I. The effect of symmetric and spatially varying equilibria and flow on MHD wave modes: slab geometry

Realistic theoretical models of magnetohydrodynamic wave propagation in the different solar magnetic configurations are required to explain observational results, allowing magnetoseismology to be conducted and provide more accurate information about local plasma properties. The numerical approach described in this paper allows a dispersion diagram to be obtained for any arbitrary symmetric magnetic slab model of solar atmospheric features. This proposed technique implements the shooting method to match necessary boundary conditions on continuity of displacement and total pressure of the waveguide. The algorithm also implements fundamental physical knowledge of the sausage and kink modes such that both can be investigated. The dispersion diagrams for a number of analytic cases that model magnetohydrodynamic waves in a magnetic slab were successfully reproduced. This work is then extended by considering density structuring modelled as a series of Gaussian profiles and a sinc(x) function. A further case study investigates properties of MHD wave modes in a coronal slab with a non-uniform background plasma flow, for which the governing equations are derived. It is found that the dispersive properties of slow body modes are more greatly altered than those of fast modes when any equilibrium inhomogeneity is increased, including background flow. The spatial structure of the eigenfunctions is also modified, introducing extra nodes and points of inflexion that may be of interest to observers.