Magnetohydrodynamic waves and instabilities in solar magnetic structures

Abstract

Motions of plasma in magnetic structures in the solar atmosphere may be successfully modelled using the theory of magnetohydrodynamics (MHD) describing oscillatory motion, in the form of standing and propagating waves, and unstable behaviour. In this thesis we consider two forms of magnetic structuring, the current sheet and the thin magnetic flux tube. The current sheet finds particular application in the solar corona and solar wind; the thin flux tube is of particular importance in solar photospheric magnetism. A model of a current sheet with a continuous magnetic field profile is studied as a waveguide. The equation of motion for small perturbations to a current sheet equilibrium is obtained from the equations of ideal linear MHD and solved numerically to determine the nature of magnetoacoustic waves propagating parallel to the applied magnetic field. A number of approximation methods are used to shed light on the significance of the numerical results. We consider a variation of this model, applicable to the solar corona, and examine the possibility of impulsively generated magnetohydro dynamic waves in the sheet. Such waves exhibit wavepacket properties, similar to those found in slab models of magnetic structures. The process of convective collapse in a vertical magnetic flux tube located in the solar photospheric network is treated using the thin flux tube equations of ideal linear MED. We consider the critical stability of a thin flux tube embedded in convection zone models of varying complexity, taking into account the effects of an overlying chromospheric atmosphere and temperature imbalance between the flux tube and its environment. The dependence of the instability on various sets of boundary conditions is discussed; the choice of boundary conditions is a subject of some debate in the current literature. Possible future directions for work which extends the description of dynamic phenomena in both the current sheet and thin flux tube structure is discussed and ideas for linking these areas of research are presented.