A nonlinear eigenvalue problem in astrophysical magnetohydrodynamics: some properties of the spectrum.

Mathematics – Mathematical Physics

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Magnetohydrodynamics: Solar Corona, Magnetohydrodynamics: Sunspots

Scientific paper

The equations of ideal magnetohydrodynamics (MHD) with an external gravitational potential - a "magnetoatmosphere" - are examined in detail as a singular nonlinear eigenvalue problem. Properties of the spectrum are discussed with specific emphasis on two systems relevant to solar magnetohydrodynamics. The system, including gravity, has been applied to the study of flare-induced coronal waves, running penumbral waves in sunspots, and linear wave coupling in a highly inhomogeneous medium.

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