Time-dependent Resonant Damping in Coronal Loops

This Thesis will extend the current theory of propagating, linear MHD waves into a cylindrical model containing a time-dependent background density. The current observations of propagating waves in the solar corona clearly show that the magnetic waveguides contain many time-dependent features which have, to date, been excluded from the majority of theoretical models investigating MHD wave propagation. Analysing a straight magnetic flux tube, to leading order in the WKB approximation, allows for the derivation of two governing equations describing the perturbed total pressure and the radial displacement. These governing equations allow for the formation of the general dispersion relation and, taking the thin-tube limit, a full expression for the wave phase can be determined. Using the wave phase, it is possible to calculate the dynamic frequency, dynamic wavenumber and amplitude of the various wave modes and then the temporal evolution of these quantities can be explored.

By introducing a thin annular layer, smoothly joining the interior and exterior of the flux tube, an investigation into the resonant damping of the propagating MHD waves can be conducted. Analytical expressions for the resonant jump conditions and the damping coefficient for the fast MHD wave can be found and their temporal evolution explored.