ABSTRACT
We study dispersion properties of fast-sausage waves in a radially structured coronal magnetic tube with continuous radial density distribution. The models, containing either a non-uniform core or inhomogeneous external medium are considered. The dispersion relations are obtained for a power law density distribution in the corresponding non-uniform region, where the power-law index controls the steepness of the tube boundary. The governing wave equations with varying coefficients were solved with the Wentzel–Kramers–Brillouin (WKB) approximation. The model with the non-uniform core supports the existence of trapped and leaky sausage modes. The density non-uniformity in the core modifies the values of cut-off wave numbers kc. The smaller values of cut-offs, normalized to the effective tube radius r0, correspond to the smaller power index p. The wave dispersion (i.e. dVph/dk) decreases for smaller p. This occurs in the range of not too small longitudinal wave numbers k > kc. For the model, containing inhomogeneous environment the basic dispersion properties are generally identical to that for the monolithic tube model, studied in Lopin & Nagorny (2015b). The waves are trapped for all wave numbers, if the power-law index 0 < n < 2. There are both trapped and leaky regimes for n ≥ 2. The wave dispersion decreases for smaller n, in the range of the intermediate values of the longitudinal wave numbers k > kc. The seismological application of the obtained results is discussed.
Polynomial mode approximation for longitudinal wave dispersion in circular rods
