Mathematical Modelling of MHD Waves in Asymmetric Waveguides with Applications to Solar Physics

The highly structured, complex and coupled system constituted by the solar atmosphere is permeated by ubiquitous magnetic fields. Together with gravity, they create a wide variety of waveguides which are able to support magnetohydrodynamic (MHD) waves. The aim of the present work is to study these waves using a family of multilayered Cartesian waveguide configurations of solar atmospheric features, in order to develop models and diagnostic tools applicable to a collection of features within the solar atmosphere. In particular, I investigate the effect of incorporating various sources of asymmetry into the classical model of a magnetic slab on the waves supported by the system. The initially considered configuration is a static magnetic slab filled with uniform, inviscid, ideal plasma, which is embedded in an asymmetric, magnetic environment. I derive the equation governing the dispersion of magneto-acoustic waves in this slab system, and describe the behaviour of quasi-kink and quasi-sausage eigenmodes. I proceed to conduct a detailed analytical and numerical investigation of trapped waves that may be supported by this slab system under various orderings of the characteristic speeds. I utilise these approximations to provide a list of potential applications of this slab model to solar atmospheric waveguides, from the global stratification of the layers of the solar atmosphere down to small-scale phenomena such as the environment of magnetic bright points. Finally, I focus on generalising pre-existent and developing new techniques of solar magneto-seismology. I investigate both propagating and standing waves in asymmetric magnetic and non-magnetic slab systems, and I use the mixed character of the eigenmodes to provide tools for diagnosing the solar atmospheric plasma and determining unknown parameters that would be difficult to measure directly, such as Alfvén speed values.