Damping rate (imaginary part of frequency) of Alfvén waves, ϖ = ω/k_zv_A, vs. normalized Alfvén frequency, a = k_zv_A/ν_H, for three different values of chromospheric temperature. Blue crosses correspond to the damping rates due to ion collision with neutral hydrogen atoms only, while red asterisks correspond to the damping rates due to ion collision with both, neutral hydrogen and neutral helium atoms. Red (blue) solid line corresponds to the damping rate derived in the single-fluid approach (Eq. (32)) with (without) neutral helium.