Left panel: simulated proton energy spectra at the shock at t = 100, 500, and 1500 s for three selected field lines. The blue line in each panel shows, for reference, the spectrum of protons constituting the seed-particle pool, I_seed (E) = p²f_seed(p), at t = 100 s. Right panel: corresponding simulated Alfvén wave power spectra P(f) at the shock plotted against f∕f_cp, where f_cp is the proton cyclotron frequency.