Spectrum of ideal magnetohydrodynamics of axisymmetric toroidal systems

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Abstract
The spectrum of ideal magnetohydrodynamics in toroidal systems is shown to concentrate around three continua where the singular fast, the Alfvén, and the slow modes become polarized purely normal and purely tangential to the magnetic surfaces. A new toroidal effect is encountered, viz., coupling of the Alfvén and slow continuum modes by the presence of geodesic curvature. Due to this effect the slow and Alfvén modes are no longer polarized purely parallel and purely perpendicular to the field lines as they are in the case of the diffuse linear pinch. The pure polarizations of these continuum modes are only found asymptotically when ω2→∞, which point turns out to be a clusterpoint of all three kinds of magnetohydrodynamic modes characterizing each of them uniquely.