Fig. 6: Simulation results illustrating the different acceleration regimes.
For representative simulation runs with d = 6.2 μm (left column), d = 18.5 μm (middle column) and d = 33.5 μm (right column) longitudinal proton phase spaces (a–c) and proton density distributions (d–f) are presented. The corresponding target density profiles are displayed in Fig. 4c. The first row shows the longitudinal proton phase spaces either at -22 fs (a, b) or at 75 fs (c). On-axis electric field component (Ey) and local laser strength parameter (\({a}_{{{{{{{{\rm{L}}}}}}}}}={[2{I}_{{{{{{{{\rm{L}}}}}}}}}/({n}_{{{{{{{{\rm{c}}}}}}}},800{{{{{{{\rm{nm}}}}}}}}}{m}_{{{{{{{{\rm{e}}}}}}}}}{c}^{3})]}^{1/2}\) with IL the laser intensity) are overlaid to demonstrate the accelerating field structure and the strength of the pulse, respectively. In addition to the proton density distribution (d–f) in the xy-plane at +120 fs, the Bz component is shown in the bottom half of f to demonstrate the magnetic field structure. The third row (g–i) provides the temporal evolution of the position of the front at which the plasma density reaches the critical (green) as well as the relativistically critical density (orange). Additionally, the position of the laser pulse peak (red) and of the highest energy protons (blue) is shown. The grey shaded area in the third row indicates the region in which the target density is initially above nc,800nm. The red dotted line shows the theoretical laser peak position in the case when no target would be present. Note the different y-scales in g, h and i.
