Particle acceleration up to the confinement limit of the system. Top panel: time evolution of the total ion spectrum γ_idN/dγ_i (color-coded solid lines). The final total electron spectrum is shown for comparison as a function of γ_eβ_e × (m_e/m_i) to compare the energy scales rather than the Lorentz factors between the two species (black dashed line). A −2.2 power-law slope is shown for comparison (dotted line). Bottom panel: time evolution of the maximum ion Lorentz factor γ_i, max (blue solid line) and the latitudinal width of the shock front cavity normalized to the full jet width (W_c, red circles). The jet confinement limit, γ_H, is marked by the horizontal dotted line. The blue dashed line shows a simple empirical formula that captures the time evolution of γ_i, max.