Dissipation and Phase Slip in Confined Superfluid Helium: Evidence for an Equilibrium Distribution of Vortices

The effects of phase slip due to the thermal creation of vortices in confined liquid 4He below the l point is discussed.In a narrow tube there is a finite probability of thermal activation of a vortex in the superfluid helium, with the vortex not parallel to the axis of the tube.In the presence of a heat flow along the tube, the vortices experience the Magnus force, which prevents exact cancellation of the motion of thermally activated vortices traversing the cross section of the tube in opposite directions.Each crossing of the tube by a vortex causes a 2p phase slip of the superfluid order parameter along the tube.A temperature gradient results, which is proportional to the rate of phase slip, thus yielding a nonvanishing thermal resistivity below the bulk l point.The calculated temperature dependence compares well with experimental data, thereby providing indirect evidence of the presence of vortices in thermal equilibrium.