Equilibrium electron density , initial density . For , , ions are fixed.
Test particle calculations of momentum change (a)–(c) and energy absorption (d)–(f) of electrons injected with momentum on the right-hand side of Fig. 1. For not-too-high the electrons enter (or cross) the skin layer, turn around, and return to their starting point with momentum . One hundred test particles are launched at 100 different phases of the laser field (dotted regions). The phase-averaged values of and are indicated by the bold lines. The laser intensity was , normally incident on 10, 50, and 250 times overdense plasma [panels (a,d), (b,e), and (c,f), respectively]. Bifurcations in the spectra are indicated by arrows.
(a) Momenta and (b) energies are plotted as functions of for and . These results have to be compared with panels (c) and (f) from Fig. 2. For an easier comparison, the bold solid lines from Figs. 2(c) and 2(d) are transferred as bold dashed curves to the present figure, showing that the differences are insignificant.
Test particle situation as in Fig. 2 showing the positions of reflection. For a given value of the momentum of injection on the ordinate the interval of possible turning positions is the projection of the segment onto the abscissa. In panel (c) , at . Parameters as in Fig. 2. The vertical lines indicate the ion and electron fronts at and , respectively.
(Color online) Particle dynamics in detail. Phase-space plots (a) and (b) vs of 100 test particles injected with initial momentum at at times , (for better visibility only phases between 0 and are shown). Index is used for color coding the trajectories. Laser parameters are , , and . Reflection occurs during one half laser period predominantly in front of the target surface (latter is indicated by the bold vertical line). If all injection phases are shown, plot (b) is fully symmetric with respect to . Due to the conservation of the canonical momentum , the final values for equal the initial momenta .
Percentage of absorption as a function of normalized injection momenta for and (bold dashed), (bold solid), and (bold dotted). For comparison, the absorption obtained from (32) is also shown (corresponding thin curves).
Vacuum heating vs skin layer absorption. Absorption for the case of a 50 times overdense target exposed to as a function of the position at which a strong repulsive potential enforces particle reflection. The injection energies were weighted according to Maxwellian distributions of temperatures (solid) and (dashed). Absorption is inefficient if particle reflection is enforced at the target surface.
Absorption for a 50 times overcritical target with at the intensities and (both solid) and corresponding results from Fig. 6 for (dashed) vs the injection energy in units of , .
Absorption in the test particle model under incidence in polarization on a 50 times overdense target for (dashed), (solid), and (dotted). Many of the injected test electrons do not return into the target already at rather low injection momenta, leading to the jagged structure centered around . For this maximum, similar considerations hold as in Fig. 8 for the analogous chaotic region localized there between and .
Reflection positions of perpendicularly injected test particles under oblique incidence of a laser beam onto targets of ion densities , 50, and . The solid vertical lines indicate the ion and electron fronts at and , respectively.
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