Stability of a Current Ring Supported in a Magnetic Field

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Abstract
The stability of a superconducting, current-carrying ring levitated in a static magnetic field is investigated theoretically. The azimuthally symmetric supporting field has components Br, Bθ, and Bz. A first-order perturbation calculation is performed to determine the oscillation frequencies of the stable modes and the stability criteria for the potentially unstable modes. In the absence of external feedback and/or image currents in the surrounding walls, the ring is unstable. The stability criteria involve the ring current and mass as well as the configuration of the external field and the surrounding walls. It is found that the ring may be stabilized by proper choice of the wall configuration, and if a given configuration is not such as to satisfy the stability criteria, the magnitude of external feedback necessary may be determined from the results.

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