Growth of Pinned Quantized Vortex Lines in Helium II

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Abstract
A model is proposed for the onset of instability of superflow in a narrow tube assuming growth of a primordial vortex pinned to irregularities on the wall. A description of subcritical and supercritical flow is obtained closely paralleling that proposed by Donnelly on a phase-slip argument. The critical velocity corresponds to the minimum radius of curvature of the pinned vortex line. The operation of a quantized-vortex-ring mill is described.