Figure 4b plots the temporal evolution of the maximum proton energy \(\mathcal {E}_{\textrm{max}}\) for the three targets in Fig. The H-rod target is just the same component embedded in the MNA target, which is irradiated by a \(10\upmu\)m-wide (FWHM) Gaussian pulse. The maximum proton energy \(\mathcal {E}_p\) is then a function only of the initial diameter D and the density. 8 Scaling of the maximum proton energy \(\mathcal {E}_{\textrm{max}}\) versus the laser intensity \(I_L\), under the different laser and target conditions. The coherent results for the maximum proton energy \(\mathcal {E}_p\) are given in Fig.