Author:

Abstract:

The Sun directly impacts many processes on our planet, from climate to the sustenance of life. While it needs no promoting, this makes it the most important astrophysical object of study. Despite its obvious importance for us, it is safe to say that the Sun-Earth connection is far from being completely understood. The Sun exerts influence mostly by its luminosity, i.e. electromagnetic radiation, but also through its magnetic activity, leading to the solar wind and space weather, i.e. a variable but continuous flux of charged particles originating from its dynamic atmosphere. Better understanding of space weather is essential as we rely more and more on space-based technologies and as we fare further away from Earth on space exploration missions. The driving force and origin of space weather is the magnetically dominated solar corona, which is still enigmatic from a physical point of view. Foremost, the almost 80-year-old mystery of how it is heated to multi-million degrees constitutes the famous coronal heating problem. The theories put forth to solve this conundrum can be put in two separate boxes (even if they might act together): the so-called direct-current models, in which the slow shear of the magnetic field lines leads to small reconnection events called nanoflares, and the alternative-current model, in which waves
generated by the turbulent convection at the Sun's surface get dissipated as they propagate upwards. In this thesis, we focus on wave behaviour in the solar corona, within the framework of magnetohydrodynamics (MHD). The importance of a better understanding of wave phenomena is twofold: on the one hand, as previously mentioned, waves are a potential candidate for coronal heating; on the other hand, as properties of waves hold clues about the medium they propagate in, they can be used as diagnostic tools for the elusive physical properties of the solar corona, within the field of coronal seismology. The corona is not homogeneous, as the complex magnetic field configuration dictates its appearance. In this sense, we distinguish the open magnetic field corona, which are cooler regions, mostly situated at the Sun's poles, and the closed magnetic field corona, which present the majestic coronal loops, arch-like plasma structures outlining the magnetic field. Coronal loops are central to coronal wave studies, as structuring introduces many interesting phenomena, such as surface waves, wave damping, mode coupling, resonant absorption, phase mixing, and so on. The analytical framework for these much-studied mechanisms is well developed, however, moving away from symmetric and linear problems to more realistic, nonlinear dynamics is made possible with recent advances in numerical computing power. Much of the work carried out and presented in this thesis is thus concerning the nonlinear aspects of wave behaviour in the structured corona, using numerical simulations, with implications for both the coronal heating problem and coronal seismology, the two prime outcomes of coronal wave studies. The first three studies presented in the results chapter focus on standing kink waves in coronal loops modeled as straight cylindrical flux tubes. The effects of radiative cooling, large amplitudes, and a twisted magnetic field on the oscillation properties are presented. In all cases, nonlinearities, among which the most prominent one is the development of the Kelvin-Helmholtz instability around the loop, are shown to induce considerable deviations from analyitical results, e.g. in damping time and oscillation period. These have an impact on some seismological estimates that are based on these values, and on wave heating. Furthermore, it is hinting at the possibly complex and turbulent internal structure of coronal loops, which is further explained by studying the effect of propagating transverse waves in an inhomogeneous plasma. It is shown for the first time that turbulence can be generated from unidirectionally propagating waves, constituting a paradigm shift in MHD turbulence in general, not only for the coronal setting. Finally, the capabilities of the promising and emerging field of dynamic coronal seismology is evaluated. Based on the ubiquity of the transverse propagating Alfvénic waves observed in the solar corona, the possibility of continuous diagnostics for physical parameters such as magnetic field strengths would constitute advances in our understanding of coronal evolution. It is shown that, despite both theoretical and observational limitations, reliable magnetic field estimates can
be achieved, robust to widely different simulated conditions, which are expected to be present in the corona.