Acceleration in laser produced plasmas include

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Unformatted text preview: Williams (1981), and Kishimoto et al. (1983). More recent works stimulated by the TNSA experiments include Kovalev and Bychenkov (2003), Mora (2003, 2005), Betti et al. (2005), Ceccherini et al. (2006), and Peano et al. (2007). 11 A list of papers describing TNSA models mostly based on a static modeling includes Passoni and Lontano (2004, 2008), Passoni et al. (2004), Albright et al. (2006), Lontano and Passoni (2006), Robinson, Bell, and Kingham (2006), and Schreiber et al. (2006). Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . the electron cloud to be spatially uniform in the plane normal to the ion motion. Note that all the models proposed to describe TNSA are, to a large extent, phenomenological, i.e., they need as input parameters physical quantities which are not precisely known. Since these descriptions give a simplified picture of the acceleration process, the best model in this context may be considered the one which provides the best fit of experimental data with the lowest set of laser and target parameters. This issue will be discussed in Sec. III.D. In principle, these difficulties could be overcome performing realistic numerical simulations, but these generally consider ‘‘model’’ problems due to intrinsic difficulties in the numerical study of these phenomena, such as, for example, the large variations of density from the solid target to the strongly rarefied expansion front. At present, a complementary use of simple models, presented in Secs. III.C.1, III.C.2, and III.C.3, and advanced simulations, discussed in Sec. III.C.4, seems the most suitable option to theoretically approach TNSA. 1. Quasistatic models Static models assume, on the time scale of interest (i.e., in the sub-ps regime), immobile heavy ions, an isothermal that laser-produced hot electron population, and a sufficiently low number of light ions so that their effect on the evolution of the potential can be neglected and they can be treated as test particles. In this limit, if Eq. (15) is used to describe hot electrons and one neglects thermal effects for cold electrons, the potential in planar geometry is determined by @2  ¼ 4e½n0h ee=Th À ðZH n0H À n0c ފ @x2 ¼ 4en0h ½ee=Th À ÂðÀxފ; (19) where we assumed the background charge to fill the x < 0 region with uniform density. The corresponding electron density and electric field can be calculated, as well as the energies of test ions moving in such potential. This can be considered the simplest self-consistent approach to describe the TNSA accelerating field. The solution of Eq. (19) in the semi-infinite region x > 0 is (Crow, Auer, and Allen, 1975)    2T x À1 ; (20) ðxÞ ¼ À h ln 1 þ pffiffiffiffiffi e 2eDh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where Dh ¼ Th =4e2 n0h . The field reaches its maximum at the surface and is given by sffiffiffi 2 Eð0Þ ¼ E0 ; e E0 ¼ Th ; eDh...
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