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Unformatted text preview: ate arose on the actual location of the region where the Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . FIG. 3. Example of the profile of energy deposition of protons and C ions in water, compared to those of electrons, x and rays, and neutrons. Protons and C ion profiles are characterized by the Bragg peak at the end of the path. The quantity plotted is the relative dose, i.e., the energy absorbed per unit mass. From Amaldi and Kraft, 2005. protons were accelerated and, consistently, on the mechanism driving the acceleration. Clark et al. (2000a) and Maksimchuk et al. (2000) suggested that protons were accelerated at the front side of the target, crossing the latter and being detected on the opposite side. In contrast, Snavely et al. (2000) provided evidence that protons were accelerated at the rear side [see also Hatchett et al. (2000)]. To support the interpretation of these latter experiments (performed at the petawatt facility of Lawrence Livermore National Laboratory, USA) the so-called target normal sheath acceleration (TNSA) model was introduced by Wilks et al. (2001). Briefly, TNSA is driven by the space-charge field generated at the rear surface of the target by highly energetic electrons accelerated at the front surface, crossing the target bulk, and attempting to escape in vacuum from the rear side. The basic theory of TNSA and related models is described in detail in Sec. III. Most of the experiments investigating proton acceleration by laser interaction with solid targets have been interpreted in terms of the TNSA framework (see Secs. III.A and III.B) that has also guided developments toward source optimization by target engineering (see Sec. III.E). A major requirement for several of the foreseen applications is an increase of the energy per nucleon up to hundreds of MeV and beyond. The next generation of laser facilities should allow intensities higher than the current record of $1022 W cmÀ2 (Yanovsky et al., 2008), but at present it is not guaranteed that the ion energy scaling observed so far will be maintained at such extreme intensities nor that TNSA will still be effective. An analysis of proton acceleration experiments performed up to 2006 suggests a $ðI2 Þ1=2 scaling of proton energy up to values of I2 ¼ 3 Â 1020 W cmÀ2 m2 (Borghesi et al., 2006; Fuchs et al., 2006b), where I and  are the laser intensity and wavelength, respectively. Figure 4 summarizes such data, together with more recent results obtained with Ti:Sa-based, ultrashort (tens of fs) pulses, exhibiting a $I2 scaling. Measurements by Robson et al. Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 753 FIG. 4 (color online). Maximum proton energy from laserirradiated solid targets as a function of the laser irradiance and for three ranges of pulse durations, reporting experiments up to 2008. Two trend lines are overlaid, the shallower one corresponding to a $I 1=2 dependence, and the steeper o...
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