Superfluid Helium Critical Velocities in a Rotating Annulus

The critical velocity of rotation to bring superfluid helium at 1.3°K into motion was measured in an annulus 2.2 mm wide, 1.8 cm deep, and 8.83 cm mean diameter. Superfluid currents were detected after the annulus was stopped, and after the normal fluid had come to rest, with a modified form of "Rayleigh disk." Well-defined critical velocities were found, and these varied from 0.81 cm/sec (1.75 rpm of the annulus) to 0.55 cm/sec (1.19 rpm) depending on the past history of the liquid. The higher critical velocity applies to liquid in which a superfluid current has not been established previously. The "memory" of the liquid helium for previous superfluid currents lasts between 50 and 75 min. A discussion is given of the evidence that these currents constitute an irrotational velocity field ($v\propto \frac{1}{r}$) in the annulus, which is free of vortex lines.