Smoothness and Vortex-Wall Interactions in Superfluid Helium

We study two aspects of the interaction between a surface and a single vortex line terminating on the surface. One is pinning, when a moving vortex becomes caught at some point on the wall. The second is the energy dissipation as the vortex moves, which appears to be dominated by a vortex-surface interaction. When we reduce the surface roughness through mechanical polishing, we find that the energy loss decreases, as expected if the dissipation comes from a ``friction" force which is weaker for smoother walls. The change is small, about a factor of 3 for several orders of magnitude difference in surface roughness. This is consistent with the very small vortex core size in ${}^4$He since even our highly polished surfaces are ``rough" on the scale of the vortex core. A more surprising finding is that the vortex is {\em more} likely to pin on the smooher walls, suggesting that this vortex-surface interaction is stronger for smoother walls. We will discuss how a mesh of small vortex lengths pinned along the container surface may contribute to these observations.