The stability of a current-carrying hollow liquid-metal cylinder

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Abstract
An investigation of the factors that influence the stability of a conducting hollow liquid-metal cylinder in a microgravity environment is carried out for the particular configuration in which a fraction of the current in the cylinder is returned down a central conducting rod. The analysis assumes that axial symmetry is maintained, that at any instant the cylinder is at a uniform temperature, and that the liquid metal is incompressible and inviscid. Vibrations in which the inner and outer boundaries of the cylinder move in phase are found to be always stable. The out-of-phase modes are unstable for long wavelengths, but these unstable modes can be excluded by a suitable choice of the length and thickness of the cylinder. The relationship of this analysis to the recent results of Chow and Harvanek [in Proceedings of the 1st National Fluid Dynamics Congress, Cincinnati, July, 1988 (American Institute of Aeronautics and Astronautics, New York, 1988), Part 3, p. 1805] on electromagnetic capillary instabilities in a hollow liquid-metal cylinder is discussed.

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