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.
Type
Thesis, PhD Doctor of Philosophy
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