60 78 v 2 1 7 O ct 2 00 0 Stable Vortex Configurations in a Cylinder

We calculate stable arrangements for a single superfluid vortex pinned to the wall of a stationary cylindrical container. We find that, independent of the details of the pinning site, stable vortices must subtend most of the cell horizontally and cannot be vertical or nearly vertical. More generally, the geometry of a container severely limits the possible vortex configurations, making macroscopic trapped vortices less common than previously believed. Vortex lines in superfluid helium have been studied for over forty years [1], but many fundamental questions remain. Moving vortices feel a drag force, known as mutual friction, from interaction with the superfluid excitations. The effects of mutual friction have been thoroughly measured in systems of many vortices [2], but there is still no microscopic theory of the interaction. Similarly, the interaction of two closely approaching vortex lines is unknown. Another unresolved issue is the structure of the vortex core, and whether it can change size and shape to alter the energy and momentum of a vor-tex. Other questions involve superfluid turbulence, which can be described as a tangle of vortex lines. In a decaying tangle , the mean vorticity has the same power-law dependence on time as for a classical system, even at such low temperatures that the normal fluid density is negligible [3, 4]. In addition , experiments [5] and simulations [6] show that superfluid turbulence follows a Kolmogorov scaling law at low temperatures. The power law, prefactor, and even the deviations from ideal scaling are the same for superfluid and classical turbulence. How the quantized vortices in the superfluid mimic so well the behavior of classical viscous vortices is unknown, as is the length scale at which differences appear. A better understanding of single vortex behavior may help answer these FIG. 1: Vortex partially trapped around a wire. The picture illustrates the possible interaction of the vortex with a second vortex pinned to the wall of the chamber. questions. A few years ago, an unusual method for observing vor-tex motion was discovered [7, 8]. A vortex line is partially trapped around a thin wire, continuing through the fluid as a free vortex, as shown in Figure 1. Although the vortic-ity is initially created by rotating the cryostat, the circulation around the wire is long-lived, and measurements can be made after the cryostat is brought to rest. In the case of a vortex partially attached to the wire, the self-velocity drives …