute to the forward ion acceleration, and they particular contribution to this process depends on laser and target parameters. In the case of proton acceleration by an infrared (~1µm), linearly polarized laser pulse usually TNSA dominates (Allen et al., Reference Allen, Patel, Mackinnon, Price, Wilks and Morse2004; Robson et al., Reference Robson, Simpson, Clarke, Ledingham, Lindau, Lundh, McCanny, Mora, Neely, Wahlstrom, Zepf and McKenna2007; Fuchs et al., Reference Fuchs, Sentoku, d'Humières, Cowan, Cobble, Audebert, Kemp, Nikroo, Antici, Brambrink, Blazevic, Campbell, Fernández, Gauthier, Geissel, Hegelich, Karsch, Pepescu, Renard-LeGalloudec, Roth, Schreiber, Stephens and Pépin2007), and SLPA can be efficient only when some specific requirements are met (Badziak et al., Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2004; Badziak, Reference Badziak2007; Sentoku et al., Reference Sentoku, Bychenkov, Flippo, Maksimchuk, Mima, Mourou, Sheng and Umstadter2002; Lee et al., Reference Lee, Park, Cha, Lee, Lee, Yea and Jeong2008) : (1) the target is made of hydrogen-rich insulator (to minimize the return electron current enabling effective transport of hot electrons through the target); (2) the preplasma density gradient scale length near the critical surface, Ln, is small, say Ln ≤ 2λ, but still Ln > >ls, where ls is the skin depth (to ensure small Debye length near the critical surface and high value of the ponderomotive force); (3) the laser beam direction is perpendicular to the target front surface and the beam diameter on the target, dL, is sufficiently large: dL > >Ln, λL, LT, where LT is the target thickness (to ensure quasi-planar acceleration geometry enabling generation of low-divergence ion beam). The particular contribution of SLPA and TNSA to the acceleration process also depends on laser light polarization and for circular polarization the role of TNSA is less important than for the linear one (Liseykina & Macchi, Reference Liseykina and Macchi2007; Liseykina et al., Reference Liseykina, Borghesi, Macchi and Tuveri2008).
In a great majority of laser acceleration experiments or numerical simulations performed so far, fundamental-frequency (1ω) beams of Nd:glass or Ti:sapphire lasers have been used as an ion driver. This is due to the fact that the dimensionless laser field amplitude a 0 ∝ I L1/2 λ, which is the most important factor determining maximum energy of accelerated ions, is higher for a 1ω laser beam than for short-wavelength (2ω or 3ω) beams. On the other hand, using 2ω or 3ω beams enables to achieve a higher laser pulse contrast ratio and, as a result, a sufficiently small value of Ln, which, in particular, is desirable for an efficient SLPA. Moreover, the critical density is higher for the short-wavelength beams (it scales as (1 + a 02/2)1/2 λ−2 (Umstadter, Reference Umstadter2001)), which suggests that attainable ion current densities and beam intensities of SLPA-driven ions can be higher as well (at least when the values of a 0 are not very different for 1ω and 2ω (3ω) beams). These possible advantages of short-wavelength lasers as ion drives seem to be especially important for FI-related ion beam applications, where maximizing the ion beam intensity (current density) at moderate ion energies is desirable and high laser contrast is necessary to avoid the ion target destruction by the prepulse of a multi-kJ short-pulse laser. However, the above issues have not riveted enough attention and have not been investigated in detail so far.
In this paper, we compare parameters of proton beams produced at the interaction of either 1ω or 2ω laser beam of relativistic intensity with a thin hydrogen-rich target. The results of measurements as well as numerical, hydrodynamic, and particle-in-cell (PIC) simulations are presented. In particular, it is shown that the contribution of the SLPA mechanism to the ion acceleration process is higher for the 2ω driver than for the 1ω one, which results in significantly higher intensity and current density of the accelerated protons.
2. RESULTS OF PIC SIMULATIONS
For the simulations, a fully electromagnetic, relativistic one-dimensional (1D) PIC code very similar to the well known LPIC ++ code (Holkundkar & Gupta, Reference Holkundkar and Gupta2008) was used. A linearly polarized laser pulse of quasi-Gaussion pulse shape (IL ∝ exp [-t 4]) interacted with an inhomogeneous, fully ionized hydrogen plasma layer of the density profile defined by the exponential front part (the preplasma layer) of the density gradient scale length Ln and the constant part of the density ne = ni = 4 × 1022 cm−3 and the thickness LT. The simulations were performed for laser pulses of the wavelengths corresponding to the first (1ω) and second (2ω) harmonic of Nd:glass laser, of duration from 0.35 ps to 2 ps and intensities up to about 5 ×1020 W/cm2 . Depending on the initial parameters the space z of the simulations was ranged from 22.8 µm to 50.6 µm, the number of Euler cells from 8570 to 19220 and the number of macro particles from 53259 to 828138.
Figures 1 and 2 present peak values of various parameters of proton beams, generated from a 1-μm hydrogen plasma target of Ln = 1 µm or 0.25 µm, by 0.35-ps (full width at half maximum) laser pulses of different wavelengths, as a function of the ILλ2 product (this product is proportional to the square of the dimensionless laser field amplitude a 02 ≈ 0.73 × 10−18ILλ2[Wcm−2,μm] and is usually used for scaling). Excluding the laser-protons energy conversion efficiency η at low laser intensities, where η for 1ω and 2ω are comparable, the parameters of a proton beam driven by the 2ω laser beam are significantly higher than those for the 1ω beam, and the highest values of these parameters are attained for the short density gradient scale length. In particular, for ILλ2 ≥ 5 × 1019 Wcm−2μm2, the peak proton beam intensity and peak current density for protons driven by 2ω reach the values in excess 1021 W/cm2 and 1014 A/cm2, respectively. One of the reasons for such extreme values of these parameters is the high value of the plasma critical density at 2ω enabling ponderomotive acceleration of a very dense proton (plasma) bunch.
Parameters of proton beams driven by 1ω or 2ω Nd:glass laser pulses as a function of ILλ2. LT = 1μm, Ln = 1μm, τL = 0.35ps.
As for Figure 1 but Ln = 0.25 µm.
The effect of the target thickness, LT , on the parameters of proton beams driven by laser pulses of different durations and wavelengths but fixed value of the dimensionless laser amplitude (ILλ2 = 5 × 1019 Wcm−2μm2) is shown in Figure 3. For the optimum target thicknesses, the conversion efficiencies are similar for 1ω and 2ω, but the remaining parameters are considerably higher for the shorter wavelengths. Moreover, for the 1ω beam high values of the proton beam parameters are observed only for very thin (<1 µm) targets and for a narrow range of LT, while shortening of the wavelength results in a shifting the optimum LT toward much thicker targets and in a broadening the LT range with high proton beam parameters and high conversion efficiency. The optimum target thickness grows with the laser pulse duration (in general, with the laser energy fluence FL ≈ ILτL). In particular, it suggests that using 2ω multi-ps laser pulses of ILλ2~(0.5–1) × 1020 Wcm−2μm2 makes it possible to produce ultraintense proton beams with high conversion efficiency from the targets of the thickness of a few tens of μm. It is an important practical advantage of a 2ω driver from the point of view of a possible application of the accelerated proton beam in FI-related and other high-energy laser experiments, which require robust targets, resistant to damage by the laser prepulse or other (e.g., X-ray) radiations.
(Color online) Parameters of proton beams driven by laser pulses of different durations and wavelengths as a function of the target thickness. ILλ2 = 5 × 1019Wcm−2μm2, Ln = 0.25 µm.
The very high intensities and current densities of proton beams driven by the 2ω beam result particularly from the fact that in the case of a short-wavelength driver, even at a moderate value of the dimensionless laser amplitude a 0~5–10, SLPA can dominate over TNSA and, as a consequence, the proton beam can be more dense and compact in space. It is due to the fact that the temperature of laser-produced hot electrons, Th, which is the factor determining efficiency of the TNSA mechanism, increases with an increase in λ (Wilks et al., Reference Wilks, Langdon, Cowan, Roth, Singh, Hatchett, Key, Pennington, MacKinnon and Snavely2001; Borghesi et al., Reference Borghesi, Fuchs, Bulanov, Mackinnon, Patel and Roth2006) while the radiation (ponderomotive) pressure is λ-independent and proportional to IL (Denevit, Reference Denevit1992; Badziak et al., Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008). Thus, the shortening of laser wavelength at ILλ2 = const. leads to quite rapid diminishing of the TNSA efficiency while the SLPA efficiency remains fixed. As a result, when λ is sufficiently small the contribution of TNSA to the ion acceleration process can be smaller than that of SLPA.
A formation of high-intensity proton bunches driven by the 1ω and 2ω laser beams of ILλ2 = 5 × 1019Wcm−2μm2 is illustrated in Figure 4. The figure presents spatial (along the propagation direction z) distributions of the electron density (Ne), the ion density (Ni), the beam intensity (Ii), and the ion current density (ji) for two different instants (t) of the acceleration process (t = 0 corresponds to the beginning of the laser-target interaction). In the case of the 1ω driver, where the TNSA contribution to the acceleration process is significant, most of ions (and electrons) are spread in space in the late phase of acceleration and only a small part of the ions driven (indirectly) by the ponderomotive pressure forms relatively dense and intense ion spikes. In the case of the 2ω driver, a remarkable part of the target plasma is strongly compressed by the ponderomotive pressure and accelerated in the form of well localized in space, very dense and very intense plasma bunch. Although there is still a subtle, multi-shock structure visible in the bunch and part of the accelerated ions is situated outside the bunch, its intensity and current density are much higher than for the case of the long-wavelength (1ω) driver. The proton pulse duration is very small and at the distance ~20–30 µm from the target the duration is below 100 fs. Though such a short pulse is also produced in the 1ω case, however the amount of protons in the compressed bunch is much smaller here than in the 2ω case.
(Color online) Spatial distributions of the electron (Ne) and proton (Ni) density as well as the proton beam intensity (Ii) and current density (ji) at different instants t for the case of 1ω (a) and 2ω (b) driver. ILλ2 = 5 × 1019 Wcm−2μm2, τL = 1ps, Ln = 0.25 µm.
3. RESULTS OF EXPERIMENT AND A COMPARISON WITH NUMERICAL SIMULATIONS
In the experiment, performed on the LULI 100 TW Nd:glass laser facility at Ecole Polytechnique (Palaiseau, France) a 1ω or 2ω Nd:glass laser pulse of high contrast ratio (~107 for 1ω and > 108 for 2ω), of 350-fs duration and intensity up to 2 × 1019 W/cm2 irradiated a thin (0.6–1 µm) polystyrene (PS) target along the target normal. Since the preplasma density gradient scale length near the critical surface, Ln, was relatively small (Ln < 3 µm for 1ω (Fuchs et al., Reference Fuchs, Sentoku, d'Humières, Cowan, Cobble, Audebert, Kemp, Nikroo, Antici, Brambrink, Blazevic, Campbell, Fernández, Gauthier, Geissel, Hegelich, Karsch, Pepescu, Renard-LeGalloudec, Roth, Schreiber, Stephens and Pépin2007) and Ln < 1 µm for 2ω) and the laser beam diameter on the target, dL, was ≈ 15–50 µm (80% energy) and, moreover the target was made of insulator, the conditions required for efficient SLPA were quite well fulfilled, especially for larger dL and/or 2ω laser beam. The proton beam characteristics were measured using the time-of-flight method (ion charge collectors (Badziak et al., Reference Badziak, Makowski, Parys, Ryć, Wołowski, Woryna and Vankov2001)), solid state track detectors (SSTDs) and radiochromic films (RCFs). The characteristics of protons of low (Ep < 0.1 MeV) and moderate (0.1 MeV ≤ Ep < 3 MeV) energy were measured by four ion collectors (ICs) situated 80 cm from the target at the angles 1°, 4°, 8°, and 30° in respect to the target normal. High-energy protons (≥3 MeV) were recorded by SSTDs (CR 39 of PM 355 type (Szydłowski et al., 2009) with Al filters) and the stack of RCFs of H-810 type (both these detectors were strongly saturated by moderate-energy protons at the target-detector distances employed: L SSTD = 123 cm, L RCF = 2.5 cm).
Figure 5 presents angular characteristics of a proton beam generated by the 1ω or 2ω laser beam for moderate-energy protons of 0.5 MeV <Ep < 3 MeV (a) and high-energy protons of Ep ≈ 3 MeV (b, c) as measured by ICs (1) and RCFs (2, 3). In the case of moderate-energy protons driven by the 1ω beam, we observed a ring-like spatial structure of the proton beam for both lower (2 × 1018 W/cm2) and higher (2 × 1019 W/cm2) laser intensities as opposed to those driven by the 2ω beam for which the proton beam structure without any remarkable dip in the beam centre was recorded (Fig. 5a). In the case of high-energy protons, the situation was different. For the 2ω driving beam, the proton beam structure was rather flat independent on laser intensity (Fig. 5c). However, for the 1ω beam, the flat spatial structure for high-energy protons was observed only at lower laser intensities, while at higher intensities the structure had always annular shape (Fig. 5b). The observed differences in the moderate-energy and high-energy proton beams structures can be explained assuming that moderate-energy proton acceleration is dominated by SLPA and high-energy protons are driven mainly by TNSA (Pukhov, Reference Pukhov2001; Badziak et al., Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008). This issue was discussed in detail in Badziak et al. (Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008), so we only notice here that the ring-like structure of high-energy protons is likely due to the target rear surface perturbation by the prepulse-driven shock wave (Xu et al., Reference Xu, Li, Yuanet, Yu, Wang, Zhao, Wen, Wang, Jiao, He, Zhang, Wang, Huang, Gu and Zhang2006), while the structure of moderate-energy protons is determined by the action of the ponderomotive force (Fp) near the critical surface (Wilks et al., Reference Wilks, Kruer, Tabak and Langdon1992; Badziak et al., Reference Badziak, Jabłoński and Głowacz2006).
(Color online) Angular characteristics of a proton beam generated by the 1ω or 2ω laser beam for (a) moderate-energy protons of 0.5 MeV < Ep < 3 MeV and (b, c) high-energy protons of Ep ≈ 3 MeV.
The effect of the ponderomotive force on the structure essentially depends on the preplasma density gradient scale length Ln (Badziak et al., Reference Badziak, Jabłoński and Głowacz2006). For a small Ln (the 2ω case) and dL ≫ Ln, the radial component of Fp is small and, as a result, the proton beam of a low angular divergence and bell-shaped (Gaussion-like) spatial structure is generated (Badziak et al., Reference Badziak, Jabłoński and Głowacz2006). When Ln is larger (the 1ω case), the radial component of Fp is higher and the beam of a larger angular divergence and a ring-like structure can be produced (Badziak et al., Reference Badziak, Jabłoński and Głowacz2006). This feature of SLPA-driven proton generation is demonstrated in Figure 6, which presents the results of simulations, carried out with the use of two-dimensional (2D) relativistic hydro code (Badziak et al., Reference Badziak, Jabłoński and Głowacz2006), for protons driven by the 1ω or 2ω laser beam of parameters corresponding to those in the experiment. A fairly good qualitative agreement with the experimental results shown in Figure 5a can be seen.
The spatial and angular distributions of proton current densities for protons driven by the 1ω or 2ω laser beam — the results of simulations using 2D relativistic hydro code. I L1ω = I L2ω = 2 × 1018 W/cm2, d L1ω = 30 µm, L n1ω = 1 µm, d L2ω = 20 µm, L n2ω = 0.25 µm.
A comparison of the proton beam intensities Ips and current densities jps at the source and the laser-protons energy conversion efficiencies for moderate-energy (0.5–3 MeV or 1–3 MeV) protons driven by the 1ω or 2ω laser beam is presented in Figure 7. The values of Ips and jps were calculated from the IC measurements using the formula (Badziak et al., Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2004, Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008): Ips ≈ Et/τsS s, jps ≈ Qt/τsS s where Et and Qt are the total energy and the total charge of protons in the considered energy range, respectively, τs is the proton pulse duration at the source and Ss is the proton beam area at the source. Since for SLPA ions τs is approximately equal to the laser pulse duration τL and Ss is close to the laser focal spot area SL = πd L2 (Badziak et al., Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2004, Reference Badziak, Głowacz, Jabłoński, Parys, Wołowski and Hora2005, Reference Badziak, Jabłoński and Głowacz2006; Liseykina & Macchi, Reference Liseykina and Macchi2007; Habara et al., Reference Habara, Kodama, Sentoku, Izumi, Kitagawa, Tanaka, Mima and Yamanaka2003), to calculate Ips and jps we assumed τs ≈ τL, Ss ≈ SL. It can be seen that in the case when ILλ2 for the 1ω beam is equal to that for the 2ω beam, the beam intensity and current density of moderate-energy protons are several times higher and the conversion efficiency is about 20–30% higher for the 2ω beam than those for the 1ω beam, in spite of the fact that the 2ω laser beam energy was more than twice as low. Also, the number (per cm2 ) of high-energy (>3 MeV) protons is higher for 2ω in this case (Fig. 8). However, for IL1ω ≈ IL2ω, the beam intensities and current densities of the moderate-energy protons are comparable for 1ω and 2ω and the laser-protons conversion efficiency is lower for the 2ω beam. These results are in fairly good agreement with our PIC simulations, which for the case (ILλ2)1ω = (ILλ2)2ω and Ep > 0.5 MeV are presented in Figure 9. The values of the (average) beam intensity and current density where calculated here in the same way as for the experiment i.e., using the formulas: Ips ≈ Et/τLS L, jps ≈ Q t /τLS L. It can be seen that for the anticipated most probable ranges of Ln: 1–3 µm for 1ω and 0.25–1 µm for 2ω, the beam intensities and current densities for the 2ω case are several (~4–6) times higher than the ones for the 1ω case, while the conversion efficiencies are comparable for both cases. Also the absolute values of the considered parameters are in a reasonable agreement with those estimated from the measurements. The observed accordance in the results of measurements and simulations is another argument which supports our earlier conclusion (Badziak et al., Reference Badziak, Jabłoński, Parys, Rosiński, Wołowski, Szydłowski, Antici, Fuchs and Mancic2008) that, in the conditions of our experiment, most of moderate-energy protons are driven by the SLPA mechanism. This conclusion is also proved by more detailed analysis of our PIC results which clearly show that relatively small number of protons is accelerated to high (multi-MeV) energies by TNSA while a bulk of protons (of lower energies) is driven by the ponderomotive pressure and the amount of these protons is higher for the 2ω driver.
(Color online) A comparison of laser-proton conversion efficiencies (a) as well as proton beam intensities (b) and current densities (c) at the source for moderate-energy (<3 MeV) protons generated by the 1ω or 2ω Nd:glass laser beam. The results obtained from the experiment at ILλ2 ≈ 2.1 × 1018Wcm−2µm2, τL = 0.35 ps, LT = 1 µm.
(Color online) The energy distributions for high-energy protons driven by the 1ω or 2ω laser beam. Points — the results of SSTD measurements, lines — the results of approximation by the Maxwellian energy distributions with the temperature Tp. ILλ2 ≈ 2.1 × 1018Wcm−2µm2, τL = 0.35 ps, LT = 1 µm.
(Color online) The laser-protons energy conversion efficiency as well as the proton beam intensity and current density at the source for the 1ω or 2ω laser driver as a function of the preplasma density gradient scale length Ln. The results of PIC simulations obtained at ILλ2 = 2.1 × 1018Wcm−2µm2, τL =0.35 ps, LT = 1 µm.
4. CONCLUSIONS
In conclusion, both numerical simulations and measurements prove that the 2ω Nd:glass laser driver produces proton beams of significantly higher intensity, current density, and energy fluence than those achieved with the use of the 1ω driver of the same value of the ILλ2 product. Even at moderate values of ILλ2~(0.5–1) × 1020 Wcm−2µm2, the 2ω picosecond driver makes it possible to produce ultraintense, multi-MeV proton beams of intensity and current density in excess of 1021 W/cm2 and 1014A/cm2, respectively. In this case, SLPA (RPA) clearly prevails other acceleration mechanisms and highly efficient (η > 10%) generation of the ultraintense proton beams is possible from the targets several times thicker than for the 1ω case, which benefits in a higher areal proton density of the proton source and its greater robustness. In addition, a higher contrast ratio of the 2ω laser beam allows for generation of proton beams of more homogeneous spatial structure and for avoiding the target destruction by the laser prepulse. The above advantages of the 2ω driver indicate that it can be a promising laser driver of proton beams required for ICF fast ignition as well as high-current proton beams desirable for application in high energy-density physics or for isotope production. However, its significant advantages should always be considered in the context of its higher cost and, typically, up to ~30–40% lower laser energy than in the case of the 1Ω driver.
ACKNOWLEDGEMENTS
The authors acknowledge the LULI laser team as well as P. Antici and M. Rosiński for their expert support to the experiment. We also thank J. Wołowski for useful discussions. The access to the LULI 100TW laser facility has been supported by the European Commission under the LASERLAB-Europe Integrated Infrastructure Initiative (contract No. RII3-CT-2003-506350). This work was also supported in part by the HiPER project under Grant Agreement No. 211737 as well as by the Ministry of Science and Higher Education, Poland, under Grant No. N202-207-438.
