ne nc 5 where is the thickness of the

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Unformatted text preview: ness of the foil. Equation (5) has some interest for the interaction with ultrathin foil targets (see Secs. IV.A.2–IV.C). B. Hot electrons Since the laser pulse cannot penetrate into solid-density regions, the absorbed energy is transported to these regions mostly by energetic (commonly named either hot or fast) electrons which may be generated during the interaction through several mechanisms. By hot electrons in the present context one typically refers to relativistic electrons whose energy is of the order of the cycle-averaged oscillation energy in the electric field of the laser in vacuum, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  (6) E p ¼ me c2 ð À 1Þ ¼ me c2 1 þ a2 =2 À 1 ; 0 where Eq. (2) has been used. Equation (6) is also called the ‘‘ponderomotive’’ energy (Wilks et al., 1992). Hot electrons penetrating into solid targets have been observed and characterized in several experiments at very high intensities and for different interaction conditions3 and play a fundamental role in applications such as laser-driven photonuclear physics and fast ignition of fusion targets. Moreover, as discussed in Sec. III, in most of the experiments reported so far, acceleration of protons and heavier ions is driven by hot electrons. The process of hot electron generation turns out to be complex and, possibly, not yet completely understood. A review of past and ongoing research on the topic can be found in recent books (Gibbon, 2005b; Mulser and Bauer, 2010). Here we give a basic discussion at a qualitative level, focusing on those aspects which are most essential and relevant to ion acceleration. At the surface of an overdense plasma, electrons are driven by the Lorentz force fL ¼ ÀeðE þ v  B=cÞ which includes both the fields of the incident and reflected laser pulses and self-generated fields. As a necessary condition for the efficient generation of hot electrons near the critical surface fL must have an oscillating component directed along the density gradient rne . This is the case for the well-known resonance absorption where the condition E Á rne Þ 0 is necessary to drive resonant plasma oscillations which in turn accelerate electrons. In a plane geometry such condition requires oblique incidence and P polarization of the laser pulse. This absorption mechanism is sensitive to the density 3 See, e.g., Key et al. (1998), Wharton et al. (1998), H. Chen et al. (2009), Tanimoto et al. (2009), and Nilson et al. (2010), and references therein. Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 755 scale length Ln ¼ ne =jrne j because the driving force is evanescent in the resonance region. In a sharp-boundary plasma where Ln ( , absorption and heating may arise because electron motion is not adiabatic, as electrons are driven from the region of strong fields to the evanescence region in a time shorter than 2=!, so that the cycle average ÀehE Á vi may not cancel out. Thus, short duration and high-intensi...
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