Physical Sciences and Mathematics Commons^™

A Nonlinear Eigenvalue Problem In Astrophysical Magnetohydrodynamics: Some Properties Of The Spectrum, John A. Adam

Mathematics & Statistics Faculty Publications

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. In the absence of a gravitational potential, the system reduces to that of importance in MHD and plasma physics, albeit in a different geometry. This further reduces to a form isomorphic to that derived in the study of plasma oscillations in a cold plasma, Alfvén wave propagation in an inhomogeneous medium, and MHD waves in a sheet pinch. In cylindrical geometry, the relevant …