Abstract
Abstract The purpose of this paper is to study the behavior of magnetohydrodynamic (MHD) wave modes that propagate in compressible magnetic flux tubes with an elliptical cross section embedded in a magnetic environment. The dispersion relation that describes the behavior of MHD wave modes permitted in an elliptical magnetic flux tube is solved numerically. Distortion of the spatial structure of the purely real eigenmodes from the well-known circular flux tube model has been considered. It has been studied under both photospheric and coronal conditions. It has been shown that (i) solutions in the form of even Mathieu functions are more sensitive to the value of eccentricity than solutions with the form of odd Mathieu functions; (ii) if the ellipticity of the cross section of the magnetic flux tube increases, a sausage mode (m = 0) cannot be easily identified; (iii) even solutions that correspond to the fluting mode (m = 3) can be misinterpreted as a kink mode (m = 1) due to their similarities. In contrast to the fluting modes that are polarized along the major axis and strongly depend on the ellipticity of the magnetic flux tube, the kink and sausage surface modes are practically unaffected by ellipticity. Several examples of the spatial structure of the eigenmodes permitted in the pores and sunspots have been visualized. The solutions obtained in the approximation of cylindrical symmetry are in agreement with previous studies.
Highlights
The high-resolution ground and space-based observations of the solar atmosphere in combination with the theory of magnetohydrodynamic (MHD) wave propagation provides us with an opportunity to understand the behavior of observed waves in more detail
MHD modes of a magnetic flux tube with an elliptical cross section embedded in a magnetic environment are discussed
The higher order modes that polarized along the major axis are strongly affected by the ellipticity of the tube, while those that are polarized along the minor axis are very slight effected by ellipticity
Summary
The high-resolution ground and space-based observations of the solar atmosphere in combination with the theory of magnetohydrodynamic (MHD) wave propagation provides us with an opportunity to understand the behavior of observed waves in more detail. Roberts (1981b) obtained the dispersion relation governing MHD wave propagation in an isolated magnetic slab and specified two main magneto-acoustic modes; the sausage and the kink These have various subcategories, e.g., slow/fast body and surface waves. One must consider either the MHD variables to be complex or compute the solutions numerically as an initial value problem It will be shown how the spatial structure of the purely real eigenmodes are distorted from the well-known circular flux tube model when an elliptical cross section is considered. This paper is structured as follows: In Section 2, we derive the general dispersion relation that describes the linear magneto-acoustic waves in a compressible magnetic flux tube with an elliptical cross section.
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