L_D/R vs. ν_in/ω for the kink wave in a magnetic flux tube with l/R = 0.2, α = 0.5, ζ = 10, F = 2/π, and ωR/v_k = 0.1. The solid line is the total damping length in the TT and TB approximations computed from Eq. (61). The dashed line is the damping length due to resonant absorption (Eq. (62)) only, and the dotted line is the damping length due to ion-neutral collisions (Eq. (63)) only. Symbols ◇ correspond to the full numerical eigenvalue results.