INTRODUCTION
One of the significant achievements of high-intensity laser plasma interaction is the generation of high energy ion beams, which is of potential applications in cancer therapy (Bulanov et al., Reference Bulanov, Esirkepov, Khoroshkov, Kuznetsov and Pegoraro2002), inertial confinement fusion (Roth et al., Reference Roth, Cowan, Key, Hatchett, Brown, Fountain, Johnson, Pennington, Snavely, Wilks, Yasuike, Ruhl, Pegoraro, Bulanov, Campbell, Perry and Powell2001), diagnostics of high density matter (Borghesi et al., Reference Borghesi, Campbell, Schiavi, Willi, Mackinnon, Hicks, Patel, Gizzi, Galimberti and Clarke2002; Li et al., Reference Li, Shen, Zhang, Jin and Wang2008). Over the last two decades, a number of experiments on the generation of forward multi-MeV ions for chirped pulse amplification laser lights at intensities over 1018 W/cm2 were reported and interpreted with remarkably different mechanisms (Clark et al., Reference Clark, Krushelnick, Davies, Zepf, Tatarakis, Beg, Machacek, Norreys, Santala, Watts and Dangor2000; Maksimchuk et al., Reference Maksimchuk, Gu, Flippo, Umstadter and Bychenkov2000; 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) for origin and acceleration. The full discussion of the model proposed by 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) was presented and demonstrated by particle-in-cell (PIC) simulation (Wilks et al., Reference Wilks, Langdon, Cowan, Roth, Singh, Hatchett, Key, Pennington, Mackinnon and Snavely2001), which is termed the target normal sheath acceleration (TNSA) mechanism. From Poisson's equation and Boltzmann statistics for electrons, the accelerating electric fields acting on the ions was estimated as E = T h/e max(L n, λD), here T h is the temperature of hot electrons, L n is the density scale length of plasma, and λD is the Debye length.
The potential applications of the laser induced ions require the energy and intensity of ions should be high enough. Mass-limited target design was shown to enhance the ion energy significantly due to the increase in the hot electron concentration (Limpouch et al., Reference Limpouch, Psikal, Andreev, Platonov and Kawata2008). Moreover, a new laser ion acceleration mechanism named laser break-out afterburner (BOA) suggested that GeV ions could be achieved from ultrathin target (Yin et al., Reference Yin, Albright, Hegelich and Fernandez2006). However, the currently available ultrashort laser facilities around the world can not meet the super high laser contrast requirement of the BOA mechanism. To improve the intensity of laser ions, circularly polarized laser pulse was demonstrated to collimate the ion beams (Kado et al., Reference Kado, Daido, Fukumi, Li, Orimo, Hayashi, Nishiuchi, Sagisaka, Ogura, Mori, Nakamura, Noda, Iwashita, Shirai, Tongu, Takeuchi, Yamazaki, Itoh, Souda, Nemoto, Oishi, Nayuki, Kiriyama, Kanazawa, Aoyama, Akahane, Inoue, Tsuji, Nakai, Yamamoto, Kotaki, Kondo, Bulanov, Esirkepov, Utsumi, Nagashima, Kimura and Yamakawa2006). Furthermore, a permanent magnet lens system was used to achieve both collimation and monochromatisation of the laser ions (Ter-Avetisyan et al., Reference Ter-Avetisyan, Schnurer, Polster, Nickles and Sandner2008).
The typical energy spectrum of accelerated ions has a quasi-thermal distribution with a cutoff energy, namely, their spectrum has almost 100% spread. However, applications of high-energy ions require high-quality ion beams with small energy spread. In order to obtain quasi-monoenergetic proton beams, a scheme using microstructured double-layer target was proposed and demonstrated by three-dimensional PIC simulations (Esirkepov et al., Reference Esirkepov, Bulanov, Nishihara, Tajima, Pegoraro, Khoroshkov, Mima, Daido, Kato, Kitagawa, Nagai and Sakabe2002). Experiments based on the scheme in Esirkepov et al. (Reference Esirkepov, Bulanov, Nishihara, Tajima, Pegoraro, Khoroshkov, Mima, Daido, Kato, Kitagawa, Nagai and Sakabe2002) was carried out successfully (Schwoerer et al., Reference Schwoerer, Pfotenhauer, Jackel, Amthor, Liesfeld, Ziegler, Sauerbrey, Ledingham and Esirkepov2006).
Critical for the acceleration of monoenergetic protons is the absorption efficiency of laser energy to hot electrons, since protons are accelerated by the electric fields induced by the charge separation of hot electrons and background ions. A target design of the re-entrant cone geometry (Kodama et al., Reference Kodama, Norreys, Mima, Dangor, Evans, Fujita, Kitagawa, Krushelnick, Miyakoshi, Miyanaga, Norimatsu, Rose, Shozaki, Shigemori, Sunahara, Tampo, Tanaka, Toyama, Yamanaka and Zepf2001) for fast ignition has attracted considerable interest. PIC simulations proved the cone target can increase the energy coupling from the laser pulse to electrons effectively via the focusing of laser light pulse (Sentoku et al., Reference Sentoku, Mima, Ruhl, Toyama, Kodama and Cowan2004) and the guiding of surface current (Nakamura et al., Reference Nakamura, Kato, Nagatomo and Mima2004). A cone target is also proposed to enhance the generation of protons in simulation (Nakamura et al., Reference Nakamura, Mima, Sakagami, Johzaki and Nagatomo2008) and experiment (Flippo et al., Reference Flippo, D'humieres, Gaillard, Rassuchine, Gautier, Schollmeier, Nurnberg, Kline, Adams, Albright, Bakeman, Harres, Johnson, Korgan, Letzring, Malekos, Renard-Legalloudec, Sentoku, Shimada, Roth, Cowan, Fernandez and Hegelich2008). But in these two references, the energy spreads of accelerated protons are almost 100% and it is not clear that if the cone target will damage the monochromaticity of protons.
In this paper, a scheme to increase the energy of quasi-monoenergetic protons is proposed. In this scheme, a cone-shaped target of high-Z material is used to interact with an intense laser light for improving the generation and confinement of hot electrons. The rear surface of this target is coated with an extra sub-micron proton layer with relatively low density to act as the source of proton for the acceleration. Due to the proton acceleration mechanisms, protons are accelerated by the sheath field produced by hot electrons on the boundary between the high-Z substrate and the proton layer. As a result, the higher energy and density of hot electrons in the cone target increase the proton energy.
PIC SIMULATIONS
Two-dimensional fully relativistic electro-magnetic PIC simulations were performed to investigate the above process. Our two-dimensional PIC code is FLIPS2D, with the finite difference method to solve the field equations and Boris' method to calculate the particle motion (Birdsall & langdon, Reference Birdsall and Langdon1991). Besides, the charge conservation method of first-order weighting of particles is exploited to make the simulation run faster (Umeda et al., Reference Umeda, Omura, Tominaga and Matsumoto2003). The scales of the simulation box are X × Y = 60λ0 × 40λ0 with a cell size of ΔX = ΔY = 0.02λ0, where λ0 is the wavelength of the incident laser light. A linearly polarized Gaussian laser beam with a focal spot of 6λ0 (full width at half maximum) is incident to the simulation box along the X axis from left to right. The laser beam rises up in 5τ0, with a sinusoidal profile, after which it maintains its peak intensity for 20τ0, and then falls to zero in another 5τ0, where τ0 is the laser period. The peak normalized vector potential is a 0 = eA/m eω0c 2 = 5.0, which corresponds to the peak incident intensity I 0 = 3.5 × 1019 W/cm2.
The geometry of the cone-shaped substrate and coated proton layer is shown in Figure 1. The width of the cone wall is 3λ0, the open hatch and the tip are 18λ0 and 2λ0 wide, respectively, and the open angle is 30°, which is the optimum angle for laser-cone interactions (Nakamura et al., Reference Nakamura, Mima, Sakagami, Johzaki and Nagatomo2008). The cone substrate consists of partially ionized plasma where the effective charge-to-mass ratio Z/A is assumed to be 1/10. The electron density of the target is 10 times the critical density (n c), which is related to the frequency of the incident laser as ω02 = 4πe 2n c/m e. The initial electron and ion temperatures are both 1.0 keV. At the rear surface of the cone substrate, there is a proton layer with density of n c.
Schematic of the cone-shaped substrate and the coated proton layer.
To demonstrate the advantage of cone target for laser proton acceleration, a scheme with film substrate is simulated. For the film target, the high-Z layer is 18λ0 wide and 3λ0 thick. The proton layers for cone substrate and film are both 1λ0 wide and 0.1λ0 thick. Because the protons on the target's rear surface are accelerated directly by the sheath field due to the TNSA mechanism, first evolution of the on-axis distributions of sheath fields for cone and film targets is plotted in Figure 2. We can see that at all times the amplitude and the range of the electric field on the rear surface of the cone target (solid line) is much higher than those for the film target (dashed line), as expected. The electrostatic field's higher and wider amplitude indicates higher acceleration for the cone target.
On-axis distribution of sheath fields for cone target (solid line) and film target (dashed line) at (a)t = 40τ0, (b)50τ0, (c)60τ0, (d)70τ0.
Enhancement of the sheath field is believed to result from the increase of hot electrons generated by the cone target. From the TNSA mechanism, the amplitude of the sheath field on the target's rear surface is proportional to the temperature of hot electrons (not thermal electrons). When an intense laser light interacts with the side wall of the cone target, electrons are confined on the surface to the tip by the self-induced surface magnetic field (Nakamura et al., Reference Nakamura, Kato, Nagatomo and Mima2004). Meanwhile, the laser pulse is focused by the conical surface (Sentoku et al., Reference Sentoku, Mima, Ruhl, Toyama, Kodama and Cowan2004), and its intensity can be increased by a few of times. The temperature of hot electrons is T h = 511[(1 + 0.73I1018W/cm2λμm2)1/2 − 1] keV due to the J × B mechanism (Wilks et al., Reference Wilks, Kruer, Tabak and Langdon1992) predominant in this regime. Thus, the temperature of hot electrons is increased significantly by the focused laser light, and so is the accelerating sheath field.
Figure 3a shows the spatial distribution of laser energy density for cone target. At the cone tip, laser energy density is increased about 6.4 times higher than the incident one. From the scaling law of J × B mechanism, the temperature of hot electrons should be increased 2.5 times higher. The energy spectra of hot electrons escaping from the targets' rear surface are plotted in Figure 3b. The electron temperature for film target is 1.14 MeV; for cone target it is 3.36 MeV, even higher than the expectation from the scaling law given above. This can be interpreted by the re-acceleration of surface hot electrons by the focused laser light at the cone tip. Therefore, higher hot-electron temperature of the cone target accounts for the higher sheath field at the target's rear surface, which is consistent with the results shown in Figure 2. The energy-transfer ratios from the laser to the hot electrons are 1.9% and 0.7% for the cone target and film target, respectively.
(Color online) (a) spatial distribution of laser energy density at t = 50τ0 for cone target; (b) spectra of electrons escaping from the rear surface of cone target (solid line) and film target (dashed line).
The above results demonstrate that the cone target can obtain higher temperature of hot electrons and the sheath field, which can accelerate protons on the rear surface, than the film target. Figure 4 shows the distribution of both heavy ions and protons in phase space at t = 70τ0 for cone target and film. At the tip of cone target or front side of film target, a fraction of ions move backward and a fraction of ions move forward, which is consistent with the direction of sheath field shown in Figure 2. Moreover, at the rear surface of the substrate, both heavy background ions and protons are accelerated forward by the sheath field. However, protons are accelerated to higher momentum because of their lighter mass. For cone target, the longitudinal momentums of protons are higher than those of film target according to the increase of sheath field discussed above. Since the angular spread of protons propagating in the vacuum is determined by the ratio of longitudinal momentum and the transverse momentum as tanθ = p y/p x, from the distributions of ions in momentum phase space p xvs. p y shown in Figures 4c and 4d, we can estimate the angular distribution of proton emission. For film substrate, protons are confined in a cone angle about 26°. For cone substrate, the cone angle is 12°, which means much better collimation than film target.
(Color online) Distribution of ions in phase space p xvs x at t = 70τ0 for (a) cone target and (b) film target. Distribution of ions in phase space p xvs p y at t = 70τ0 for (c) cone target and (d) film target.
Figure 5a shows the energy spectra of protons measured at t = 70τ0, just after the incident laser light interacts with plasma. For the film target (dashed line), the peak proton energy is E 0 = 2.0 MeV, and the energy spread is ΔE FWHM/E 0 = 13.1%. For the cone target (solid line), the peak proton energy is E 0 = 6.9 MeV, 3.5 times higher than that of the film target, and the energy spread is ΔE FWHM/E 0 = 16.3%. The total energy transported from the laser to protons for the cone target is also about three times increased than the film target, which is consistent with the increase of hot electrons' temperature by cone target. It is confirmed that this cone substrate plus sub-micron proton layer scheme can increase the energy of protons and the coupling from laser to protons by about three times while maintaining the protons' monochromaticity.
(a) Energy spectra of protons at t = 70τ0 for cone target (solid line) and film target (dashed line). (b) Energy spectra of protons at t = 70τ0 for a 0 = 5.0, 10.0, 20.0 and 30.0.
Figure 5b shows the energy spectra of protons vs. laser intensities. Energy of proton beam is proportional to the normalized laser vector potential, which is consistent with TNSA mechanism and scaling law of J × B mechanism. When a 0 = 30, proton beam's energy can be as high as 83 MeV. If three-dimensional effect of the laser focusing from cone target is taken into account, the energy can be high to around 100 MeV. The current petawatt laser facility has intensity over 1.0 × 1020 W/cm2 and duration about 500 fs, which is longer than that in our simulations and should be advantageous for proton acceleration. If the scheme discussed in this report is carried out under such laser pulse condition, 200 MeV monoenergetic proton beams which are appropriate for cancer therapy may be achieved.
CONCLUSION
In this paper, a target design of a cone-shaped substrate, on the rear surface of which a proton layer is coated, is studied by two-dimensional PIC simulations. It is shown that this scheme can increase the energy of protons and the coupling from laser to protons by about three times while maintaining the monochromaticity of proton beams. This effect is owed to the laser focusing and electron guiding by cone substrate.
ACKNOWLEDGEMENTS
This work was supported by the National Key Laboratory of Laser Fusion. Y. G. thanks the financial support from the Natural Science Foundation of China under grant No. 10975121, and the Science and Technology Foundation of CAEP under grant No. 2006Z0202.
