Magnetohydrodynamic Waves in Cylindrical and Multi-slab Environments

The investigation of magnetohydrodynamic (MHD) wave propagation in different equilibrium configurations is important for the development of solar magneto-seismology (SMS). The applicable models of solar atmospheric waveguides are studied in the framework of Cartesian and cylindrical geometries. First, a magnetised plasma slab sandwiched between an arbitrary number of non-magnetic/ magnetic layers are considered and an analytical approach is used for the derivation of its dispersion relation. The amplitudes of the eigenmodes depend on the equilibrium structuring and the model parameters; this motivates an application as a solar magneto-seismology tool. Specific cases of two- and three-layered slabs are studied in detail and their potential applicability to magnetic bright points is discussed. Furthermore, the resonant damping of propagating kink waves is studied in a straight magnetic flux tube with the density varying along the tube taking into account the magnetic loop expansion. Also non-stationary magnetic tubes to model, for example, cooling coronal loops is considered. In particular, it was found that cooling enhances the wave amplitude and the loop expansion makes this effect more pronounced. After, we analyse 10 driven kink oscillations in coronal loops to further investigate the ability of expansion and cooling to explain complex damping profiles. The used approach could allow to infer some important diagnostic information (such as, for example, the density ratio at the loop foot-points) from the oscillation profile alone, without detailed measurements of the loop and without complex numerical methods. The results imply the existence of correlations between the density ratio at the loop foot-points and the amplitudes and periods of the
oscillations. As well, we compare our results to previous models, namely purely Gaussian and purely exponential damping profiles, through the calculation of χ
2 values, finding the inclusion of cooling can produce better fits in some cases. The current study indicates that thermal evolution should be
included in kink-mode oscillation models in the future to help us to better understand oscillations that are not purely Gaussian or exponential. Finally, fluting oscillations in a thin straight expanding magnetic flux tube in the presence of background flow are considered. The method of multiple scales is used for the derivation of the system of governing equations. We have found that the amplitude increases due to cooling and is higher for a higher expansion factor. Higher values of the wave number lead to localisation of the oscillation closer to the boundary. We show that the higher the value of the ratio of internal and external plasma densities, the higher the amplification of oscillation due to cooling. So, not only the wave number plays an important role in the evolution of the cooling system, but also the
density ratio and the variation of tube expansion are relevant parameters in the cooling process of an oscillating flux tube.