Linear growth rate of the instability Γ as function of the wavenumber k for two polarisation modes: circular right-handed (blue solid line) and left-handed (red solid line). Results for the simulations with three different values of CR density are presented: top panel corresponds to n_cr/n_i = 0.01, middle panel corresponds to n_cr/n_i = 5 × 10⁻³, and bottom panel corresponds to n_cr/n_i = 2 × 10⁻³. In each panel, the solid orange and green lines correspond to the theoretical growth rate using the solution of the full dispersion relation Eq. (16). Black dotted line follows the expectation in test-particle limit from Eq. (13).