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Kink and Sausage Modes in Nonuniform Magnetic Slabs with Continuous Transverse Density Distributions

We examine the influence of a continuous density structuring transverse to coronal slabs on the dispersive properties of fundamental standing kink and sausage modes supported therein. We derive generic dispersion relations (DRs) governing linear fast waves in pressureless straight slabs with general transverse density distributions, and focus on the cases where the density inhomogeneity takes place in a layer of arbitrary width and in arbitrary form. The physical relevance of the solutions to the DRs is demonstrated by the corresponding time-dependent computations. For all profiles examined, the lowest-order kink modes are trapped regardless of longitudinal wavenumber $k$. A continuous density distribution introduces a difference to their periods of $\lesssim 13\%$ when $k$ is the observed range, relative to the case where the density profile takes a step-function form. Sausage modes and other branches of kink modes are leaky at small $k$, and their periods and damping times are heavily influenced by how the transverse density profile is prescribed, the lengthscale in particular. These modes have sufficiently high quality to be observable only for physical parameters representative of flare loops. We conclude that while the simpler DR pertinent to a step-function profile can be used for the lowest-order kink modes, the detailed information on the transverse density structuring needs to be incorporated into studies of sausage modes and higher-order kink modes.