Structure and dynamics of vortices in superfluid helium-3

Abstract In this thesis, the structure and the dynamics of vortices are studied from the standpoint of the hydrodynamical theory of superfluids. In the hydrodynamical theory a superfluid is described by a continuous order parameter field. In the case of superfluid helium-4 this field is a complex-valued function of position and time. However, in superfluid helium-3 the order parameter is a complex-valued 3 × 3 matrix. The first part of this work consists of studies on structures that appear in the order parameter field, when a vessel filled with superfluid helium-3 in the A phase (3He-A) is rotated in an external magnetic field. Among the most common of these structures are the so-called continuous vortices. They exist in several different forms. In addition to vortices, other possible structures include the vortex sheet of 3He-A that was discovered at the Low Temperature Laboratory of Helsinki University of Technology (currently Aalto University) in late 1993. In this thesis, these structures were studied by finding stationary vortex configurations that minimize the free energy of the superfluid. An algorithm for minimizing the free energy was implemented by writing a computer program. This program was then used to study the structure of a few vortex types, inferred to be the most probable ones. In addition, regular lattices formed by these vortices, including the vortex sheet, were studied. A phase diagram for vortex lattices was constructed by comparing the free energy of various lattice structures as a function of rotational velocity and external magnetic field. The study of vortex structures also lead to a discovery of a new type of vortex in 3He-A, later named the LV3 vortex. In the second part of the work, the dynamics of vortices was studied using a filament model of vortex motion, which also has its theoretical justification in the hydrodynamical model of superfluids, but where the detailed structure of the vortex core is not relevant. The specific problem under consideration here was the motion of a quantized vortex in a rotating elongated cylinder filled with superfluid, and how the motion of the vortex depends on temperature and the rotational velocity of the vessel. The study of vortex motion was simplified using scaling laws. A new type of scaling law was discovered, which both simplified the specific problem under study, and made the results more general. In summary, the research in this thesis touched upon two somewhat complementary areas, i.e. the structure of continuous vortices in 3He-A and the dynamics of thin vortex lines, which is more applicable to superfluid 4He or to the B phase of superfluid helium-3 (3He-B). However, these areas complement each other in advancing the general scientific understanding about the properties of superfluids