Application of the method of matched asymptotic expansions to the radial oscillations of a magnetic cylinder

Details Application of the method of matched asymptotic expansions to the radial oscillations of a magnetic cylinder Application of the method of matched asymptotic expansions to the radial oscillations of a magnetic cylinder

Sep 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978ap%26ss..58..227g&link_type=abstract

Astrophysics and Space Science, vol. 58, no. 1, Sept. 1978, p. 227-243.

Astronomy and Astrophysics

Astrophysics

2

Asymptotic Methods, Eigenvalues, Plasma Cylinders, Plasma Oscillations, Stellar Magnetic Fields, Stellar Models, Harmonic Oscillation, Lorentz Force, Numerical Integration, Perturbation Theory

Scientific paper

The singular perturbation problem of linear and adiabatic oscillations of a gaseous mass with a magnetic field that does not vanish on the free surface of the equilibrium configuration is considered. The equations for studying the one-dimensional eigenvalue problem of linear, radial, and adiabatic oscillations of a homogeneous cylindrical plasma with a constant longitudinal magnetic field are reviewed, and exact solutions to the eigenvalue problem are obtained for various magnetic-field strengths. The method of matched asymptotic expansions (MMAE) is applied to obtain uniformly valid expansions for the eigenfunctions and first-order approximations for the eigenvalues. The perturbation results for the eigenfunctions and eigenvalues determined by the MMAE for the first four radial modes and the first three harmonic modes are compared with the exact results, and the accuracy of the former is evaluated. It is shown that the MMAE allows a very accurate determination of both the eigenfunctions and the eigenvalues.

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