The Effect of Loop Curvature on Coronal Loop Kink Oscillations

We will review analytical and numerical efforts in modelling the influence of curvature on coronal loop oscillations. We will mainly focus our attention on fast kink mode oscillations. A curved slab model will be presented, where it becomes clear that curvature introduces wave leakage into the system, because of changes in the equilibrium. The importance of leakage will be assessed through the use of a slab and cylindrical model where lateral leakage is allowed. A full analytical model for a semi-toroidal loop will be constructed for a system with no leaking waves but with an inhomogeneous layer that introduces damping due to the process of resonant absorption. The model for a semi-toroidal loop will be extended to also include leakage, and will be studied numerically. The numerical results will be compared to the analytical model.