Aplicación de la propuesta y análisis de los resultados:

Understanding the mechanism for the excitation of MHD waves is one of the main current goals in coronal physics. The generation and the consequent evolution of MHD modes do not only depend upon the properties of the magnetic waveguide (density stratification, geometrical structure, multi-stranded internal structure, etc.), but also on the characteristics of the driver (e.g. impulsiveness, spatial location, spatial broad- ness). Impulsive energy releases, such as flares and CMEs, are usually regarded as drivers for the excitation of fast and slow MHD waves (see Sec. 2, 6 and 7), while details of the excitation mechanisms remain unknown. Here, we briefly describe the state-of-the-art of mechanisms for the excitation of kink modes in coronal loops.

The first evidence of kink oscillations with TRACE (Aschwanden et al. 1999; Nakariakov et al. 1999) in association with a flare led to the conclusion that a flare- generated blast wave may be responsible for the excitation of transverse displacements of a coronal loop: the loop is pushed outward by the flare-generated shock wave and then freely oscillates with the period prescribed by the density contrast ρ0/ρe inside

and outside the loop, and its length-to-width ratioL/a. In this scenario, horizontally and vertically polarised oscillations are not necessarily excited with similar efficiency, because of the effect of the location of the loop within the set of field lines having the same magnetic connectivity (Selwa et al. 2011). This result is consistent with obser- vations, as vertical kink oscillations (e.g. Wang and Solanki 2004; White et al. 2012; Kim et al. 2014) have been detected much more rarely than horizontal. However, this scenario is not fully confirmed by numerical simulations, which show that it is difficult to excite perturbations with the observed displacement amplitude in a loop with a low

ρ0/ρe, e.g. of 2 or 3, typical for EUV coronal loops (e.g. Terradas et al. 2007; McLaugh-

lin and Ofman 2008; Ofman 2009a). In addition, it is easy to find events where kink oscillations are not triggered by a strong flare when no CME is accompanied.

The preferential excitation of horizontal oscillations of coronal loops may be ex- plained in terms of Alfv´enic vortex shedding due to a plasma upflows associated with the lift-off of a coronal mass ejections or eruptions. Indeed, the loop top is regarded as an obstacle or bluff body that modifies the flow pattern and generates a sequence of vortices shed alternately from either side of the loop, forming a downstream von K´arm´an vortex street. If the magnetic field in the plasma that is dragged in the ver- tical direction by the flow is parallel to the loop, the loop top experiences a periodic force which is perpendicular to both the flow velocity and the axis of the loop, and hence is in the horizontal direction, see Fig. 38. The period of the force is determined by the flow speedvand the loop’s minor radius,a, as

Pvort≈10a/v. (57)

The oscillations are most effectively excited when the force caused by vortex shed- ding is in resonance with the natural frequency of the kink oscillations, e.g. with the

Upflow

Fig. 38 Sketch of the excitation mechanism for horizontally polarised kink oscillations of coronal loops by a steady up flow, based upon periodic shedding of Alfv´enic vortices.

frequency of the global mode,Pvort ≈Pkink (see Eq. (41)). This model could explain

the selectivity in the excitation of the loops oscillations (only those whose natural kink frequency matches the vortex shedding frequency are excited) and the initial growth of the oscillation amplitude, detected in some cases (Nakariakov et al. 2009; Gruszecki et al. 2010). However, observational confirmation of this mechanism is still absent.

Oscillating loops detected close to topologically unstable magnetic regions, i.e. near the magnetic separatrix, led to the idea of excitation by rocking motions at the pho- tospheric level. In this model, a small displacement of the loop footpoint caused, e.g., by a wave propagating in the photosphere, is magnified by the sensitivity of the equi- librium magnetic topology to a small perturbation (Schrijver and Brown 2000; White et al. 2013). Thus, in this model the observed large-amplitude displacements of the loop in the corona are not connected with any natural mode of oscillation, but are sim- ply adiabatic gradual occurrence of a series of equilibria. This model is not commonly accepted, as the observed periodicities are close to the expected natural frequencies of kink oscillations.

Furthermore, the evidence of the new regime of low-amplitude decay-less kink os- cillations against the standard rapidly-decaying regime (Sec. 6.1) raises new questions about the mechanism of excitations. These transverse oscillations of a new kind are not

(a)

(b)(b)

(c)

Fig. 39 Schematic illustration of the most common mechanism for the excitation of the high- amplitude decaying kink oscillations of coronal loops. (a) Pre-eruption state of the solar active region. (b) Displacement of a coronal loop (solid black curve) from its equilibrium position (dashed black line) by an erupting and expanding plasma structure (low-coronal eruption, LCE), e.g. a flux rope (grey loop-shaped structure). (c) Oscillatory relaxation of the loop to its equilibrium state after the eruption. (From Zimovets and Nakariakov 2015).

seen to be associated with flares or any bursty energy releases. The constant amplitude may result from some balance between persistent external driving, e.g. by granulation motion and leakage of sunspot oscillations, and damping, e.g. by resonant absorption. Recently, Zimovets and Nakariakov (2015) have performed detailed statistical study of a large sample of kink oscillation events in the corona observed in the EUV band by the AIA/SDO in 2010–2014. Special attention was payed to the high-amplitude rapidly decaying kink oscillations of coronal loops. The decay-less kink oscillations were not studied in that work. Almost all events studied were found to be accompanied by flares andlower coronal eruptions/ejections(LCEs for short). Thus, both these phenomena of solar activity could equiprobably be the cause of excitation of the oscillations. However, careful analysis of the observational data revealed that it is the LCEs which do excite the loop oscillations, but not the blast waves from flares. It is schematically illustrated in Fig. 39, c.f. also Fig. 7. Before the oscillation event, coronal loops are in their equilibrium state (Fig. 39a). During the event, an erupting plasma structure — a magnetic flux rope or a system of unstable loops (i.e. an LCE) — interacts with some (but not necessarily all) loops by its ram and/or magnetic pressure, causing the loops to displace from their equilibrium positions (Fig. 39b). After the erupting object has left the interaction region, the disturbed loops relax to the pre-eruption or to a new equilibrium state (Fig. 39c). Because of the inertia, the loops overshoot the equilibrium, and the decaying kink oscillations occur. Most events (95%) were established to follow the same scenario. Probably, the efficiency of this mechanism depends on the interaction time of the LCEs with loops and on relative angles between their axes. This should be checked in further researches. The found scenario is consistent with the previously observed domination of the horizontal polarisation of the kink oscillations of loops. However, it should be noted that in 5% of the studied events it was not possible to unambiguously determine the cause of the oscillations because of limitations of the observational data. It is not excluded that kink oscillations in those events could be excited by some other mechanisms than the discussed above.

Concerning the excitation of propagating kink waves (Sec. 7.2), observational works (e.g. Tomczyk and McIntosh 2009) showed that the waves have a power spectrum in which a power bump at the p-mode frequencies, about 5 minutes, is observed. Actually, the p-modes that are acoustic oscillations of the solar interior do not usually propagate

in the corona, as they are evanescent above the photosphere. However, in the presence of magnetic structuring of the plasma, they can perhaps leak upwards and be somehow converted in kink waves. In particular, De Pontieu et al. (2005) proposed that p-modes could reach coronal heights by nonlinear steepening of field-aligned acoustic waves in the case when the field is inclined away from the vertical. More realistic models for such a transfer of p-mode energy in the corona are needed to assess this possibility.

10 Interaction of MHD waves with partly-ionised boundaries

The ionosphere is the geophysical shell where the energy transfer from the Earth’s envi- ronment to the atmosphere occurs. Therefore, the description of processes in this region is of key importance for the solar-terrestrial physics, and it is particularly important for the MHD wave interaction with the ionosphere. ULF variations of the terrestrial electromagnetic field are effective tools for a continuous monitoring of dynamical phe- nomena in the magnetosphere and ionosphere. To apply effectively the ground-based magnetometer data it is important to know how well the ground distribution of the ULF field reflects the relevant wave structure in the magnetosphere.

In the context of the solar corona, the effects of partial ionisation come into play at the footpoints of coronal plasma structures, rooted at the dense and partly-ionised chromosphere. Also, a partly-ionised plasma can be found in solar prominences and cool jets.