Mode classification and wave propagation in a magnetically structured medium

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Abstract
We examine the structure of motions that can occur in a vertical magnetic flux tube with a rectangular cross-section. A polytropic stratification is assumed in the vertical direction. We use a gauged version of Helmholtz's theorem, to decompose the perturbations into an irrotational component and a solenoidal component, which we further split into the sum of poloidal and toroidal components. These components are identified with p, g and toroidal modes of a fluid. The normal modes of the tube are determined using a Rayleigh–Ritz variational technique. Our technique efficiently isolates all the modes to high orders. We first consider some special cases, in order to highlight some interesting properties of the modes. Next, we choose a parameter range to study the properties of oscillations in intense flux tubes on the Sun. Both eigenfrequencies and eigenvectors are determined. It turns out that for intense flux tubes the fundamental is a modified convective mode (g1 in our notation), whose frequency is in remarkable agreement with the fundamental frequency, obtained from a thin flux tube calculation. For high mode orders, our g modes are essentially slow modes. The t modes are identified with Alfvén waves and the p modes with modified fast waves. We also calculate the height variation of the displacement and pressure perturbations, parallel to the tube axis for the modes. Finally, we discuss some of the observational implications of our study.

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