Damping rate of the fast (upper panel) and slow (lower panel) magneto-acoustic waves, i.e. with the imaginary part of ω normalized by kv_A, vs. the normalized wavenumber a = k_zv_A/ν_in. The blue solid lines correspond to the solution of the single-fluid dispersion relation and the dashed line corresponds to the slow magneto-acoustic damping rate of Braginskii (the expressions used are from Forteza et al. 2007). Red asterisks are the solutions of the two-fluid dispersion relation, Eq. (57). The values are calculated for 10% of neutral hydrogen, ξ_n = 0.1, and for c_sn/v_A = 0.1. The damping rates are calculated for waves propagating with a 45° angle with regard to the magnetic field.