Application of the Method of Matched Asymptotic Expansions to the radial oscillations of a magnetic cylinder |
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| Authors: | M Goossens J Cornette |
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| Institution: | (1) Astronomisch Instituut, Katholieke Universiteit Leuven, Belgium |
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| Abstract: | This study deals with the singular character of the perturbation introduced into the eigenvalue problem of the linear and adiabatic oscillations of a gaseous configuration by a magnetic field that is non-zero on the boundary surface of the configuration. This singular character implies that a regular perturbation scheme cannot yield uniformly valid expansion for the eigenfunctions.This investigation considers the application of the Method of Matched Asymptotic Expansions (M.M.A.E.) to the latter singular perturbation problem in order to obtain uniformly valid expansions for the eigenfunctions and first-order expressions for the eigenfrequencies. As an illustrative example, the M.M.A.E. is applied to the eigenvalue problem of the linear, radial, and adiabatic oscillations of a homogeneous cylindrical plasma with a constant longitudinal magnetic field. |
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