MHD wave modes in the solar magnetic flux tubes with elliptical cross-section

by Anwar Ali Aldhafeeri

Hosted by Plasma Dynamics Group, The University of Sheffield on November 7, 2019


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 waveguide’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.