Magnetohydrodynamic waves in structured atmospheres

Abstract

The effect of structuring, in the form of magnetic or density inhomogeneities, on the magnetohydrodynamic (mhd) waves of an infinite plasma is investigated. The appropriate dispersion formulae, in both Cartesian and cylindrical polar coordinate geometries, are derived. The main properties of the allowable modes in structured plasmas are described, particularly those featuring in a slender inhomogeneity. The inclusion of non-adiabatic effects is examined, specifically for a thermally dissipative, unstratified, finite structure and for a slender inhomogeneity in a stratified medium. The dissipative time scales of slender structures are shown to have a dependence on the Peclet number. Growth factors appropriate to these time scales for the overstable motions of a thermally dissipative, Boussinesq fluid are derived. For the linear analysis of a slender structure it is shown that the dispersive nature of the waves is deducible from the simplified one-dimensional equations. The analysis is extended, for slender structures, to nonlinear motions and the governing equation representing an effective balance between nonlinear, dispersive and dissipative effects, the Benjamin-Ono-Burgers equation, is established. The solutions of this equation are considered and, for weakly-dissipative systems, are shown to be slowly decaying solitons. The importance, in the context of group velocity, of the dispersive nature of waves in ducted structures is discussed and analogies are made with other ducted waves, for example, the Love waves of seismology. It is suggested that the behaviour of such waves, following an impulse, may account for the range of oscillatory behaviour, the quasi-periodic and short time scales, observed in both the solar corona and Earth's magnetosphere. Density variations across a structure and the structure's curvature, with possible applications to coronal loops, are also considered. Further suggestions for possibly identifying some of the theoretical results with observed behaviour in sunspots, chromospheric fibrils and spicules are also made.