Comparison of timescales and determination of the maximum energy of protons, E_max, p. Central panel: E_max, p versus the shock-accelerated particle pressure, P̃, normalised to the ram pressure for different jet velocities, U, in units of km s⁻¹ (black labels). Solid and dashed orange lines show values of E_max, p constrained by the Coulomb and pion losses, respectively. Solid green lines show E_max, p constrained by the downstream diffusion timescale. Upper and lower panels: timescales involved in the calculation of E_max, p (Eqs. (3)–(7)) for three sets of U and P̃; B = 100 μG, n = 10⁶ cm⁻³, ℓ_⊥ = 400 AU, and R = 12 612 AU.