On the origin of the name 756 andrea macchi marco

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Unformatted text preview: ghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . simplicity), and a ‘‘cold’’ plasma, i.e., we neglect thermal pressure. Following these assumptions we write Maxwell’s equations for the electrostatic field and Euler’s equation for the electron fluid having velocity vx : @x Ee ¼ 4 ¼ 4e½n0 ÂðxÞ À ne Š; (7) @t Ee ¼ À4Jx ¼ 4ene vx ; (8) dvx e ¼ ð@t þ vx @x Þvx ¼ À ðE þ Ed Þ: me e dt (9) Switching to Lagrangian variables x0 and  ¼ ðx0 ; tÞ defined by x ¼ x0 þ , d=dt ¼ vx , a straightforward calculation along with the constraint of Ee being continuous at x ¼ x0 þ  ¼ 0 yields the following equations of motion describing electrostatic, forced oscillations of electrons across a steplike interface:  À!2  À eE =m ðx0 þ  > 0Þ; d2  p d e (10) ¼ 2 2 x À eE =m dt ðx0 þ  < 0Þ: þ!p 0 d e From Eq. (10) we see that electrons crossing the boundary (x ¼ x0 þ  < 0) feel a secular force !2 x0 leading to dep phasing from Ed and acceleration (Mulser, Ruhl, and Steinmetz, 2001). Equation (10) can be solved numerically for a discrete but large ensemble of electron ‘‘sheets’’ (corresponding to a set of values of x0 > 0), with the prescription to exchange the values of x0 for two crossing sheets to avoid the onset of singularity in the equations.6 Representative trajectories of electrons moving across the interface are found as in Fig. 5. Electrons whose trajectory extends in vacuum for half or one period of the driving field and then reentering at high velocity inside the plasma are observed. Similar trajectories are found in electromagnetic and self-consistent simulations (see Sec. II.B.2). Note that the cold plasma assumption is consistent with the requirement that the external field should be strong enough to overcome the potential barrier which, in an equilibrium state, confines warm electrons inside a bounded plasma (such a barrier corresponds to a Debye sheath; see also Secs. II.C.1 and III.C.1). For !p ) ! and nearly total reflection, the laser field component normal to the surface has an amplitude E? ’ 2E0 sin, with E0 ¼ ð4I=cÞ1=2 the amplitude in vacuum. The sheath field is Es ’ Te =eD ¼ ð4n0 Te Þ1=2 , so that the condition E? > Es may be rearranged as 4ðI=cÞsin2  > n0 Te . This implies (at nongrazing incidence) that the radiation pressure should exceed the thermal pressure and thus counteract the thermal expansion and steepen the density profile, making the assumption of a steplike plasma more self-consistent. For S polarization or normal incidence there is no component of the electric field perpendicular to the surface. However, for high intensities the magnetic force term becomes important and may drive electron oscillations along the density gradient also for normal incidence. This effect is commonly named ‘‘J  B’’ heating (Kruer and Estabrook, 6 This numerical implementation basically corresponds to the pio...
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This document was uploaded on 09/28/2013.

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