Individual Vortex Lines Research Articles

Relativistic finite temperature multifluid hydrodynamics in a neutron star from a variational principle

We develop a relativistic multifluid dynamics appropriate for describing neutron star cores at finite temperatures based on Carter's convective variational procedure. The model includes seven fluids, accounting for both normal and superfluid/superconducting neutrons and protons, leptons (electrons and muons) and entropy. The formulation is compared to the non-variational relativistic multifluid hydrodynamics of Gusakov and collaborators and shown to be equivalent. Vortex lines and flux tubes, mutual friction, vortex pinning, heat conduction and viscosity are incorporated into the model in steps after the basic hydrodynamics is described. The multifluid system is then considered at the mesoscopic scale where the currents around individual vortex lines and flux tubes are important, and this mesoscopic theory is averaged to determine the detailed vortex line/flux tube contributions to the macroscopic "effective" theory. This matching procedure is partially successful, though obtaining full agreement between the averaged mesoscopic and macroscopic effective theory requires discarding subdominant terms. The matching procedure allow us to interpret the magnetic $H$-field inside a neutron star in a way that is consistent with condensed matter physics literature, and to clarify the difference between this interpretation and that in previous astrophysical works.

Observation of quantum turbulence in superfluid He3 -B using reflection and transmission of ballistic thermal excitations

We report measurements of quantum turbulence generated by a vibrating grid in superfluid $^3$He-B at zero pressure in the zero temperature limit. Superfluid flow around individual vortex lines Andreev-reflects incoming thermal ballistic quasiparticle excitations, and allows non-invasive detection of quantum vortices in $^3$He-B. We have compared two Andreev reflection-based techniques traditionally used to detect quantum turbulence in the ballistic regime: quasiparticle transmission through and reflection from ballistic vortex rings and a turbulent tangle. We have shown that the two methods are in very good agreement and thus complement each other. Our measurements reveal that vortex rings and a tangle generated by a vibrating grid have a much larger spatial extent than previously realised. Furthermore, we find that a vortex tangle can either pass through an obstacle made from a mesh or diffuse around it. The measured dependence of vortex signal as a function of the distance from the vibrating grid is consistent with a power-law behaviour in contrast to turbulence generated by a vibrating wire which is described by an exponential function.

A study of thermal counterflow using particle tracking velocimetry

The motion of solid hydrogen particles in He II thermal counterflow has been measured using the particle tracking velocimetry technique. The tracers can move with the velocity comparable to the velocity of the normal fluid. However, below some transition velocity, the particles can be trapped on individual vortex lines and towed by the vortex tangle in the direction of superfluid flow. Above this transition velocity, the Stokes drag with the normal fluid dislodges the trapped particles from vortex cores and such particles move in the same direction as the normal fluid, albeit with lower average velocity. We discuss the measurement of the transition velocity and the mechanism by which tracers may be trapped by or dislodged from quantized vortices.

Magnetic force microscopy study of interlayer kinks in individual vortices in the underdoped cuprate superconductorYBa2Cu3O6+x

We use magnetic force microscopy to both image and manipulate individual vortex lines threading single crystalline YBa$_2$Cu$_3$O$_{6.4}$, a layered superconductor. We find that when we pull the top of a pinned vortex, it may not tilt smoothly. Sometimes, we observe a vortex to break into discrete segments that can be described as short stacks of pancake vortices, similar to the "kinked" structure proposed by Benkraouda and Clem. Quantitative analysis gives an estimate of the pinning force and the coupling between the stacks. Our measurements highlight the discrete nature of stacks of pancake vortices in layered superconductors.

NMR Spectroscopy of the Double-Quantum Vortex in Superfluid 3He-A

The double-quantum vortex line with continuous (singularity-free) structure is the most common linear defect in rotating 3 He-A. Its well-known experimental signature is a frequency-shifted satellite peak in the NMR spectrum. It arises from the absorption of spin wave excitations, which are localized bound states in the dipole-unlocked soft vortex core. In first approximation, the intensity of the satellite peak is proportional to the number of vortex lines. With increased measuring resolution we have found that the absorption contribution of individual vortex lines is not identical, but displays small variations, which depend on the non-uniform global orbital 1 texture. We attribute the effect to small texture-dependent changes in the 1 distribution in the soft core, which modify the attractive potential of the localized spin waves. This property can be used for studying the global order-parameter texture in the rotating container.

Motion and Homogenization of Vortices in Anisotropic Type II Superconductors

The motion of vortices in an anisotropic superconductor is considered. For a system of well-separated vortices, each vortex is found to obey a law of motion analogous to the local induction approximation, in which velocity of the vortex depends upon the local curvature and orientation. A system of closely packed vortices is then considered, and a mean field model is formulated in which the individual vortex lines are replaced by a vortex density.

Lagrange identification of absolutely unstable regimes in wakes

The development of a pulsewise perturbation in a two-dimensional incompressible wake is simulatd numerically using a vortex dynamics method. The main attraction of using vortex methods lies in their Lagrangian nature, which in inviscid flows preserves the identity of rotational fluid elements and thereby allows for the tracking of individual vortex lines or tubes. Because of the non-linearity of this novel approach to identify regions of local absolute and local converctive instability, the analysis is not restricted tio small amplitudes. Moreover the basic state does not have to be locally parallel, and the method is easily applicable to unsteady flows. A comparison of the resulting stability features of the symmetric wake profiles as determined by the numerical simulation with the prediction of the Orr-Sommerfeld analysis confirms the validity of the linear, local stability theory. An extension of the vortex dynamics method to rotational flow fields in which the effects of viscosity become important is enabled by the particle strength exchange scheme.

Magneto-optical observation of twisted vortices in type-II superconductors

When magnetic flux penetrates a type-II superconductor, it does so as quantized flux lines or vortex lines, so called because each is surrounded by a supercurrent vortex. Interactions between such vortices lead to a very rich and well characterized phenomenology for this 'mixed state'. But an outstanding question remains: are individual vortex lines 'strong', or can they easily be cut and made to pass through one another? The concept of vortex cutting was originally proposed to account for dissipation observed in superconducting wires oriented parallel to an applied magnetic field, where the vortex lines and transport current should be in a force-free configuration1–6. Previous experiments, however, have been unable to establish the vortex topology in the force-free configuration or the size of the energy barrier for vortex cutting. Here we report magneto-optical images of YBa2Cu3O7–δ samples in the force-free configuration which show that thousands of vortex lines can twist together to form highly stable structures. In some cases, these 'vortex twisters' interact with one another to produce wave-like dynamics. Our measurements also determine directly the current required to initiate vortex cutting, and show that it is much higher than that needed to overcome the pinning of vortices by material defects. This implies that thermodynamic phases of entangled vortices7–10 are intrinsically stable and may occupy a significant portion of the mixed-state phase diagram for type-II superconductors.

Photographing a superfluid vortex

It has long been realised that superfluid helium cannot rotate bodily: it is believed that, instead, rotation of the container may result in the formation of one or more individual quantised vortex lines. Particular interest therefore attaches to a report by Williams and Packard of the University of California at Berkeley in a recent issue of Physical Review Letters (33, 280; 1974) that they have been successful in obtaining photographs apparently showing for the first time the positions of individual vortex lines in superfluid 4He.

Rotating Superfluid in Neutron Stars

A rotating perfect fluid subject to axisymmetric, azimuthal, time-independent forces is shown to have a uniform angular acceleration on each coaxial cylindrical surface. In a rotating superfluid, uniform rotation is mimicked by a dense corotating paraxial array of quantized vortices. The above classical result is approached when external forces on the vortices vary on a scale large compared with the intervortex spacing. In such cases, despite forces which may vary greatly along individual vortex lines, the vortices move radially but remain parallel to the rotation axis. This resistance to bending suppresses the development of superfluid turbulence in the interiors of rapidly rotating neutron stars. Subject headings: hydrodynamics - neutron stars - rotation, stellar