Damping time, in units of the internal filament Alfvén crossing time, τAf = a/vAf, as function of the three relevant parameters for kink oscillations in one-dimensional thread models: a) the magnetic Reynolds number, Rm = vAfa/η; b) the density contrast, ρf/ρc; and c) the transverse inhomogeneity length-scale, l/a. Solid lines indicate the 1D solution, while symbols represent the numerical 2D solutions obtained with Lthread = L. In a) and c) the density contrast is ρf/ρc = 200. In b), l/a = 0.2. In b) and c) Rm = 106. All computations have been performed in a two-dimensional grid with Nr = 401 and Nz = 51 points, with 250 grid-points in the radial transitional layer. Lengths are normalised to a = 1 and L = 50a.
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