Search

Electrical and mechanical power, together with other forms of useful work, are generated worldwide at a rate of about 1012 watts, mostly using heat engines. The efficiency of such engines is limited by the laws of thermodynamics and by practical considerations such as the cost of building and operating them. Engines with high efficiency help to conserve fossil fuels and other natural resources, reducing global-warming emissions and pollutants. In practice, the highest efficiencies are obtained only in the most expensive, sophisticated engines, such as the turbines in central utility electrical plants. Here we demonstrate an inexpensive thermoacoustic engine that employs the inherently efficient Stirling cycle1. The design is based on a simple acoustic apparatus with no moving parts. Our first small laboratory prototype, constructed using inexpensive hardware (steel pipes), achieves an efficiency of 0.30, which exceeds the values of 0.10–0.25 attained in other heat engines5,6 with no moving parts. Moreover, the efficiency of our prototype is comparable to that of the common internal combustion engine2 (0.25–0.40) and piston-driven Stirling engines3,4 (0.20–0.38).

Under certain circumstances1,2, a superconducting Josephson junction can maintain a quantum phase difference of π between the two samples that are weakly connected to form the junction. Such systems are called ‘π-junctions’ and have formed the basis of several experiments designed to investigate the much-debated symmetry of the order parameter of high-temperature superconductors3,4,5,6,7,8. More recently, the possibility that similar phenomena might occur in another macroscopic quantum system — a pair of weakly coupled Bose–Einstein condensates — has also been suggested9. Here we report the discovery of a metastable superfluid state, in which a quantum phase difference of π is maintained across a weak link separating two reservoirs of superfluid 3He. The existence of this state, which is the superfluid analogue ofa superconducting π-junction, is likely to reflect the underlying ‘p-wave’ symmetry of the order parameter of superfluid 3He, but a precise microscopic explanation is at present unknown.

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.

A calculation is presented of thermoviscous effects in both steady and oscillating flow of an isotropic superfluid through small apertures and channels. These calculations, which are based on the two-fluid model, are motivated by the work of Robinson and Atkins which included only the thermal effects of flow through a superleak. This paper extends these calculations to include the effects of normal fluid flow, compressibility, and thermal expansion. These effects are found to be both dissipative and reactive(nondissipative). The motivation for the extension is to provide a clear understanding of the reactive and dissipative forces at work in superfluid flow experiments. In the paper which immediately follows this one, predictions based on the results of this paper are compared with a wide array of experimental data. This work takes on importance due to the recent discovery of gyroscopic effects, and the possible development of sensitive gyroscopes in experimental cells whose geometry is similar to the one considered in this paper.

Arguments first proposed over thirty years ago, based on fundamental quantum-mechanical principles, led to the prediction1,2,3 that if macroscopic quantum systems are weakly coupled together, particle currents should oscillate between the two systems. The conditions for these quantum oscillations to occur are that the two systems must both have a well defined quantum phase, φ, and a different average energy per particle, μ: the term ‘weakly coupled’ means that the wavefunctions describing the systems must overlap slightly. The frequency of the resulting oscillations is then given by f = (μ2− μ1)/h, where h is Planck's constant. To date, the only observed example of this phenomenon is the oscillation of electric current between two superconductors coupled by a Josephson tunnelling weak link4. Here we report the observation of oscillating mass currents between two reservoirs of superfluid 3He, the weak link being provided by an array of submicrometre apertures in a membrane separating the reservoirs. An applied pressure difference creates mass-current oscillations, which are detected as sound in a nearby microphone. The sound frequency (typically 6,000–200 Hz) is precisely proportional to the applied pressure difference, in accordance with the above equation. Thesesuperfluid quantum oscillations were first detected while monitoring an amplified microphone signal with the human ear.

In order to study the effects of thermal and quantum fluctuations on the intrinsic critical velocity for vortex production, it is advantageous to drive superfluid4 He through a small aperture at constant pressure head. For 2π phase slip events, this gives a constant Josephson frequency and a corresponding constant vortex nucleation rate. In the usual relaxation transient experiments, the pressure head decays in time preventing observation at fixed nucleation rate. Therefore, we have developed a constant pressure-head drive system using feedback control. The technique, which senses the pressure difference across a flow aperture with a capacitive pressure gauge, can maintain pressure drives as low as 0.5mPa (f j =35Hz).

We have developed a small valve (2.35 cm in diameter by 2.8 cm long) for use in superfluid helium. The valve uses a hydraulically actuated, closely guided Torlon tip that seals against a polished stainless steel seat. The geometry of the tip and seat was designed to provide a reproducible and robust sealing surface. Leak tests have been performed for hundreds of closings at 77 K and for about ten closings at 4.2 K with no detectable leak down to 10−10 atm-cc/sec. Several times during these tests, the valve was subjected to 150% of the force needed to form a seal. No adverse effects were found. Volume flow tests reveal some features of how this type of valve closes.

We present preliminary measurements of the intrinsic critical velocity for vortex production due to flow through a submicron aperture at temperatures from 1.65K toT λ−T=3×10−3 K and fluid drive pressures (Josephson frequencies) from 0.5mPa (f j=35Hz) to 250mPa (f j=17kHz). The critical velocity is probed using a constant pressure drive technique which maintains a constant phase slip nucleation rate for several minutes. The measured critical velocity qualitatively agrees with a model of thermally activated vortex half rings.

Backhaus et al. reply — Avenel et al. have suggested a mechanism that might explain the recently discovered1 metastable π-state in a superfluid 3He weak-link array. We are pleased that our experiment is leading to new ideas that may extend the understanding of weak-link arrays. We agree with Avenel et al.'s comment that, when the individual apertures are in a (short coherence length, low temperature) hysteretic regime, collective phenomena quite distinct from single weak-link behaviour might be observed. Nevertheless, in the temperature regime in which the coherence length is comparable to the aperture dimensions, we have shown that the collective behaviour of the array is similar to that of a single weak link2,3.