1cat to the laser intensity i the nonlinear

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Unformatted text preview: The nonlinear, relativistic index nNL ¼ ð1 À ne = nc Þ1=2 becomes imaginary when ne > nc , showing an increase of the cutoff density for a plane monochromatic wave: this effect is known as relativistic self-induced transparency or, briefly, relativistic transparency. However, the problem of laser penetration inside a plasma is not trivial (Cattani et al., 2000; Goloviznin and Schep, 2000; Shen and Xu, 2001) because of both the nonlinearity in the wave equation and the self-consistent modification of the plasma density profile due to radiation pressure effects. These latter may be described via the ponderomotive force (PF).2 In an oscillating, quasimonochromatic electromagnetic field described by a dimensionless vector potential aðr; tÞ whose envelope is sufficiently smooth in space and time, the relativistic PF is [see, e.g., Bauer, Mulser, and Steeb (1995) and Mulser and Bauer (2010)] fp ¼ Àme c2 rð1 þ hai2 Þ1=2 : (4) For a plane wave impinging on an overdense plasma, the resulting PF, more effective on the lightest particles, is in the inward direction and tends to push and pile up electrons inside the plasma. Ponderomotive effects will be further discussed below (see Secs. II.B and II.C). In a multidimensional geometry, a laser pulse of finite width may produce a density depression around the propagation axis also because of the ponderomotive force pushing the electrons in the radial direction. Jointly with the relativistic effect and target expansion driven by electron heating, this mechanism may lead to a transition to transparency as soon as the electron density drops below the cutoff value (Fuchs et al., 1999). Investigations of ion acceleration in the transparency regime are described in Sec. IV.C. 1 Consistently with our definitions, given the value for I , the peak value of the dimensionless vector potential of the plane wave will be pffiffiffi given by a0 for linear polarization and by a0 = 2 for circular polarization. 2 Throughout this review we refer to the ponderomotive force as the slowly varying, effective force describing the cycle-averaged motion of the ‘‘oscillation center’’ of a charged particle in an oscillating nonuniform field, over a time scale longer than the oscillation period. ‘‘Fast’’ oscillating components are not included in the definition of ponderomotive force here adopted. Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . The penetration of the laser pulse depends not only on the electron density but also on the target size when the latter becomes close to or smaller than one wavelength. As a simple but useful example, the nonlinear transmission and reflection coefficients can be calculated analytically for a subwavelength foil modeled as a Dirac deltalike density profile (Vshivkov et al., 1998; Macchi, Veghini, and Pegoraro, 2009), obtaining a transparency threshold a0 >  ne ‘  ; nc  (5) where ‘ is the thick...
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This document was uploaded on 09/28/2013.

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