The equilibrium and the stability of the Jeans spheroids with toroidal magnetic fields

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Magnetic Fields, Magnetohydrodynamic Stability, Plasma Control, Prolate Spheroids, Toroidal Plasmas, Eigenvectors, Energy Technology, Equilibrium Equations, Harmonic Oscillation, Jeans Theory, Modal Response, Reactor Design

Scientific paper

The effect of a toroidal magnetic field on the equilibrium and stability of homogeneous masses distorted by the tidal effects of a secondary mass is examined. It is shown that if the toroidal magnetic field is assumed to be axisymmetric about the direction of the line joining the centers of mass of the primary and the secondary, then the equilibrium configuration is a prolate spheroid. Also determined are the characteristic frequencies of the various modes of oscillations belonging to the second harmonics. It is found that the magnetic field shifts these frequencies to higher values than the ones which prevail in the absence of a magnetic field.

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