Dissipation by pinned vortex lines in the superfluid helium film

The status of theoretical and experimental work on dissipation in the helium film is reviewed, and it is concluded that there does not yet exist a satisfactory theoretical interpretation of dissipation in the film which can account for the complete range of observed phenomena below the superfluid transition temperature T. Although the most recent theory, which accounts for dissipation in terms of intrinsic fluctuations in the flow, has been successful in a temperature interval just below T, attempts to extend the theory to include all temperatures below T have not met with the same degree of success. A new model is proposed which accounts for dissipation in superfluid helium film transport in terms of the continuous generation of pinned vortex lines. In principle, this model is similar to one advanced by Vinen, involving the growth and decay of a tangled array of vortex lines. Qualitatively, it is shown that the present mechanism can account for many of the phenomena observed in helium film transport experiments at temperatures well below the transition. For example, sharp changes in the flow rate are associated with changes in the number of pinned vortex lines. In addition, the theory predicts that at superfluid stream velocitiesv_sthat just barely exceed the critical velocityv_c0for the appearance of dissipation, the rate of dissipation Q is given by Q=AN(v_s–v_c0)^3/2 whereN is the number of pinned vortex lines, andA is a constant determined by the vortex line parameters. The value of 3/2 for the exponent is a clear prediction of the theory, and it represents the first precise, numerical prediction by any theory of a physical quantity which is associated with dissipation in the helium film, and which can be measured experimentally.The research for this paper was supported by the Defence Research Board of Canada, Grant number 9550-57.