Non-Axisymmetric Oscillations of Thin Prominence Fibrils |
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Authors: | Email author" target="_blank">M?V?DymovaEmail author M?S?Ruderman |
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Institution: | (1) Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, U.K. |
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Abstract: | We study non-axisymmetric oscillations of thin prominence fibrils. A fibril is modeled by a straight thin magnetic tube with
the ends frozen in dense plasmas. The density inside and outside the tube varies only along the tube and it is discontinuous
at the tube boundary. Making a viable assumption that the tube radius is much smaller than its length, we show that the squares
of the frequencies of non-axisymmetric tube oscillations are given by the eigenvalues of the Sturm–Liouville problem for a
second-order ordinary differential equation on a finite interval with the zero boundary conditions. For an equilibrium density
that is constant outside the tube and piecewise constant inside we derived a simple dispersion equation determining the frequencies
of non-axisymmetric oscillations. We carry out a parametric study of this equation both analytically and numerically, restricting
our analysis to the first even mode and the first odd mode. In particular, we obtained a criterion that allows to find out
if each of these modes is a normal or leaky mode. |
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