Quasineutrality also breaks down in general in the

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Unformatted text preview: selfsimilar solution for isothermal plasma expansion; Eq. (22). The front of charge separation at x ¼ xf ðtÞ and the rarefaction front at x ¼ Àcs t are also indicated. The electric field is uniform in the Àcs t < x < xf ðtÞ region. Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . 767 the inertia of ions is important and the assumption of quasineutrality must be abandoned. Ultimately, a self-consistent analysis can be developed through numerical simulations (see Sec. III.C.4). Still assuming, for simplicity, that only a single ion population and a single-temperature Boltzmann electron population are present, and ni ðt ¼ 0Þ ¼ n0 ÂðÀxÞ, Eq. (20) can be used to define the initial conditions for the electric field at the time t ¼ 0 at which the ion acceleration process begins. The following interpolation formulas for the electric field and ion velocity at the ion front: sffiffiffi 2 E0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; E ðtÞ ’ e 2 þ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi uf ðtÞ ’ 2cs lnð þ 2 þ 1Þ; (23) (24) pffiffiffiffiffi where  ¼ !pi t= 2e, give the correct behavior at t ¼ 0 for both the electric field [see Eq. (21)] and the front velocity, and reduce to previous expressions for !pi t ) 1. These formulas fit well numerical calculations by Mora (2003) using a Lagrangian fluid code. Related results of similar studies using fluid and kinetic descriptions can be found in the literature.12 The major drawback of Eq. (24) is that the maximum velocity of ions, and hence the cutoff energy, diverges logarithmically with time. This is not surprising, being an unavoidable consequence of the isothermal assumption and the chosen boundary conditions: the system has an infinite energy reservoir in the electron fluid and thus it is able to accelerate ions indefinitely. Nevertheless, the simplicity of Eq. (24) has proven to be attractive; thus it has been suggested to insert a phenomenological ‘‘maximum acceleration time’’ tacc at which the acceleration should stop. Such a formula has been used in attempts to fit experimental data (Fuchs et al., 2006b). We return to this point in Sec. III.D. There is no easier way to remove this unphysical behavior from the 1D planar model but to give a constraint of finite energy (per unit surface). In this way, the electron temperature decays in time due to the plasma expansion and to collisional and radiative losses. The electron cooling cooperates with the effects of finite acceleration length and maximum electron energy in the determination of a finite value for the maximum energy gain. The expansion of plasma slabs (foils) of finite thickness, and hence of finite energy, has been considered analytically and numerically. In these models the electron temperature is taken as a function of time Th ¼ Th ðtÞ, determined either by the energy conservation equations (Betti et al., 2005; Mora, 20...
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This document was uploaded on 09/28/2013.

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