Comparison of the trajectories of two typical energetic protons of the ambient plasma in the single- and double-shock cases in the left column (1) and right column (2), respectively. In their evolution between 0 and 2.5 ns we can distinguish different phases (I, II, II*a, II*b, III), that are detailed in the main text. In (a1–a2) and (b1–b2), the maps of the E_x and of the E_y fields in the x − t space, together with the trajectories of the chosen protons, are shown, respectively. Note the different scales for the electric fields E_x and E_y color maps. In (c1–c2), the proton trajectories in the v_x − v_y space and the temporal points delimiting the different phases, are plotted. The color of the proton trajectories in (a1–a2), (b1–b2), and (c1–c2) follows the evolution of their kinetic energy K on a color scale from 0 to 20 keV. In (d1–d2), are shown the temporal evolution of the kinetic energies of the two tracked protons (full green line), the work done by E_x (dashed red line) and by E_y (dashed blue line).