Left: total loss-rate (black solid line) and acceleration rates (red lines) for different values of the efficiency parameter η: the Cygnus X-1 model (solid line, η = 6 × 10⁻⁴), η = 10⁻² (dashed line) and η = 0.1 (dotted line). Middle: acceleration rate (red solid line, η = 6 × 10⁻⁴), total loss rate (black lines), and proton–proton loss-rate (green lines) for different bulk Lorentz factors: that of Cygnus X-1 (solid line, Γ = 1.25), Γ = 1.034 (dashed line), and Γ = 5 (dotted line). Right: acceleration rate (red solid line) for the case of Cygnus X-1, and total loss rate (black lines) and proton–proton loss-rate (green lines) for different jet luminosities, i.e. L_jet: that of Cygnus X-1 (solid line, L_jet = 10³⁸ erg s⁻¹), L_jet = 10³⁹ erg s⁻¹ (dashed line), and L_jet = 10⁴⁰ erg s⁻¹ (dotted line). All panels refer to the jet base.