Transverse Oscillations of Non-Planar Coronal Loops

In this thesis a non-planar coronal loop model is introduced. The loop has helical geometry and therefore has non-zero curvature and torsion. A curvilinear coordinate system is introduced, which uses the loop axis as a coordinate line and the loop boundary as a coordinate surface. We assume that the density along the loop is stratified. The governing equation for kink oscillations of the loop is derived under the assumption of the thin tube approximation. It is found that the governing equation has the same form as the governing equation for a straight loop with density varying along the tube. Therefore we find that the curvature and torsion do not directly affect the eigenfrequencies, although they still affect the eigenfrequencies indirectly through modifying the density profile along the loop. The main effect of the loop torsion is that it alters the polarization of the oscillation. We find that, for a loop with non-zero torsion, the direction of polarization rotates with the principal normal as we move along the loop. Observational signatures of kink oscillations of a non-planar loop are discussed.

We also investigate whether the non-planarity of a loop has any effect on the results of coronal seismology. We consider two seismological applications: the estimate of the density scale height in the corona using the ratio of the periods of the fundamental harmonic and first overtone of kink oscillations, and the estimate of the magnetic field strength obtained from the period of the fundamental harmonic and the loop length. We show that the non-planarity of the loop does not affect the period ratio, and therefore does not change estimates of the density scale height, and we find that density stratification and loop non-planarity only have a weak effect on estimates of the magnetic field strength.