Axisymmetric MHD Modes in Twisted Magnetic Fields

Vortex flows in the solar atmosphere may contribute significantly to the energy flux requirements for heating the quiet Sun atmosphere. This thesis presents evidence that the expected number of vortices in the solar photosphere is significantly larger than estimated and most importantly their lifetime is, in the mean, much shorter than previously believed. This suggests that vortex flows are highly dynamic and that their formation and dissolution is highly temporally localised. The measurements and statistics that support this evidence were made possible by use of an automated vortex identification approach which allowed for a much larger sample. In fact the number of identified vortices is several orders of magnitude larger compared with the latest research on the subject.

Given that vortices in the solar photosphere can introduce magnetic twist, a pertinent question then is: "How would that magnetic twist affect axisymmetric MHD modes?". Part of this thesis visits this question and the theoretical models used offer interesting answers. Firstly, even for weak magnetic twist the long wavelength cut-off for the sausage mode that is present in models without magnetic twist, is removed! It is shown that magnetic twist naturally couples axisymmetric Alfven waves with sausage waves. A coupling that results, among other things, in sausage waves exhibiting Doppler signatures similar to these expected to be observed in Alfven waves. These modes can also be excited by a larger variety of drivers compared to the pure sausage and axisymmetric Alfven waves. Something that makes them more pertinent to the question of energy propagation than their pure cousins (sausage and Alfven waves).

Lastly, a calculation is presented, for the first time, of a dispersion relation for resonantly damped axisymmetric modes, in the spectrum of the Alfven continuum and also an approximation is presented of the damping time in the long wavelength limit. It is shown that the damping times can be comparable to that observed for the kink mode in the case that there is no magnetic twist.