Experiments on a High Quality Grid Oscillating in Superfluid 4He at Very Low Temperatures

We have investigated a copper-mesh grid oscillating at its fundamental (0, 1) Bessel mode in superfluid ⁴He for temperatures 10<T<1500 mK at a pressure of P=5 bar. The high quality factor (Q～10⁵) of the oscillator allowed us to observe new features of its response to a periodic drive which, at the lowest T, was found to depend on the prehistory of the helium. The experiments have confirmed the existence of two critical velocities, and we discuss whether these critical velocities are associated with quantized vortices.     

Normal phase propagation along a current carrying superconducting wire and its heat transfer to a cooling He II bath

A theoretical and experimental study of the longitudinal propagation velocity of a normal phase along a superconducting cylindrical wire suspended in a superfluid helium bath is presented. The theoretical model supposes a moving nonplanar separating boundary between the normal and superconducting phases and takes into account the latent heat absorbed during the destruction of the superconducting state. The comparison of the measured and calculated normal zone propagating velocities versus the circulating electrical currents shows an excellent agreement for all the bath temperatures considered. A boundary thermal conductance across the wire wall and superfluid helium bath interface is inferred by adjusting the calculated velocities with the experimental data. The deduced boundary thermal conductance is similar to the Kapitza conductance in the sense that both are proportional to the superfluid helium bath temperature raised to a constant power. Furthermore the deduced boundary conductance seems unaffected by the dynamical aspect of the longitudinal destruction process of the superconducting state and by the heat flux range across the solid and He II separating boundary covered by the normal zone propagation velocity versus the circulating electrical current plots. To the authors knowledge this is the first study of heat transfer using the data obtained from longitudinal normal zone propagation experiments.     

Persistent current states in rotating superfluid helium

Persistent current states in superfluid helium contained in a rotating superleak are studied for various velocities and initial conditions. The change in the superfluid component velocity as the normal component velocity changes is interpreted in terms of a circulation-free potential flow and the entrance of vortices. The appearance of vortices of opposite sign to that of preexisting ones in the superleak is discussed and this is related to the history-dependent nature of persistent currents. An analogy between a superfluid helium system such as ours and a highly irreversible type-II superconductor is made.     

Influence of Quantum Turbulence on the Processes of Heat Transfer and Boiling in Superfluid Helium

We demonstrate that in a wide range of heat fluxes the dynamics of heat transfer in superfluid helium is determined by the existence of remanent quantized vortices. The vortex density dynamics determines the rise of temperature near the heater and the boiling-up of superfluid helium. It permits to understand the results of the experiments of several groups.     

The Nucleation of Superfluid Turbulence at Very Low Temperatures by Flow Through a Grid

Recent experiments by Nichol et al. (cond-mat/0309245 v2) have been concerned with the dynamical behaviour of a grid oscillating in superfluid ⁴He at a very low temperature, where the normal fluid can be ignored. An interesting enhancement of the effective mass of the grid was observed above a first threshold velocity, without significant increase in damping. Only above a second larger threshold was there a large increase in damping, resulting, we presume, from the generation of turbulence. We show now how the increase in effective mass can be understood in terms of an adiabatic response of the remanent quantized vortices that are knoum to be present, usually, in superfluid helium. Only at the larger threshold is the adiabatic response replaced by a dissipative evolution into a turbulent tangle of vortex lines. We present a semi-quantitative analysis of the experimental results, which suggests strongly that the remanent vortices must take the form of a rather high density of vortex loops attached to the grid. But confirmation of our ideas must await the completion of further experiments and a programme of non-trivial computer simulations.     

The generation of particles to observe quantized vortex dynamics in superfluid helium

We describe a method to prepare a sample of superfluid helium-4 with hydrogen particles suspended within it. The method is to dilute hydrogen gas with helium at room temperature, and bubble the mixture through liquid helium at a temperature above the superfluid phase transition temperature, T_λ ≈ 2.17 K. The procedure yields a suspension of micron-sized particles whose total volume is about 10⁵ times smaller than the fluid volume. The fluid and suspension are then cooled to a temperature below T_λ. We show that the particles, so prepared in superfluid helium, are useful for studying superfluid flows and, in particular, the dynamics of quantized vortices. In addition, the particle-superfluid helium system is rich in not yet fully explained interactions. We review preliminary investigations that include observing the vortex lattice in rotating helium, vortex reconnection in quantized vortex turbulence, and vortex ring decay. These data illustrate the basic mechanisms of dissipation in superfluid turbulence.     

Flow phenomena of superfluid helium through a porous plug phase separator

A porous plug, which separates vapour from superfluid helium (He II), is an indispensable component for space cryogenics. Precise measurement of the temperature distribution inside a number of porous plugs has been successfully carried out to reveal the actual flow phenomena of superfluid helium and the vapour flow through the plugs. It was found that He II flows ideally through the upstream portion of the porous plug, thus the London equation can be applied there. Superfluid helium turns into vapour near the exit of the porous plug. The flow of the normal component of He II remained laminar in the cases examined in the experiment. The liquid-vapour phase boundary was formed just at the exit of the porous plug and moved toward the upstream side as the mass flow rate increased. A thermodynamic consideration of He II phase separation using a porous plug is also presented in this Paper.     

Can Superfluid Vortex Lines Excite Normal Fluid Turbulence in 4He?

When helium II is made turbulent the superfluid component forms a dense tangle of quantized vortex lines which can be easily detected experimentally using the second sound technique. On the contrary little is known about the normal fluid component: on the experimental side progress has been hindered by the lack of simple flow visualization, and on the theoretical side attention has been concentrated on the effect that a given normal flow has on the superfluid vortices, not vice-versa. Attempting to fill this gap, we discuss results of recent calculations in which we find that normal fluid vorticity structures can be generated by superfluid vortices. In particular we address the issue of whether the superfluid vortices can make the normal fluid turbulent.     

Numerical Simulations of Superfluid Turbulence under Periodic Conditions

This paper is devoted to numerical simulation of vortex tangle dynamics in superfluid helium. The problem is solved on the base of the so called reconnection ansatz consisting of the equation of motion for vortex lines plus reconnection of a loop. A new algorithm, which is based on consideration of crossing lines, is used for the reconnection processes. Calculations are performed for a cubic box. Periodic boundary conditions are applied in all directions. We use the 4th order Runge-Kutta method for the integrations in time. The dynamics of quantized vortices with various counterflow velocities is studied. The density of vortex lines and number of reconnections as functions of vortex line density are calculated.      

Questions Related to the Oscillatory Flow of He II through a Grid at Low Temperatures

No Heading The flow of pure He II at low temperatures and a range of pressures is probed using an electrostatically-driven oscillating grid. With increasing oscillation amplitude, a (history dependent) first threshold is reached where the initially pure superflow abruptly changes: the resonant frequency decreases and the response becomes strongly nonlinear, attributable to quantized vortices responding to the motion of the grid so as to increase its effective mass without additional damping. On further increase of oscillation amplitude a second threshold is reached, probably marking the onset of superfluid turbulence. The increase in effective mass is believed to be due to a boundary layer of vortex loops that can evolve into turbulent flow at the second threshold. Open questions and problems for future research are formulated.     

Numerical Studies of Quantum Turbulence

We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose–Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross–Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed to revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose–Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates, e.g., two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, some of which have not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally, we discuss open problems.     

Are Vortices in Rotating Superfluids Breaking the Weak Equivalence Principle?

Due to the breaking of gauge symmetry in rotating superfluid Helium, the inertial mass of a vortex diverges logarithmically with the vortex size. The vortex inertial mass is thus much higher than the classical inertial mass of the vortex core. An equal increase of the vortex gravitational mass is questioned. The possibility that the vortices in a rotating superfluid could break the weak equivalence principle in relation with a variable speed of light in the superfluid vacuum is debated. Experiments to test this possibility are investigated on the basis that superfluid helium vortices would not fall, under the single influence of a uniform gravitational field, at the same rate as the rest of the superfluid helium mass.     

Phase Slips and Josephson Weak Links in Superfluid Helium

When superfluid ⁴He flows through a submicron aperture, the velocity is limited by a critical value which marks the onset of quantized vortex creation. The evolution of the vortices causes the quantum phase across the aperture to change by 2π, leading to a detectable drop in flow energy. Recent studies of these phase slip events have provided new insights into the nucleation mechanisms for quantum vortices. By contrast, superfluid ³He passing through a submicron aperture exhibits nonlinear hydrodynamics, characterized by a Josephson-like current phase relation. Recent experiments have revealed a multitude of effects analogous to phenomena observed in superconductors. The experiments also reveal unexpected effects such as bistability, π-states, and novel dissipation mechanisms. PACS numbers: 67.57.-z, 74.50.+r, 67.40.Hf, 67.40. Vs.     

Equilibrium vortex density in a rotating two-dimensional superfluid

The equilibrium state of a two-dimensional superfluid in rotation is discussed. It is shown that, in equilibrium, the presence of polarizable vortex-antivortex pairs does not affect the critical angular velocity at which free vortices enter the system, nor does it affect the free vortex density at higher angular velocities.     

The Onset of Vortex Production by a Vibrating Wire in Superfluid 3He-B

We present measurements of the force-velocity response of a vibrating wire resonator in superfluid ³He-B at very low temperatures. At low velocities the response is dominated by intrinsic (vacuum) damping whilst at high velocities it is dominated by pair-breaking. At intermediate velocities there is a series of small plateaus where the velocity often shows small oscillations. We believe that the behaviour results from the stretching of vortices pinned to the wire. The vortices grow and self-reconnect, emitting a vortex ring. The behaviour is very sensitive to the presence of surrounding vortices generated by a neighbouring vibrating wire.     

Propagation of a Turbulent Fronts in Quantum Fluids

This paper is part of our series of studies on the dynamics of inhomogeneous vortex tangles. We consider here the motion of turbulent fronts. There are a number of experiments in which the authors observed the development of superfluid turbulence in quantum fluids in the form of propagating fronts. There are also experiments in which the authors observed the appearance of the moving structures (“plugs”), regions with the high vortex line density in the counterflowing superfluid helium. These phenomena have both scientific and applied interest. For example, the possibility of spontaneous formation of “plugs” can radically affect heat transfer in channels with superfluid helium, which is used as a refrigerant for cooling superconducting devices. There are a number of hypotheses for how the fronts and “plugs” appear and what their dynamics are, in particular, how to evaluate the velocity of propagations. In the present work we elaborate the approach of the combustion-like propagation of the superfluid turbulent domain. A key assumption is that propagation of the front occurs in diffusion manner of diffusion with the source of the vortices behind the front, just like the combustion process. Additionally, there is a drift motion of the vortex tangles due to polarization of the vortex loops. Interplay of these effects determines the speed of the turbulent front propagation. We performed a comparison with the experimental data.     

Vortex Nucleation and the Levitation of Charged Helium II Drops

Intrinsic nucleation of quantized vortices in Helium II can be studied by means of rotating freely suspended superfluid drops at angular velocities above some critical value. The motivation for doing so is described, as well as recent progress in the electrostatic levitation of Helium II drops charged with positive ions. To date, stable levitation has been achieved for drops of order 100–150 micrometers in diameter, with a surface charge density about a factor of ten smaller than Rayleigh limit, and a diameter a similar factor less than the maximum allowed in normal gravity. We discuss the possibility of rotating these drops via the surface charge density and discuss the advantages of a microgravity environment, including the attainment of significantly larger suspended drops. Recent efforts to find optical seed particles for angular velocity measurements are discussed.     

Influence of Normal Fluid Disturbances on Interactions of Solid Particles with Quantized Vortices

Two-dimensional Lagrangian trajectories of the inertial particle in helium II are analyzed in the vicinity of the triple-vortex structure, i.e. the superfluid vortex and the normal dipole-like vortex structure induced by the mutual friction. It is shown that the vortices in the normal fluid can deflect the particle which otherwise would have collided with the superfluid vortex and, provided that the relative velocity of the particle and the vortex is not too large, would have been trapped by it. A geometrical impact parameter, which in the considered two-dimensional model, plays a r?le of the cross-section of particle–vortex collision, is determined and calculated as a function of temperature, externally applied superfluid velocity, and the Stokes number defined by the size of the local vortex structure, superfluid line velocity, and particle viscous response time.     

Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid ⁴He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.     

Non-linear effects in two dimensional superfluids

We review the relationship between superfluidity, Bose condensation and vortices in two dimensional superfluids. The theory of the dynamic response of superfluid films, due to Ambegaokar et al., is reviewed and then extended to describe the non-linear response of both helium and superconducting films.