Influence of the beam velocity in the weak-beam limit n₁ ≪ n₀ (i.e., r_n = 10⁻³). Panel a: maximum values of ω_i for different beam velocities obtained from the solutions of the linear dispersion relation (dots) and simulations (crosses) with fit function (solid line). Panel b: integrated growth rates from numerical solutions of the dispersion relation (dots) and from simulations (crosses) with fit function (solid line). Panel c: fractional bandwidth Δω_r at the point where ω_i is at its maximum, normalised to the corresponding real part of frequency ω_r, obtained from linear theory (dots) and simulation (crosses). All three figures for ρ₀ = ρ₁ = 1, r_n = 10⁻³.