From a target with microgrooves imprinted on the rear

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Unformatted text preview: 9 W cmÀ2 . Bottom: The effect of electron removal by magnetic fields, showing that the proton beam emittance is not significantly affected. The images are for 6.5 MeV protons and the target thickness is 40 m. From Cowan et al., 2004. Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . 764 emittance, as shown in Fig. 14 (Cowan et al., 2004). This last observation is important since, in order to take advantage of the exceptionally small proton beam emittance in future applications, e.g., to capture them into a postaccelerator, removal of the comoving electrons without significantly perturbing the protons is crucial. The ultralow emittance stems from the extremely strong, transient acceleration that takes place from a cold, initially unperturbed surface and from the fact that during much of the acceleration the proton space charge is neutralized by the comoving hot electrons. Using the ion beam as a projection source, having a low-emittance beam is equivalent to projecting from a virtual pointlike source located in front of the target, with much smaller transverse extent than the ionemitting region on the target surface (Borghesi et al., 2004; Nuernberg et al., 2009). As discussed in Sec. V.A, this property of laser-driven ion beams allows one to implement pointprojection radiography with high spatial resolution. C. TNSA modeling The experimental observations and the considerations summarized in Sec. III.A suggest the following assumptions, leading to the formulation of a relatively simple system of equations which can be investigated analytically and numerically (Passoni et al., 2004). First, we assume an electrostatic approximation, so that the electric field E ¼ Àr where the potential  satisfies Poisson’s equation   X (14) r2  ¼ 4e ne À Zj nj ; j with the sum running over each species of ions, having density nj and charge Zj . As a consequence of the laser-solid interaction, the electron density ne may be described as composed of at least two qualitatively distinct populations, which will be labeled cold and hot in the following, having densities nc and nh such that ne ¼ nc þ nh . In the simplest approach, thermal effects are neglected for the cold population, while nh is given by a one-temperature Boltzmann distribution (notice that in this section ‘‘e’’ indicates the mathematical constant e ¼ expð1Þ ¼ 2:718 28 Á Á Á while e indicates as usual the elementary charge), nh ¼ n0h ee=Th : (15) This expression can be a reasonable first approximation to account for the presence of the self-consistent sheath field and has been used in many works on TNSA9 but, as discussed below, it can lead to serious problems when the main goal is the estimation of the maximum energy of the accelerated ions. Alternatively, the electron dynamics can be included via either fluid or kinetic equations. It is mostly appropriate to consider two different ion species, a light (L) and a...
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