Creation of Quantized Vortex Rings by Charge Carriers in Superfluid Helium

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Abstract
A brief review of the current state of understanding of the vortex-ring transition in superfluid helium leads to a reexamination of the early suggestion that the critical velocity for vortex-ring creation is determined by energy and momentum conservation. The energy and impulse of a sphere and a vortex ring moving coaxially through an ideal fluid are evaluated. This allows an approximate determination of the velocity at which a moving sphere can create a vortex ring with a given size and location. By minimizing this velocity with respect to the size and location of the ring, one finds that the ring first appears girdling the sphere in the plane perpendicular to the direction of motion. The critical velocity when this ring appears is evaluated for sphere radii and masses derived from the usual models of the charge carriers in helium. The results are in good qualitative agreement with the experimentally observed critical velocities.