Velocity of second sound and mutual friction in rotating helium II

Abstract

The dependence of $u_2$, the velocity of second sound, on the angular velocity $\omega$ has been measured in rotating helium II in the temperature range $1.40<~T<~2.05$ K. A linear dependence of $u_2$ on $\omega$ was observed for the entire experimental range of angular velocities $\omega <~4$ rad/sec. The slopes can be accurately described by the relation $\frac{\Delta u_2}{u_{20}}=-\left(\frac{1}{2}\right)\frac{B_2\omega }{\sigma }$, where $\frac{\sigma }{2\pi }$ is the second-sound frequency. The mutual friction parameter $B_2$ in this relation was previously calculated from experimental values of the parameters $B_1$ and $B_1^{}{}_{}{}^{\prime }$ by Mehl. Experimental values of $B_2$ determined from the slopes $\frac{\Delta u_2}{\Delta \omega }$ are in excellent agreement with the calculated values over the entire temperature range $1.40<~T<~2.05$ K. This agreement provides new support for the correctness of the Hall-Vinen theory of the interaction of second sound with vortex lines. The dependence of the parameter $B_1$ on second-sound frequency has also been measured. The agreement of the results with the Hall-Vinen theory also provides new support for the detailed correctness of this theory.