Figure 2.

(a) and (b) highlight the dynamics of transiting protons through the HC obtained by particle tracing simulations, carried out using a source delivering a poly-energetic and divergent beam of protons in the setup shown in Fig 1a, with dimensions of the HC target used for the case shown in Fig. 1b. The simulation used the EM pulse profile measured in the experiment by proton probing, in a similar way as described in ref.¹⁶ and follows the propagation of protons with initial energy in the range of 25-35 MeV ( i.e. with energies close to synchronisation with the moving field for this specific target design). (a) shows the change in energy of protons while travelling along the HC axis Z (with proton source at z=0 mm and HC spanning from z = 1.5 to 9.2 mm, as per the experimental setup). (b) shows their divergence at $\mathit{z}=20\text{mm}$, i.e. $\sim 1\text{cm}$ after emerging from the HC. In both graphs, the vertical axis refers to final output energy of the protons while the colormap indicates their energy at the source. (c–e) show the energy spectrum, temporal and spatial spread respectively for protons in the collimated beam, having half angle divergence $\theta <0.4^{\circ }$.