## Abstract

Many previous studies of MHD modes in the magnetic flux tubes were focussed on deriving a dispersion relation for cylindrical waveguides. However, from observations it is well known that, for example, the cross-sectional shape of sunspots and pores are not perfect circles and can often be much better approximated by ellipses. From a theoretical point of view, any imbalance in a waveguideâ€™s diameters, even if very small, will move the study of the problem from cylindrical to elliptical coordinates. In this talk, I will therefore describe a model that predicts the MHD wave modes that can be trapped and propagate in a compressible magnetic flux tube with an elliptical cross-section embedded in a magnetic environment. I will discuss the resultant dispersion relations for body and surface modes, then then I will show how the ellipticity of a magnetic flux tube effects these solutions (with specific applications to the coronal and photospheric conditions). From a practical point of view the information from these dispersion diagrams does not show how these MHD modes will manifest themselves in observational data. Therefore, I will also present several visualisations of the eigenfunctions of these MHD wave modes and explain how the eccentricity effects each wave mode.