Used to resolve the strong density variations in the

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Unformatted text preview: ansion takes a single ion species into account and a limited set of parameters, such as the initial electron temperature and the initial thickness of the plasma; this is equivalent to fixing the total energy of the system. Such simplified simulations already reproduce qualitative features observed in the experiment and may match measured quantities such 14 See, e.g., Kemp and Ruhl (2005), Brantov et al. (2006), Robinson, Bell, and Kingham (2006), Robinson and Gibbon (2007), Psikal et al. (2008), Robinson, Gibbon, Pfotenhauer et al. (2009), and Brady and Arber (2011). Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 FIG. 18. Electric field profiles at different times from the numerical simulation of the collisionless expansion of a slab of warm plasma. Thick and dashed lines show results from a PIC code (Betti et al., 2005) and a hydrodynamics code (Mora, 2003), respectively. Both simulations assume a 40 m thick proton plasma slab with initial density n0 ¼ 3 Â 1019 cmÀ3 and electron temperature Te0 ¼ 500 keV. The inset shows the detail of the field distributions at early times, with the field in the PIC simulation extending over a finite distance. From Romagnani et al., 2005. as the ion front velocity, with a proper choice of initial parameters. As an example, Fig. 18 shows simulation results performed to support experimental observations by Romagnani et al. (2005), using both a hydrodynamics and a PIC code. The two approaches use different initial conditions, i.e., a Boltzmann equilibrium for fixed ions and a zero charge density distribution, respectively. The latter condition enables one to resolve in the PIC calculation the propagation of the electron front, resulting in the electric field vanishing at the front position and showing a strong temporal maximum at the earliest instants, in agreement with experimental observations. The use of supercomputers allows one to perform multidimensional PIC simulations and to simulate the laser-plasma interaction and the generation of hot electrons, rather than imposing a priori their number and temperature. The computational challenges and limitations of such large-scale simulations have been discussed in Sec. II.D. In addition, most PIC simulations do not include collisions, which may play an important role in the transport of hot electrons through the target (see Sec. II.B.3). Nevertheless, PIC simulations have been vastly used as a valuable support in the interpretation of measurements of ion acceleration and were able to reproduce at least qualitatively several observed features of the TNSA picture; see, e.g., Pukhov (2001), Wilks et al. (2001), and Fuchs et al. (2005). As an alternative to the PIC method, Gibbon et al. (2004) used a gridless, electrostatic ‘‘tree’’ particle code to simulate ion acceleration from wire targets. Such a code has the advantages of an unlimited spatial region for particles and of ‘‘automatic’’ inclusion of collisions at the cost of being pure...
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