Magnetohydrodynamic surface waves in the solar atmosphere

Abstract

In this thesis the nature of magnetoacoustic surface waves at a single magnetic interface is examined for the case of parallel propagation. Above the interface is an isothermal medium permeated by a horizontal magnetic field. The lower region is a field-free medium of different density to the magnetic atmosphere. We consider both the incompressible and compressible situations and the effect of including gravity. In each case a transcendental dispersion relation is solved numerically for a range of parameters and the resulting dispersion curves plotted. In the first chapter we provide a general introduction to the work, reviewing previous work in this area and considering applications of surface waves. In the second chapter we consider the existence of surface waves for the case when the media are incompressible either side of the interface. We consider the cases of both uniform and non-uniform distributions of densities and the effect of including gravity. We show that the f-mode exists in a restricted band of horizontal wavenumber. In the subsequent chapters we consider the effect of compressibility on surface waves. The media either side of the interface are taken to be isothermal. In the absence of gravity the interface may support one or two surface modes determined by the relative temperatures and magnetism of the two media. This case is studied in Chapter 3 where phase-speeds and penetration depths of the waves and the associated pressure perturbations are investigated for a variety of field strengths and sound speeds. In Chapters 4 and 5 we consider the effect of gravity on the compressible modes described in Chapter 3. In Chapter 4 an exact dispersion relation is obtained for the case of a constant Alfven speed, whilst in Chapter 5 the case of a uniform magnetic field is considered. In the absence of the magnetic field the transcendental dispersion relation may be reduced to a polynomial. This polynomial possesses two acceptable solutions, only one of which may exist at any given circumstance depending on the densities either side of the interface. If the gas density within the field exceeds that in the field-free medium, then the f-mode may propagate; otherwise, a magnetic surface gravity mode propagates. As in the incompressible case, the f-mode exists in a restricted band of horizontal wavenumber. An analytical form for the wave speed of the f-mode is obtained for small values of the Alfven speed. It is shown that the f-mode is related to the fast magnetoacoustic surface wave, merging into that mode at short wavelengths.