The Interpretation of Phase-Slip and Critical-Velocity Data from the Flow of Superfluid ⁴He through a 2 μm by 2 μm Aperture

An analysis has been made of phase-slip and critical-velocity data for both the ac and dc flow of superfluid ⁴He through a 2 μm by 2 μm aperture in a 0.1-μm-thick titanium foil between 0.86 and 2.10 K. Single-2π phase slips were resolvable over the entire range of temperature in the ac flow measurements, carried out between 10 and 20 Hz, making it possible to determine the width of the critical-velocity distribution throughout the temperature range from these measurements. These data have been interpreted in terms of the thermal nucleation of vortex half-rings at the walls of the aperture, involving a velocity- and temperature-dependent energy barrier. The barrier can be modeled with moderate success using an approach close to that of Avenel and Varoquaux and coworkers.