Amplitude to a0 due to the onset of relativistic

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Unformatted text preview: ipathi et al., 2009)22 which might be, 20 For a constant intensity I, Eqs. (31) are identical to those for a charge accelerating during Thomson scattering from a plane wave; see Landau and Lifshitz (1962) who leave the solution as an exercise for the reader. 21 The expression for  also follows from ‘‘photon number’’ conservation and frequency downshift (see Sec. IV.A.1). In the reflection of N photons from the mirror, the energy transferred to the mirror is N ℏð! À !r Þ ¼ ½2 =ð1 þ ފN ℏ!  ðN ℏ!Þ. 22 Some give a similar condition for the optimal thickness but with slightly different numerical factors (Yan et al., 2008, 2009a; Ji et al., 2009). 776 (a) Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . (b) FIG. 25 (color online). (a) Energy per nucleon vs time from the analytical solution [Eq. (32)] of the LS model with R ¼ 1. The dashed line gives the asymptotic $t1=3 behavior. (b) Scaling of the energy per nucleon as a function of the dimensionless pulse fluence a2  (where  is the pulse duration in units of the laser 0 period) and of the surface density  [Eq. (5)] for  ¼ 1 (black line), 3.16 (green line), 10 (blue line), 31.6,(orange line) and 100 (red line). The values on the upper horizontal axis give the fluence in J cmÀ2 corresponding to a2  for  ¼ 0:8 m. 0 however, relaxed by the effect of frequency decrease in the moving foil frame, increasing Rð!0 Þ [see Eq. (31)]. For a0 >  , all electrons are pushed away from the foil. In this regime the ions in the foil undergo a Coulomb explosion producing a broad ion spectrum. In a composite target the ion field after electron expulsion might be used for monoenergetic acceleration of a proton layer (Bulanov et al., 2008; Grech et al., 2009). The interest in the LS regime was greatly stimulated by three-dimensional PIC simulations of thin-foil acceleration by Esirkepov et al. (2004) which showed that the temporal dependence and typical values of the ion energy were well described by the LS model. The simulations assumed a laser pulse with peak amplitude a0 ¼ 316 (I2 ¼ 1:4  1023 WcmÀ2 ) and 8 cycles duration, and a proton slab of density 49nc and 1 thickness. Most of the ions in a thinfoil target are accelerated coherently up to relativistic energies ($ 1:5 GeV) as shown in Fig. 26. According to Esirkepov et al. (2004), in order for RPA to become the dominant acceleration mechanism the ions have to acquire relativistic energies already within one laser cycle, so that they can promptly follow electrons which are displaced in the longitudinal direction by the ponderomotive force. Later theoretical studies of such a so-called radiation pressure dominant (RPD) regime include Rayleigh-Taylor-like instability of the foil (Pegoraro and Bulanov, 2007) and the effects of radiation friction which play a significant role at ultrarelativistic intensities (Tamburini et al., 2010). Of particular interest is the po...
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This document was uploaded on 09/28/2013.

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