PhD thesis defense: Nonlinear evolution of torsional Alfvén waves in solar atmospheric flux tubes

The Sun is a dynamic star made of plasma with a magnetized atmosphere, where magnetohydrodynamic (MHD) waves are frequently observed. In this Thesis, the nonlinear evolution of standing torsional Alfvén waves in solar coronal structures, such as coronal loops,  prominence threads, and coronal flux ropes, is investigated using three-dimensional numerical simulations. The open-source PLUTO code is used, which solves the nonlinear MHD equations using a finite volume formulation and implements the Adaptive Mesh Refinement technique. A coronal loop and a prominence thread are modeled as straight flux tubes filled with plasma that is denser than their environment. In turn, a coronal flux rope is modeled as a twisted magnetic field embedded in a uniform coronal plasma. The effect of the solar photosphere is included in the models through the line-tying boundary condition at the feet of the structures.

 

Standing torsional Alfvén waves are excited by perturbing the component of velocity perpendicular to the magnetic field lines. Owing to the spatially-varying Alfvén frequency across the flux tube, caused by the nonuniformity of density and/or magnetic field, Alfvén waves oscillate independently from each other in adjacent magnetic surfaces. As a result, such waves develop phase mixing, which generates shear flows and transports the wave energy towards larger and larger perpendicular wavenumbers as time increases. In this initial phase, the dynamics is quasi-linear.  Simultaneously, other MHD waves can appear during the evolution due to either linear or nonlinear coupling. Slow magnetoacoustic waves are nonlinearly generated due to the ponderomotive force, while fast magnetoacoustic sausage waves are linearly generated if magnetic twist is present. 

 

Eventually, the phase-mixing shear flows trigger the Kelvin-Helmholtz instability (KHi), whose onset is unavoidable in flux tubes with a straight magnetic field. In weakly twisted tubes, the onset of the KHi is delayed, but the dynamics is similar to that in straight tubes. However, in strongly magnetically twisted tubes, the magnetic tension can nonlinearly inhibit the KHi growth. The KHi onset time depends on several parameters of the model, such as the length of the flux tube, the initial velocity amplitude, or the transverse nonuniformity length scale. The KHi excites higher azimuthal modes than the torsional mode, and increases dramatically the values of vorticity and current density with respect to those found during the previous quasi-linear stage.

 

During the nonlinear evolution of the KHi, turbulence is naturally driven as the large KHi vortices break into smaller and smaller vortices. Turbulence is anisotropic and develops predominantly across the magnetic field direction. It further accelerates the energy transport to small scales initiated by the phase mixing.  In a prominence thread, important dissipative mechanisms  in the partially ionized prominence plasma, such as Ohm’s and ambipolar diffusion, are considered. However, it is found that the heating caused by these effects is irrelevant. In a coronal flux rope, the nonlinear KHi evolution leads to the presence of secondary instabilities that cause plasma compression. Such dynamics spontaneously generates permanent overdense filaments that are locally aligned with the  magnetic field. 

 

Finally, possible observational imprints of the described evolution are explored using synthetic modelling of EUV emission in the case of the coronal plasma and of the H alpha line in the case of prominence threads. It is found that some stages of the dynamics could be discernible in  observations with a sufficiently high spatial resolution.