For the case of two electron components rev mod phys

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Unformatted text preview: an (1978), Wickens, Allen, and Rumsby (1978), Gurevich, Anderson, and Wilhelmsson (1979), True, Albritton, and Williams (1981), Kovalev, Bychenkov, and Tikhonchuk (2002), and Diaw and Mora (2011). 768 Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . electric field (Tikhonchuk et al., 2005), obtaining for the velocpffiffiffi ity profile vL ’ cL 2ð1 þ x=cH tÞ1=2 . Noticeably, the L ions velocity and density profiles vary slowly in space compared to the H ion ones, and the L ion flux is almost constant. Beyond the H ion front, only L ions are present and they can be described again by a single species expansion with vL ’ cL þ x=t [see Eq. (22)]. However, matching of the velocity profiles in the region behind the H ion front implies the existence of a transition region where the velocity is approximately constant. This corresponds to a plateau region in the phase space and to a peak in the L ion energy spectrum. The heuristic reason for plateau formation is that the L ions are accelerated more efficiently behind the H ion front than ahead of it. Figure 17 shows the velocity spectrum from numerical results (Tikhonchuk et al., 2005) using a Boltzmann-Vlasov-Poisson model (Bychenkov et al., 2004) based on Eqs. (14), (15), and (18), compared with analytical estimates from the self-similar solution. According to the above model the peak energy of L ions is pffiffiffiffiffiffiffi (26) E L ’ ZL Th lnð4 2 N=eÞ: As an important indication from this model, the mass ratio and the relative concentration of the two species might be engineered to optimize the L ion spectrum. Several simulation studies14 have been devoted to this issue and to the modeling of observations of multispecies spectra in both planar and spherical (droplet) targets (see Sec. III.E). 4. Numerical simulations Even in their simplest formulation TNSA models are highly nonlinear and the set of available analytical solutions is limited. A numerical approach can be used to overcome these limitations and to address additional effects. Referring to the 1D problem of plasma expansion, an hydrodynamic two-fluid approach may be used to take charge separation effects into account as reported by Mora (2003). The hydrodynamic model, however, cannot take into account kinetic effects such as non-Maxwell distribution and breakdown of equilibrium conditions. To address these effects a numerical solution of the Vlasov equation for the distribution function of electron and ions in phase space is needed. To this aim the PIC approach (see Sec. II.D) may be used, with the drawback of much larger computational requirements compared to hydrodynamics simulations. The reason is that, in order to obtain full numerical convergence and accurate, low-noise results, a very large number of particles should be used to resolve the strong density variations in the plasma expansion. In its simplest formulation the 1D simulation of collisionless plasma exp...
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