In these two panels, the proton flux is plotted as in Fig. D.2 with the exception of the Alfvénic speed V_a for which different values are assumed as indicated. When diffusive reacceleration vanishes, we expect the proton flux to be given by the analytic solution u_loss. The relative difference between the numerical result u (direct inversion) and u_loss is calculated with the low-energy boundary prescription L3. As V_a increases from 1 m s⁻¹ to 2.5 km s⁻¹, u becomes more stable and wiggles disappear. The transition occurs for a critical value of V_a  ∼  1.75 km s⁻¹. The number of bins per decade of energy is N_dec = 50.