Magnetoelastic stability of a superconduting ring in its own field (Q1081415)

The stability of the flexural vibrations of a superconducting ring in its own magnetic field is investigated. This problem is formulated as a perturbation problem: the final magnetic fields due to the deflected ring are considered as perturbations of the rigid-body fields. Both the rigid- body problem and the linearized perturbed problem are solved analytically. These solutions are expressed in Legendre functions. A so- called ring equation for the in-plane flexural vibrations of the slender ring is constructed. From this equation a frequency-current dispersion relation is derived. It turns out that the ring is stable against in- plane vibrations and that the eigenfrequency increases with increasing current.