Title:

MHD wave interaction with coronal active region plasmas

Interaction of magnetohydrodynamic (MHD) waves with various structures in a magnetised plasma was considered theoretically in the context of the interpretation of recently observed phenomena in the corona of the Sun. The main emphasis was put on the development of analytical models, utilising various asymptotic techniques based upon the presence of a small parameter. In the consideration of waves guided by fieldaligned plasma nonuniformity, such as coronal jets and plumes, the small parameter was the ratio of the diameter of the guiding nonuniformity to the wavelength, the approach known as the \thin uxtube approximation". In the consideration of nonlinear effects, the wave amplitude was taken to be finite, but small, and hence could be treated as a small parameter too. In the thesis, we addressed several specific timely problems of modern solar physics: the interpretation of recently discovered transverse waves on soft Xray coronal jets in terms of a kink fast magnetoacoustic wave; modelling of enigmatic torsional waves (also known as twisting waves or waves of the electric current) guided by cylindrical coronal structures, such as loops, plumes, filaments and jets, accounting for the effects of the magnetic twisting and rotation of the equilibrium plasma configuration; weakly nonlinear effects appearing during the propagation of the torsional waves along coronal magnetic waveguides, concentrating on the nonlinearly induced compressible perturbations; and nonlinear steepening of fast magnetoacoustic waves in the vicinity of a magnetic nullpoint, in the context of the possible triggering of magnetic reconnection by the deposition of currentdriven anomalous resistivity. In the first Chapter, we give an overview of the solar atmosphere and dynamical processes observed there such as MHD waves and plasma ows. Also, the set of MHD equations is introduced, and the main modes of a basic coronal plasma structure, a magnetic cylinder, are considered by the method of dispersion relation. In Chapter 2, we considered the longwavelength limit in the magnetic cylinder dispersion relations, and derived explicit expressions, which link the phase and group speeds for linear kink magnetoacoustic waves guided by hot plasma jets surrounded by a static plasma. With the use of the derived expressions, we showed that transverse waves recently discovered by Hinode/XRT on coronal jets are the kink waves. In the observationally determined range of parameters, the waves are not found to be subject to either the KelvinHelmholtz instability or negative energy wave instabilities, and hence they are likely to be excited at the source of the jet. We also carried out forward modelling of the observables, and demonstrated its consistency with XRT observations. In Chapter 3 we considered long wavelength axisymmetric magnetohydrodynamic waves, and derived asymptotic dispersion relations linking phase speeds with the plasma parameters using the second order thin ux tube approximation. We showed that when uniform twist and rotation are both present, the phase speed of torsional waves depends upon the direction of the wave propagation. In addition, the twist and rotation causes compressibility of the torsional waves. The phase relations show that in a torsional wave the density and azimuthal magnetic field perturbations are in phase with the axial magnetic field perturbations and antiphase with tube crosssection perturbations. In a zeroβ nonrotating plasma cylinder confined by the equilibrium twist, the density perturbation is found to be about 66 percent of the amplitude of the twist perturbation in torsional waves. In Chapter 4, we considered the nonlinear phenomena accompanying longwavelength torsional waves in an untwisted and nonrotating magnetic ux tube. We showed that propagating torsional waves induce compressible perturbations by nonlinear forces, these compressible perturbations oscillate with double the frequency of the torsional waves. In contrast with plane shear Alfvén waves, the amplitude of compressible perturbations is independent of the plasmaβ. But, as in the shear Alfvén wave, the amplitude of compressible perturbations are proportional to the torsional wave amplitude square. It was also shown that standing torsional waves induce compressible perturbations of two kinds, those which grow with the characteristic time inversely proportional to the sound speed, and those which oscillate at double the frequency of the inducing torsional wave. The growing density perturbation saturates at the level, inversely proportional to the sound speed. In Chapter 5, we studied the generation of fast magnetoacoustic shocks in the vicinity of a magnetic nullpoint. In the weakly nonlinear limit, we derived a simple wave evolutionary equation, which provided us with the qualitative information about the nonlinear evolution of the fast wavepulse: formation of the shock and deformation of the initial shape of the perturbation depending upon the polar angle. We compared our analytical solutions with numerical solutions and found that the speed of the fast magnetoacoustic pulse depends on the initial amplitude of the pulse. In our parametric studies we showed that although the initial amplitude of the magnetoacoustic pulse is responsible for the time the pulse overturns, the initial width of the pulse should not be ignored. We showed that narrower and higher amplitude pulses overturn at larger distance from the nullpoint. In the context of the sympathetic flaring a stronger initial pulse does not guarantee a stronger effect.
