Figure 2. Modelling the intra-pulse acceleration.

(a) False-colour image (logarithmic scale) of the angularly resolved electron energy distribution at the target rear side, at the time the peak of the laser pulse reaches the front side (t=0). The components of the spatial distribution of the electric field amplitude in target normal direction (E_x), and parallel to the target surfaces (E_y), are plotted in (b) and (c) for t=0, and in (d) and (e) for t=44 fs, respectively. The field distributions are normalized using the maximum field values of The edge size of the boxes (b–e) corresponds to 18 μm. The trajectories of protons reaching more than 90% of the maximum energy (E_>0.9) are overlaid in black. (f) For these protons, the increase of the deflection angle α_cent with time is shown in green, together with the evolution of the maximum energy of protons emitted under sample angles α of 6° (blue), −1° (black) and −5° (red). For illustration of the timescale, the laser pulse profile is given by the red shaded region and the black gaussian-shaped curve. For the duration of the laser pulse τ, the asymmetry of the electron distribution translates into a non-target-normal emission of energetic protons that can be detected experimentally.