Attenuation of Second Sound in Helium II between Rotating Cylinders

Abstract

In an annular resonant cavity, we have shown that the attenuation of second sound is the same for solid-body rotation, rotation of the outside cylinder only, and rotation of the inside cylinder only, if plotted against $\left|\mathrm{curl} {\mathbf{v}}_s\right|$, where the superfluid velocity ${\mathbf{v}}_s$ is calculated by classical hydrodynamics. Additional attenuation due to secondary flow was observed when the inside cylinder only rotated faster than 0.4 rad/sec. In solid-body rotation, we find that the attenuation plotted as a function of angular velocity deviates from linearity by not more than 1%, out to 6 rad/sec. We measured the perpendicular mutual-friction coefficient $B$ at 50-mdeg intervals between 1.2 and 2.08°K, with an uncertainty of ± 2% in the smoothed values; our values of $B$ are 4 to 8% higher than previous measurements by Hall and Vinen. We also measured the velocity of second sound to ±1%.