Propagation of Quantized Vortices Driven by an Oscillating Sphere in Superfluid 4He

We performed numerical simulation of quantum turbulence at 0 K generated from remnant vortices attached to an oscillating sphere. The remnant vortices are extended by the sphere motion and form a tangle with emitting vortex loops. As time passes, the length of vortices in a computational volume becomes statistically steady. We investigate in the statistical steady state the distribution of the length of vortex loops and anisotropy of their propagation direction caused by the sphere oscillation. The propagation direction of the emitted vortex loops is anisotropic along the oscillation direction of the sphere. The obtained results are consistent with results obtained in the experimental study using vibrating wires in superfluid ⁴He.     

Time-of-Flight Experiments of Vortex Rings Propagating from Turbulent Region of Superfluid 4He at High Temperature

We report the time-of-flight of quantized vortex rings generated by a vibrating wire in superfluid ⁴He which contains normal fluid component. A cover box of vibrating wires and slow cooling of superfluid reduce the number of vortices attached to wire surfaces, enabling us to study vortex rings propagating from a turbulent region. Using two vibrating wires as a generator and a detector of vortices, the time-of-flight of vortices propagating a distance of 0.88 mm was measured at 1.25 K. We find that the time-of-flights distribute from 0.06 s to 27.4 s, much larger than the lifetimes of circular vortex rings limited in the size of a generator amplitude. These results imply that large vortex rings with non-circular shape or vortex tangles are created by the generator, propagating slowly and colliding with the detector before complete disappearance.     

Vortex Rings in Superfluid 3He–B at Low Temperatures

Turbulence in classical fluids has far-reaching technological implications but is poorly understood. A better understanding might be gained from studying turbulence in quantum systems. In a pure superfluid (at low temperatures), there is no viscosity and vortex lines are quantised. Quantum turbulence consists of a tangle of quantised vortex lines which interact via their self-induced flow. We have recently developed techniques for detecting vortices in superfluid ³He–B in the low temperature limit. We find that the transition to turbulence from a moving grid occurs by the entanglement of emitted vortex rings. Here, we discuss the propagation of the ballistic vortex rings emitted at low grid velocities. We have measured the temperature at which the rings decay before reaching the detectors. Our results, at two different pressures, confirm that the vortex rings decay in accordance with mutual friction.     

Anomalous Trajectories of H2 Solid Particles Observed Near a Sphere Oscillating in Superfluid Turbulent 4He

Using a relatively low cost apparatus, consisting of a glass dewar and a digital camera capable of taking images at 240 frames per second we have observed trajectories of frozen H₂ particles which follow the flow of liquid helium below 2 K, around a sphere oscillating at 38 Hz. In some of the images the motion is compatible with laminar flow, while at high amplitudes, where we can reach Reynolds numbers of a few thousand in the normal component, the flow is clearly turbulent. In some of the videos taken we find particles being suddenly accelerated to several times the velocity of the oscillating sphere.     

Onset of Convection in Superfluid 3He-4He Mixture Heated from Below

The thermal instability of ³He-⁴He mixtures caused by heating the liquid from below has been studied experimentally. The temperature gradients were measured which appeared in the mixture with initial concentration 9.8% of ³He below 0.5 K in the presence of different heat flows from the heater at the cell bottom. At a certain critical heat flow the effective thermal conductivity of the liquid was observed to increase sharply which was naturally attributed to the convective heat transfer. It is shown that the thermal convection develops at high temperature gradients. In this case the Rayleigh numbers exceed many orders of magnitude those for heating from above. Thus the convective instability develops in a system in which the light liquid is at the top and where no prerequisite for instability is seemingly available. The resugts obtained are analyzed in terms of the theory of convective instability in binary mixtures. It is suggested that the phase separation, of superfluid mixtures caused by a heat flow could be a destabilizing factor initiating convection. The vortex formation in superfluid helium and the related turbulent flows appearing at high temperature gradients can be another factor favourable for instability of the liquid.     

Vortex Nucleation by Negative Ion in Superfluid He4

In superfluid He⁴, moving ions nucleate vortex loops by quantum tunneling through the barrier for T<0.3K, while thermal phonons activate the system over the barrier at higher temperature. The energy barrier height and the nucleation rate are calculated numerically, and these are well fitted with the experimental data for low pressures P<16bar and low electric fields E<10⁵V/m.     

Detection of Vortices in Superfluid 4He in the T=0 Limit Using Charged Vortex Rings

We describe the experiment to study the dynamics of quantized vortex lines in superfluid ⁴ at temperatures down to 40 mK, i.e., without any normal component. This was achieved by monitoring the trapping of small charged vortex rings by an array of rectilinear vortex lines produced by rotating the cryostat. The design of the experimental cell is described. Our first observations of the response of the superfluid in the T =0 limit to starting and stopping rotation are presented.     

Quantum Statistics of Three-Dimensional Vortex Filament in Superfluid 4He

The quantum statistics of three-dimensional vortex filament in superfluid ⁴ He is investigated by the use of path integral techniques. The free energy evaluated in the saddle point approximation decreases abruptly at a certain critical value of the applied superflow velocity. This critical behavior is in quantitative agreement with the experimental result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the damped harmonic oscillator approximation.     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

Vortex Dynamics in Superfluid 4He at Very Low Temperatures

Recently McClintock et al. observed the free decay of a vortex tangle in superfluid ⁴He at mK temperatures. Since the system at such low temperatures is free from normal fluid and usual mutual friction, the mechanism of the free decay is unknown. In order to understand this phenomenon, this work studies numerically the vortex dynamics without the mutual friction. The absence of mutual friction prevents the vortex from smoothing. The resulting kinked structure promotes vortex reconnection, thus making lots of small vortex loops. Such cascade process as breakup of vortices to smaller ones can decay the vortex line density. This paper describes the decay of vortex tangle under the localized induction approximation, and that of four vortex rings under the full nonlocal calculation.     

Vortex Mutual Friction in Superfluid 3He

We give a full account of our extensive measurements of vortex mutual friction in rotating superfluid ³He, in both the A- and B-phases. The B-phase results are in qualitative agreement with a theory based on the concept of “spectral flow”; the agreement becomes quantitative if an effective energy gap of 0.63 Δ is used, but the Justification for such a substitution is not clear. The vortex core transition, at first not seen because of metastability and hysteresis, has now been observed. Detailed investigation suggests that the high temperature vortex state is a temperature dependent mixture of at least two vortex types. The A-phase mutual friction is found to be well described by two hydrodynamic coefficients, the orbital viscosity and the orbital inertia. The latter corresponds to an orbital angular momentum per Cooper pair of (0.0015 ± 0.0017 ) ħ, consistent with the prediction of the spectral flow theory. We find that the most uniform l texture is obtained by cooling through T_c while rotating, and then stopping rotation. Detailed investigation of textural memory effects shows that the uniform l-up and l-down textures are associated with opposite directions of rotation. We discuss the various types of texture that may be formed in our experiments. Finally, we compare our mutual friction results with those found in ⁴HeII.     

Thermal Resistance of 4He Below but Very Near the Superfluid Transition

We report high-resolution measurements at saturated vapor pressure of the thermal resistivity R of superfluid ⁴He over the reduced-temperature range 3×10^–7<t1–T/T <3×10^–5 (T is the transition temperature for Q=0) and heat-current-density range 4<Q<200 W/cm². For smaller Q and t, no thermal resistance was detectable below a transition at T _c(Q)<T . For Q10 W/cm² we find that the results can be described well by R=(t/t ₀)^–2.8 K cm/W with t ₀=(Q/Q ₀)^0.904 and Q ₀=393 W/cm². Thus R has an incipient divergence at T which is, however, supplanted by T _c(Q) where R remains finite. The results imply RQ ^(m–1) with m=3.53±0.02. This differs from the original assumption m=3 of Gorter and Mellink, and from experimental results obtained well below T . However, it agrees with measurements by Leiderer and Pobell at larger currents and further below but still close to T . Our measurements could not resolve a critical heat current for the onset of resistance.     

Dynamics of the Cluster of Vortex Points in Two-Dimensional Superfluid 4He

We have simulated the dynamics of cluster of quantized vortex points with the same circulation in two-dimensional superfluid ⁴He. In two-dimensional quantum turbulence, vortices are always distributed uniformly, but often form some clusters. We study the dynamics of a cluster at zero temperature and finite temperatures. At zero temperature the cluster rotates. The radius and the density of the cluster hardly change because of the conservation of the energy and the angular momentum. On the other hand, at finite temperatures, the cluster rotates with forming a lattice structure and expanding because of the mutual friction.     

Thermoviscous Effects in Steady and Oscillating Flow of Superfluid 4He: Experiments

The correct interpretation of superfluid flow experiments relies on the knowledge of thermal and viscous effects that can cause deviations from ideal behavior. The previous paper presented a theoretical study of dissipative and reactive(nondissipative) thermoviscous effects in both steady and oscillating flow of an isotropic superfluid through small apertures and channels. Here, a detailed comparison is made between the theory and a wide array of experimental data. First, the calculated resistance to steady superflow is compared with measurements taken in a constant pressure-head flow cell. Second, the resonant frequency and Q of three different helmholtz oscillators are compared with predictions based on the calculated frequency response. The resonant frequency and Q are extracted numerically from the frequency response, and analytical results are given in experimentally important limits. Finally, the measured and calculated frequency response are compared at a temperature where the Helmholtz oscillator differs significantly from a simple harmonic oscillator. This difference is used to explain how the thermal properties of the oscillator affect its response. The quantitative agreement between the theory and experiment provide an excellent check of the previously derived equations. Also, the limiting expressions shown in this paper provide simple analytical expressions for calculating the effects of the various physical phenomena in a particular experimental situation.     

He4 State Equation Below 0.8 K

This work develops the Helmholtz potential A(ρ, T) for He⁴ below 0.8 K. Superfluid terms, related to temperature and momentum gradients, are neglected with negligible loss of accuracy in the derived state properties (specific heats, first sound velocity, expansivity, compressibility, etc.). Retained terms are directly related to a bulk fluid compressibility plus phonon and roton excitations in this quantum fluid. The bulk fluid compressibility is found from the empirical equation c₁³ ≈ c₁₀³ + b; P, where c₁ is the velocity of first sound, P is the pressure, and c₁₀ and b are constants; this empirical equation is found to apply also to other helium temperature ranges and to other fluids. The phonon excitations lead to a single temperature-dependent term in A(ρ ,T) up to 0.3 K, with only two more terms added up to 0.8 K. The roton potential, negligible below about 0.3 K, is a single term first derived 60 years ago but little used in more recent work. The final A(ρ ,T) is shown to fit available experimental specific heat data to about ±2% or better. The magnitude of the pressure-independent Gruneisen parameter below 0.3 K is typical of highly compressed normal liquids. Extension of the equation above 0.8 K is hampered by lack of data between 0.8 and 1.2 K     

Thermal Instability of Superfluid Phase-Separated 3He-4He Solution Heated From Below

No Heading The phase separation influence on thermal instability of ³He-⁴He superfluid mixtures heated from below is studied in the temperature range of 70 – 550 mK. The experiments are carried out in a cylindrical cell of 2.38 cm in diameter and 4.7 cm in height with the initial concentration of 9.8 %³He. The thermal instability is registered by observing the anomaly in the dependences of temperature and concentration gradients in the cell as a function of heat flux. The instability is shown to occur only in the phase-separated solutions. We explain this behavior by the influence of capillary effects on the interface of the two-phase liquid. The experimental results are analyzed in terms of the critical Rayleigh and Marangoni numbers.PACS numbers: 44.25.+f, 67.30.–q, 67.80.Gb     

Quantum Evaporation from Superfluid 4He

The quantum evaporation experiments of Brown and Wyatt ² have been re-analysed in the light of a recent measurement of the high-energy phonon spectrum created by a pulse-heated thin film ¹⁰ . Two sources of systematic error become significant at the level of the precision required by this new analysis: firstly, in the detector position which is recalibrated by using large-angle roton evaporation; and secondly, in the liquid height due to capillary action affecting the level-detectors. These effects have been included in an improved simulation of the experiment which has brought the angular dependence of the measured and theoretical phonon-atom evaporation results into agreement within the mechanical tolerances of the apparatus. The reanalysis suggests that the roton-atom evaporation probability increases with wave vector.     

The Superfluid Transition and Vortex Dynamics in Submonolayer Superfluid 4He Films in Porous Glass Under Rotation

A combination of a rotating dilution refrigerator and high-Q torsional oscillator technique has been used to study dynamics of vortices in thin ⁴ He films adsorbed on the porous glass (d=1m pore size). Under rotation an additional dissipation peak with the amplitude proportional to the angular velocity is seen at the middle of the superfluid transition, on the low temperature side of the stationary peak which is present even at =0. We attribute this peak to the 3D Type vortices created in multiply connected ⁴ He film by the rotation. Peak shape of the rotation-induced dissipation could be interpreted as a freezing of the 3D vortices well below T _c