corresponding to an intensity i n if the surface

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Unformatted text preview: =ð1 À Þ. The resulting pressure is P ¼ jÁpj=Át ¼ ðN ℏ=cÞð! þ !r Þ=r ¼ ð2I=cÞð1 À Þ=ð1 þ Þ. 18 For simplicity we assume I to be independent of time. Generalization to a time-dependent profile I ðtÞ is discussed by Robinson, Gibbon, Zepf et al. (2009). 19 For theoretical or simulation studies of HB by circularly polarized laser pulses, see also Liseikina and Macchi (2007), M. Chen et al. (2008), Liseykina et al. (2008), Yin et al. (2008), and Naumova et al. (2009) for a single ion species case, and Robinson, Kwon, and Lancaster (2009) and Zhang et al. (2009) for two ion species plasmas. Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 applications since it allows control of the background density, the use of a pure proton target, and high-repetition rate since the gas is flowing. In a recent experiment (Palmer et al., 2011) employing 10 m wavelength, $6 Â 1015 W cmÀ2 circularly polarized pulses (a0 ’ 0:5), and a hydrogen gas jet with density of a few times nc , protons of energy up to 1.2 MeV and a narrow energy spread were observed (see Fig. 24). The observed ion energies were fairly consistent with a linear scaling with I=ne as predicted by the HB model. The energies were actually higher than expected considering the vacuum laser intensity, suggesting that self-focusing in the underdense region could have increased the intensity in the plasma. We note that Palmer et al. (2011) reported on protons accelerated by a shock driven by radiation pressure, similarly to several who refer to HB or piston acceleration in thick targets as acceleration in the electrostatic shock sustained by the laser pressure at the front surface (Zhang, Shen, Yu et al., 2007; Schlegel et al., 2009; Zhang et al., 2009). In the context of ion acceleration by a laser, we prefer to reserve the term ‘‘shock’’ for the regime described in Sec. IV.B which implies the generation of a true electrostatic shock wave, able to propagate into the plasma bulk and drive ion acceleration there. From the point of view of fluid theory, a shock wave launched with velocity vsho requires the sound speed, and thus the electron temperature, to be large enough to prevent the Mach number M ¼ vsho =cs from exceeding the critical value Mcr ’ 6:5 above which one does not have a shock but a ‘‘pure piston’’ (Forslund and Freidberg, 1971). Thus, formation of a true, high speed shock wave may be inhibited for circular polarization because of the reduced electron heating. Experimental evidence of HB acceleration in solid targets is less clear at present. Badziak et al. (2004) reported a series of observations of high-density, $keV energy ion pulses (plasma ‘‘blocks’’) for subrelativistic irradiation (< 1018 W cmÀ2 ) of solid targets (but in the presence of significant preplasma). These results were interpreted using a model of ponderomotive skin-layer acceleration at the critical surface, a concept that sounds rather similar to HB-RPA. Akli e...
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