The natural frequencies and stability criterion for cylinderical inviscid conducting liquid bridges and jets subjected to axial alternating magnetic fields in the absence of gravity are obtained. For typical conducting materials a frequency greater than 100 Hz is enough for a quasi-steady approximation to be valid. On the other hand, for frequencies greater than 105 Hz an inviscid model may not be justified owing to competition between viscous and magnetic forces in the vicinity of the free surface. The stability is governed by two independent parameters. One is the magnetic Bond number, which measures the relative influence of magnetic and capillary forces, and the other is the relative penetration length, which is given by the ratio of the penetration length of the magnetic field to the radius. The magnetic Bond number is proportional to the squared amplitude of the magnetic field and inversely proportional to the surface tension. The relative penetration length is inversely proportional to square root of the product of the frequency of the applied field and the electrical conductivity of the liquid. It is shown in this work that stability is enhanced by either increasing the magnetic Bond number or decreasing the relative penetration length.
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