Acoustic Emission by Quartz Tuning Forks and Other Oscillating Structures in Cryogenic 4He Fluids

We report on experimental investigations of acoustic emission by quartz tuning forks resonating at frequencies 32 kHz, 38 kHz, 77 kHz and 100 kHz immersed in cold gaseous ⁴He and its normal and superfluid liquid phases. Frequency dependence of the observed low-drive-linewidth at 350 mK together with the temperature and pressure dependences (1.3 K < T < 4.2 K, 0 < p < 25 bar) of the observed damping of the high frequency (77 and 100 kHz) resonators measured in normal liquid ⁴He and its superfluid phase provide strong and direct evidence of the importance of sound emission by these tuning forks. Three analytical models of acoustic emission by vibrating tuning forks are developed and compared with the experimental results. We also discuss the importance of sound emission for experiments with the commonly used 32 kHz tuning forks as well as other oscillating structures??spheres, wires, grids and various micromachined sensors. We compare the relative importance of dissipative losses due to laminar viscous/ballistic drag and acoustic emission in liquid and superfluid ⁴He.     

Probing Andreev Reflection in Superfluid 3He-B Using a Quartz Tuning Fork

Direct measurements of the Andreev reflection of the quasiparticles excitations in superfluid ³He-B in the ballistic regime at 0.5 bar using a quartz tuning fork are presented. Based on these measurements, we were able to determine the value of the ratio Δ(0)/kT _c to be 1.71, in reasonable agreement with previous measurements. Moreover, it seems that Andreev reflection of excitations gives a possibility to determine the value of the constant λ characterizing the velocity field profile. This value for a tuning fork was estimated to be 1.28, different from that for cylindrical wire (λ～0.95), suggesting that the anti-phase oscillatory motion and the geometry of the tuning prongs lead to an enhancement of the velocity of the superfluid flow.     

The Damping of a Quartz Tuning Fork in Superfluid 3He-B at Low Temperatures

We have measured the damping on a quartz tuning fork in the B-phase of superfluid ³He at low temperatures, below 0.3T _c. We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid ³He-B and in superfluid ⁴He at low temperatures. In superfluid ⁴He the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid ³He the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid ³He-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid ⁴He.     

Cavitation in Liquid Helium Observed in a Flow Due to a Vibrating Quartz Fork

A quartz fork vibrating at high amplitude is used to study cavitation in He I and He II along the saturated vapor pressure (SVP) curve and at slightly elevated pressures. Cavitation is observed as a breakdown of the resonance response at critical velocity when slowly sweeping the frequency of the drive across the resonance and confirmed by visual observation of a bubble occurring in He II in the space between the prongs of the fork. On decreasing the temperature from 4.2 K along the SVP curve the critical velocity slowly increases from about 0.4 m/s to 1 m/s, until a steep increase up to about 2 m/s occurs within about 20 mK just below the superfluid transition. We discuss our results, including the measured dependence of the critical velocity versus overpressure at fixed bath temperature.      

Hysteresis,Switching and Anomalous Behaviour of a Quartz Tuning Fork in Superfluid 4He

We have been studying the behaviour of commercial quartz tuning forks immersed in superfluid ⁴He and driven at resonance. For one of the forks we have observed hysteresis and switching between linear and non-linear damping regimes at temperatures below 10 mK. We associate linear damping with pure potential flow around the prongs of the fork, and non-linear damping with the production of vortex lines in a turbulent regime. At appropriate prong velocities, we have observed metastability of both the linear and the turbulent flow states, and a region of intermittency where the flow switched back and forth between each state. For the same fork, we have also observed anomalous behaviour in the linear regime, with large excursions in both damping, resonant frequency, and the tip velocity as a function of driving force.     

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.     

Measuring the Prong Velocity of Quartz Tuning Forks Used to Probe Quantum Fluids

Recently, quartz tuning forks have been used to probe the dynamics of quantum fluids. For many of these measurements it is important to know the velocity amplitude of the tips of the vibrating fork prongs. We have used different techniques to establish, with an accuracy of a few percent, the relationship between the electrical and mechanical properties of several commercial quartz tuning forks with fundamental resonant frequency ～32 kHz. The velocity is usually inferred from an electro-mechanical calibration that models a quartz prong as a clamped, rectangular cantilever beam. We have tested the accuracy of this calibration using three methods: measurement of the amplitude at which the fork prongs touch each other; direct optical measurement of the moving fork prongs using strobe microscopy; and a Michelson interferometry technique operating with a 670 nm laser. All three methods yield consistent results. The velocity so determined is found to be 10% lower than that of the standard electro-mechanical calibration.     

Cavitation Bubbles Generated by Vibrating Quartz Tuning Fork in Liquid $$^$$He Close to the $$\lambda $$λ-Transition

We report direct optical observation of cavitation bubbles in liquid helium, both in classical viscous He I and in superfluid He II, close to the \(\lambda \)-transition. Heterogenous cavitation due to the fast-flowing liquid over the rough surface of prongs of a quartz tuning fork oscillating at its fundamental resonant frequency of \(4\,\mathrm {kHz}\) occurs in the form of a cluster of small bubbles rapidly changing its size and position. In accord with previous investigators, we find the cavitation threshold lower in He I than in He II. In He I, the detached bubbles last longer than one camera frame (10 ms), while in He II the cavitation bubbles do not tear off from the surface of the fork up to the highest attainable drive.     

Transition to Turbulence and Critical Velocity in Superfluid Solution of 3He in 4He

By the method of oscillating tuning fork, we carried out researches of the transition to turbulence in superfluid solution of 5% ³He in ⁴He at temperatures of 100 mK–300 mK. The critical velocity υ _c of the turbulence appearance is determined through measuring the volt-ampere characteristics. It is established that in the mixture the temperature dependence of the critical velocity is non-monotonous and differs strongly from that in pure ⁴He. Unlike ⁴He, the step-like anomalies on resonance curves were observed which, presumably, is connected with instability of the vortex system under the conditions where the core of the vortex is filled by the atoms of ³He. It is shown that such anomalies appear at the temperatures below 0.9 K, at the same time at temperatures below ～0.5 K they appear even at υ<υ _c .     

The Frequency Dependence of the Added Mass of Quartz Tuning Fork Immersed in He II

We measured the dependences of the resonance frequency of tuning forks immersed in liquid helium at \(T = 0.365\hbox { K}\) in the pressure interval from saturated vapor pressure to 24.8 atm. The quartz tuning forks have been studied with different resonance frequencies of 6.65, 8.46, 12.1, 25.0 and 33.6 kHz in vacuum. The measurements were taken in the laminar flow regime. The experimental data allow us to determine the added mass of a quartz tuning fork in He II. It was found that the added mass per unit length of the prong fork is frequency dependent. Some possible qualitative explanations for such dependence are proposed. In addition, we observed, at \(T = 0.365\hbox { K}\), the changes in added mass with pressure according to the pressure dependence of He II density.     

Acoustic Resonances in Helium Fluids Excited by?Quartz Tuning Forks

Ordinary quartz tuning fork resonators, operated at about 30 or 200 kHz frequency, couple to acoustic first and second sound resonances in helium fluids under certain conditions. We have studied acoustic resonances in supercritical ⁴He, normal and superfluid ⁴He, and in isotopic mixtures of helium. Suggestive temperature, pressure, and concentration dependences are given. Furthermore, we propose a thermometric reference point device based on second sound resonances in helium mixtures, and indicate possible differences in the nature of second sound resonances in superfluid ⁴He and helium mixtures.     

High Quality Tuning Forks in Superfluid 3He-B Below?200?��K

We have investigated the influence of the damping force acting on high quality tuning forks (Q??10⁶) of different sizes and geometries in superfluid ³He-B at temperatures below 200 ??K and a pressure of 0.1 bar. The measurements show that at low velocities, the damping of the largest fork expressed in terms of its resonance characteristic width ??f ₂ rises up as its velocity increases. This is in contradiction to the damping of the fork due to Andreev reflection and it may be caused by the interaction of this fork with excitations trapped in the Andreev bond states. We present our preliminary experimental results.     

Frequency Characteristics of a Quartz Tuning Fork Immersed in He II

The effect of dissipation on frequency characteristics of tuning forks was measured, the dissipation being induced by acoustic radiation of different wavelengths, excited by tuning forks. The tuning forks have been immersed in the superfluid helium. The fork resonance frequencies 32, 77 and 99 kHz have been measured at T=370 mK in the pressure range between SVP and 24.9 atm. Most of the tuning forks have been studied in a commercial can. It is found that at wavelength λ>0.6 cm the frequency dependence is determined by the relationship between density and pressure. It is established that a decrease in wavelength enhances influence of the acoustic radiation on the fork oscillation frequency. In the case where the sound wavelength is equal to the can internal diameter an acoustic resonance occurs. The frequency reaches values higher than the fork frequency in vacuum. Further reduction of the sound wavelength leads to the situation when the resonant frequency is similar to the frequency at long wavelengths.     

Response of a Mechanical Oscillator in Solid 4He

We present the first measurements of the response of a mechanical oscillator in solid ⁴He. We use a lithium niobate tuning fork operating in its fundamental resonance mode at a frequency of around 30 kHz. Measurements in solid ⁴He were performed close to the melting pressure. The tuning fork resonance shows substantial frequency shifts on cooling from around 1.5 K to below 10 mK. The response shows an abrupt change at the bcc-hcp transition. At low temperatures, below around 100 mK, the resonance splits into several overlapping resonances.     

Quantum Turbulence Generated and Detected by a Vibrating Quartz Fork

Flow due to a commercially available vibrating quartz fork is studied in gaseous helium, He I, He II and ³He–B, over a wide range of temperatures and pressures. On increasing the driving force, the flow changes in character from laminar (characterized by a linear velocity versus drive dependence) to turbulent (characterized by a square root velocity versus drive dependence). In classical fluids, we characterize this transition by a critical Reynolds number, Re _c =U _cr δ/ν, where U _cr is the critical velocity, ν stands for the kinematic viscosity, $\delta=\sqrt{2\nu/\omega}$ is the viscous penetration depth and ω is the angular frequency of oscillations. U _cr of order 10 cm/s observed in He II and 1 mm/s in ³He–B agree with those found with other vibrating objects such as spheres, wires and grids, as well as with available numerical simulations of vortex motion in an applied ac flow.     

Direct Measurement of the Critical Velocity Above Which a Tuning Fork Generates Turbulence in Superfluid Helium

The dynamics of an electrically-driven 8 kHz quartz tuning fork has been studied experimentally in liquid helium-4 in the temperature range 1.3<T<4.2 K under the saturated vapour pressure. The fork has relatively large dimensions compared to standard 32 kHz fork used in recent investigations. The velocity of the tip of the fork prong is measured by the indirect electromechanical equivalent method and is compared with the velocity of another 8 kHz fork (from the same batch) determined by direct optical measurement of the oscillation amplitude through Michelson interferometry. A comparison of these results has provided absolute values for the critical velocity of the transition to the turbulent state.     

Investigations of oscillating superleak second-sound transducers

An investigation has been made of the performance of oscillating superleak transducers with channel diameters 0.1, 0.2, and 0.4 µm for excitation and detection of second sound in superfluid⁴He. The results indicate that the sound amplitude decreases with increasing channel diameter and increasing temperature due to normal fluid Poiseuille flow in the channels of the oscillating filter paper. The sound amplitude also depends strongly on the surface roughness of the stationary backing plate of the transducers, reaching a maximum for scratches with typical dimensions of about 20 µm.     

Quartz Tuning Fork Viscometers for Helium Liquids

Mechanical resonators, in the form of vibrating wires or torsional oscillators, have long been employed as sensors in liquid ³He and ³He–⁴He mixtures. The damping of resonators is due to the viscosity of the surrounding liquid which is a strong, well-known function of temperature for bulk Fermi liquids. It is therefore possible to use the viscous damping for thermometry in the millikelvin regime. An alternative sensor is the small quartz tuning fork which is driven by the piezoelectric effect and requires no external magnetic field. In this paper, we present measurements of the viscous damping of such a tuning fork when immersed in a 6.2% ³He–⁴He mixture, between 3 and 100 mK, and at zero and high (10 T) magnetic field. The measurements indicate that damping of the tuning fork resonance is dominated by the liquid helium properties and is insensitive to the applied magnetic field. The response of the tuning fork to the saturated helium mixture demonstrates that it could potentially be used for thermometry in any magnetic field. There is evidence of slip at the interface between the fork and the helium suggesting specular scattering from the smooth surface of the quartz. The fork is also able to detect the superfluid transition in pure liquid ³He.     

脉冲管制冷机内部交变流动过程实验研究第一部分实验装置与数据处理系统

鉴于脉冲管制冷机内部流动过程是复杂的动态交变流动,运行参数、结构参数和调相机构等对内部流动规律的影响还不是十分清楚,建立了脉冲管制冷机内部动态参数测试装置,介绍了实验系统的组成,测试设备和数据采集与处理方法.该实验台能准确测量蓄冷器入口和脉冲管热端的压力波和速度波,通过对它们的幅值与相位的分析,能够系统的得到各种因素对脉冲管制冷机内部流动状态的影响规律.     

Transit times of pressure waves in an acoustic delay line

The transit times of the pressure waves of He, Ar, N₂ and air propagating in an acoustic delay line designed for practical use in a beam line of a synchrotron radiation source have been measured. It is found that the propagation velocity of a pressure wave increases with the increase in the starting pressure of the test gas in the reservoir and with the decrease in the pressure at the wave front. The speed of the pressure increase in the last segment of the acoustic delay line depends strongly on the kind of gas and on the size of the aperture in baffles installed in the acoustic delay line. A qualitative discussion of the propagation mechanism of the pressure wave is given.