The 11th of October of 2019 Samuel F. Rial Lesaga defended his PhD Thesis: Temporal evolution of MHD wave in solar coronal arcades.

The aim of this thesis is to go a step further in the theoretical modeling of coronal loops. Following that direction, our main goal is to be able to theoretically reproduce part of the observed complexity that these structures display when asudden release of energy occurs in the solar corona. Since not too much time ago, the theoretical models of these features have been rather simple. In order to have simple solutions, these models use big approximations, such as, straight instead of curved structures, one-dimensional/two-dimensional structures, etc.

In order to go beyond that simple models, our aim is to increase the complexity of the theoretical models by adding what we think can be some key ingredients just like the curvature or three-dimensionality. In this work we will adopt the approach of increase the complexity of the model step by step to create a solid base of knowledge that helps us understand the underlying physics. Therefore we will begin with a well known two-dimensional problem and then we will allow perturbations propagate in the third direction as a first step towards three dimensionality. These are known as 2.5 dimensional models. Afterwards, we will add more ingredients such as a sharp model of coronal loop, di↵erent density profiles, curvature, etc. The study of coronal loop oscillations can be done from several points of view but in this thesis we will focus in two of them. The first one is to solve the time-dependent MHD equations by means of a temporal code. In the first two papers Rial et al. (2010) and Rial et al. (2013) we use this approach.

The second approach consists in solve the normal modes of the system. The standard method to do so can be in general a difficult task because an specially designed numerical code is needed. For that reason another goal of this thesis is to develop a technique that allow us to find an alternative way to find the normal modes of any system. In Rial et al. (2019) we explain how this technique works as well as its advantages and disadvantages. The fortmat of this thesis is the compendium of this articles:

- Rial, S., Arregui, I., Oliver, R. and Terradas, J.: 2019, Determining normal mode features from numerical simulations using CEOF analysis: I. Test case using transverse oscillations of a magnetic slab, ApJ 876(1), 86, doi:10.3847/1538-4357/ab1417
- Rial, S., Arregui, I., Terradas, J., Oliver, R. and Ballester, J. L.: 2010, Threedimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades, ApJ 713, 651661, doi:10.1088/0004-637X/713/1/651.
- Rial, S., Arregui, I., Terradas, J., Oliver, R. and Ballester, J. L.: 2013, Wave Leakage and Resonant Absorption in a Loop Embedded in a Coronal Arcade, ApJ 763, 16, doi:10.1088/0004-637X/763/1/16.

**File PhD thesis:**

**Title:**Temporal evolution of MHD wave in solar coronal arcades**Autor:**Samuel F. Rial Lesaga**Date:**11/10/2019**PhD program:**Física**Departament:**Física**Directors:**Dr. Íñigo Arregui Uribe-Echevarría i Dr. Ramón Oliver Herrero

*Figure 5 of the thesis. Snapshots of the two-dimensional distribution of the normal and perpendicular velocity components for ky L = 5 (top panels) and ky L = 60 (bottom panels). Some magnetic field lines (black curves) and the edge of the coronal loop (white lines) have been represented.**(Animations and color version of this figure are available in the online journal.*