Snapshots of the proton distributions at time ω_pct = 300, when all simulations are approaching the end of the linear phase, from simulations with electron κ indices κ = 20, 7, and 5. Left: Beam phase-space distribution. Middle and right: Beam and core velocity distributions, respectively, averaged in x (blue lines), cut at x/λ_Dc = 0 (orange line) and at x/λ_Dc = 25 (green line). The vertical dashed lines indicate the theoretical estimates of the resonant velocity.