Relativistic particle energy distributions for protons (left panel) and electrons (right panel). The coloured scale shows the distribution at each cell. The black line represents the total energy distribution (i.e. the sum over all cells). The green line corresponds to an alternative scenario with optimistic acceleration and injection, where the maximum energy is given by $E_{\max }=q_{\mathrm{e}}\sqrt{4\left(0.5L_{\mathrm{out}}\right)/c}$, the luminosity injected into protons is $L_{\mathrm{inj}}^p=0.1L_{\mathrm{out}}$, and with a harder spectral index p > −2. The optimistic approach is not applicable for electrons due to synchrotron losses at energies E ≳ 120 GeV.