In this thesis, we focus on studying the properties of the large-amplitude prominence oscillations (LAOs) using the realistic prominence models and the triggering of such motions by external perturbations. LAOs involve motions with velocity amplitudes above 20 km/s, and large portions of the filament move in phase, indicating a strong connection with the magnetic field structure of the filament. Such motions are triggered by solar energetic events such as distant or nearby flares, jets, and eruptions. The motivation of this work comes from the recent studies that have shown that LAOs are very common in prominences and open a new window to study the prominence structure by means of a technique known as prominence seismology, which combines observations and theoretical modeling of LAOs. This study is based on time-dependent numerical simulations performed with the magnetohydrodynamic (MHD) code MANCHA3D.

In the first part of this work, we perform 2.5D numerical simulations of LAOs using a magnetic flux rope model formed from a sheared arcade configuration using converging motions at the foot points. We artificially load the prominence mass in the magnetic dips of the flux rope, and then we apply horizontal and vertical perturbations to excite the different oscillation modes. Horizontal triggering excites the large-amplitude longitudinal oscillations (LALOs) together with the vertical small-amplitude oscillations (SAOs) caused by the back-reaction of the magnetic field. The period of the longitudinal oscillations decreases with decreasing of the radius of curvature of the magnetic field lines, in agreement with the pendulum model. Vertical perturbation triggers the vertical LAOs of the prominence plasma and the symmetric oscillations along the magnetic field. These latter motions are caused by compression and rarefaction of the plasma. The vertical LAOs are very synchronized in the different prominence regions, and their period remains constant with height. This suggests that the vertical mode corresponds to the global normal mode of the prominence structure. Analysis of the time-distance diagram of the transverse velocity reveals the presence of the fast magnetoacoustic waves emitted from the prominence region. This makes us suggest that wave leakage can be responsible for the damping of the vertical LAOs in this experiment. We have compared the properties of the modes of the longitudinal and transverse oscillations in the prominence models with the different shear angles of the magnetic structure and the prominence density contrasts. We have found that only the variation of the shear angle slightly affects the period of the LALOs. This is associated with the variation of the radii curvature in the 2D projection in these models. The period of the vertical oscillations slightly depends on the density due to the effect of the prominence inertia. We have also studied the excitation of the LAOs in the flux rope prominence by an external perturbation. This experiment shows that the wave from the energetic event strongly perturbs the flux rope magnetic field structure. The prominence mass follows those changes in the magnetic field configuration and moves from the equilibrium position due to the motion of the magnetic field. This strong perturbation of the rope produces the motion of the prominence plasma, but there is no direct wave front from the energetic event reaching the prominence mass.
The external disturbance perturbs the flux rope exciting oscillations of both polarizations. Their properties are a mixture of those excited by purely horizontal and vertical excitation. For the experiment with horizontal triggering, we perform convergence studies, and we find that the damping of the oscillation is mainly numerical, but the numerical effects can be reduced by increasing the spatial resolution. This motivates the numerical experiments presented in the following.

In the second part of the work, we have studied the influence of spatial resolution on numerical experiments of LALOs. We perform time-dependent numerical simulations of LALOs using the 2D magnetic configuration with the prominence mass loaded at its dips. We trigger LALOs by perturbing the prominence mass along the magnetic field. We perform the experiments with four values of spatial resolution: 240, 120, 60, and 30 km. We have studied the properties of LALOs in the different prominence regions. At the bottom and central prominence regions, we obtain that LALOs are strongly damped even using the high-resolution simulations. Comparing the damping time in the different experiments, we find that it increases significantly when we gradually increase a spatial resolution. However, the difference between the experiments with spatial resolution $30$ and $60$ km is relatively small. This suggests that a further improvement of the spatial resolution should not significantly affect the damping time. This also indicates that some physical mechanism might be responsible for the attenuation in this prominence region rather than the numerical dissipation. At the top prominence region, the plasma motions are surprisingly amplified in the first phase, during 130 minutes, and slowly decay in the second phase. The amplification becomes even more efficient with the improvement of the spatial resolution. In order to understand further the reason for the strong damping at the bottom and the amplification at the top, we have analyzed the temporal evolution of the different energy contributions. The analysis reveals that a portion of the energy is emitted in the surrounding corona due to wave leakage. The time-distance diagram of the transverse velocity confirms the existence of waves propagating upward. The Lorentz force acts in an opposite way at the upper prominence region than at the bottom. It does positive work during the initial stage of oscillations and can be responsible for the acceleration of the plasma. We have analyzed the time-integral of the incoming Poynting flux at the top and bottom prominence regions. The analysis reveals that a significant portion of the magnetic flux that leaves the bottom region is transferred to the top. We conclude that the strong attenuation of the oscillations at the bottom region is caused partially by the wave leakage and the energy and momentum transfer across the field lines from the bottom to the top prominence regions. We conclude that the high-resolution experiments are crucial when studying the periods and the damping mechanism of LALOs. The period agrees well with the pendulum model only when using a sufficiently high spatial resolution. The results suggest that numerical diffusion in simulations with insufficient spatial resolution can hide important physical effects, such as the amplification of the oscillations.

In the last part of this thesis, we have studied the excitation of LAOs by external perturbations considering both the flux rope and dipped arcade magnetic configurations. We consider two different types of external disturbances. The first type is associated with an eruptive event near the flux rope prominence. The second type implies using an artificial perturbation located at a certain distance from two flux rope prominences or the dipped arcade containing the prominence. In the first experiment, when the eruption acts as an external perturbation, we obtain that this eruption does not produce LAOs in the prominence located in its vicinity. However, the eruption produces changes in the magnetic configuration of the prominence and triggers the SAOs. During the eruption, an elongated current sheet is formed behind the erupting flux rope. The reconnection inflows also affect the prominence magnetic field. In addition, the current sheet becomes unstable, and magnetic islands start to form in it. After these plasmoids are formed, they move upward or downward. Those plasmoids that propagate downward cause perturbations in the velocity field by colliding with the post-reconnection loops. This velocity perturbation propagates in the surroundings and enters the flux rope causing the disturbance of the prominence mass. The analysis of the oscillatory motions of the prominence plasma in the flux rope shows that only SAOs are excited due to the nearby eruption and the plasmoid instability. The motions have a complex character showing a mixture of longitudinal and transverse oscillations with short and long periods.

Another series of experiments with a distant artificial perturbation shows that the wave created by such an energetic event can propagate across the magnetic field, reaching both the closer and further flux rope prominences. The study of the motions reveals the excitation of the transverse LAOs and longitudinal SAOs in both prominences. The properties of the oscillations, such as amplitudes, periods, and damping times, are similar in both flux ropes. In the upper region of the flux ropes, the amplitude of the longitudinal SAOs gradually increases during the first minutes after the wave front propagation. In this experiment, the wave front produces the inclination of the magnetic field of the flux rope. Later the magnetic field recovers its initial configuration. The prominence plasma follows the motion of the flux rope, increasing the amplitude of the longitudinal oscillation.

Finally, we have studied the external triggering of LAOs in a dipped arcade model. The analysis shows that even though the normal vector of the wave front is parallel to the spine of the magnetic configuration, this perturbation does not excite LALOs. When the wave front approaches the prominence, it pushes the dense plasma down. Therefore, the wave triggers the vertical LAOs and motions due to compression and rarefaction along the magnetic field.