Vibrating Wire Resonator Research Articles

Metal wire embrittlement monitoring by the measurement of wire oscillation frequency

In the process of irradiation of materials by fluxes of heavy particles (protons, neutrons, alpha particles), damage to material structure is often observed. As a result of the accumulation of such damages, there is a subsequent change in the properties of materials, in particular, its embrittlement and hardening. Monitoring of the embrittlement process is important for nuclear reactor vessels exposed to high neutron fluxes. In this work, to observe the effect of heavy irradiation particles on the mechanical properties of metals, we propose to use vibrating wire resonators, in which the natural frequency of oscillations of the wire strongly depends on its tension. The change in the elastic characteristics of the wire alters the value of the natural frequency of wire oscillations. The natural oscillations are generated by a special circuit. Preliminary experiments to study the embrittlement effect of a stretched wire are performed by heating the wire with an electric current. In the case of short pulses, a significant increase in frequency is achieved, which is explained by the process of hardening of the material as a result of the thermal impact on the wire (rapid heating and cooling).

Effect of magnetic scattering on the superfluid transition of He3 in nematic aerogel

We present the results of high magnetic field experiments in pure $^{3}\mathrm{He}$ (in the absence of $^{4}\mathrm{He}$ coverage) in nematic aerogel. In this case the aerogel strands are covered with few atomic layers of solid paramagnetic $^{3}\mathrm{He}$, which enables the spin-exchange mechanism for $^{3}\mathrm{He}$ quasiparticles scattering. Our earlier NMR experiments showed that in low fields, instead of the polar phase, the $A$ phase is expected to emerge in nematic aerogel. We use a vibrating wire resonator with the sample of aerogel attached to it and measure temperature dependencies of resonance properties of the resonator at different magnetic fields. A superfluid transition temperature of $^{3}\mathrm{He}$ in aerogel, obtained from the experiments, increases nonlinearly in applied magnetic field. And this increase is suppressed compared with that for the bulk ${A}_{1}$ phase, which we attribute to an influence of the magnetic scattering channel, previously considered theoretically for the case of $^{3}\mathrm{He}$ confined in isotropic silica aerogel. However, we observe the essential quantitative mismatch with theoretical expectations.

Characterization of micrometer-size laser beam using a vibrating wire as a miniature scanner.

A new method for profile measurements of small transverse size beams by means of a vibrating wire is presented. A vibrating wire resonator with a new magnetic system was developed and manufactured to ensure that the wire oscillated in a single plane. Presented evidence gives us confidence that the autogenerator creates vibrations at the natural frequency of the wire in a plane of the magnetic system, and these vibrations are sinusoidal. The system for measuring the laser beam reflected from the vibrating wire by means of a fast photodiode was upgraded. The experiments allowed the reconstruction of a fine structure of the focused beam of the semiconductor laser using only a few vibrating wire oscillations. The system presented here would eventually enable the implementation of tomographic measurements of the thin beam profile.

Dynamical similarity and instabilities in high-Stokes-number oscillatory flows of superfluid helium

We present a unified analysis of the drag forces acting on oscillating bodies submerged in superfluid helium such as a vibrating wire resonator, tuning forks, a double-paddle oscillator, and a torsionally oscillating disk. We find that for high-Stokes-number oscillatory flows, the drag force originating from the normal component of superfluid helium exhibits a clearly defined universal scaling. Following classical fluid dynamics, we derive the universal scaling law and define relevant dimensionless parameters such as the Donnelly number. We verify this scaling experimentally using all of our oscillators in superfluid $^{4}\mathrm{He}$ and validate the results by direct comparison with classical fluids. We use this approach to illustrate the transition from laminar to turbulent drag regime in superfluid oscillatory flows and compare the critical velocities associated to the production of quantized vortices in the superfluid component with the critical velocities for the classical instabilities occurring in the normal component. We show that depending on the temperature and geometry of the flow, either type of instability may occur first and we demonstrate their crossover due to the temperature dependence of the viscosity of the normal fluid. Our results have direct bearing on present investigations of superfluids using nanomechanical devices [Bradley et al., Sci. Rep. 7, 4876 (2017)].

A Quasiparticle Detector for Imaging Quantum Turbulence in Superfluid $$^3$$ 3 He-B

We describe the development of a two-dimensional quasiparticle detector for use in visualising quantum turbulence in superfluid $$^3$$ He-B at ultra-low temperatures. The detector consists of a $$5 \times 5$$ matrix of pixels, each a 1 mm diameter hole in a copper block containing a miniature quartz tuning fork. The damping on each fork provides a measure of the local quasiparticle flux. The detector is illuminated by a beam of ballistic quasiparticles generated from a nearby black-body radiator. A comparison of the damping on the different forks provides a measure of the cross-sectional profile of the beam. Further, we generate a tangle of vortices (quantum turbulence) in the path of the beam using a vibrating wire resonator. The vortices cast a shadow onto the face of the detector due to the Andreev reflection of quasiparticles in the beam. This allows us to image the vortices and to investigate their dynamics. Here we give details of the design and construction of the detector and show some preliminary results for one row of pixels which demonstrates its successful application to measuring quasiparticle beams and quantum turbulence.

Anomalous Damping of a Low Frequency Vibrating Wire in Superfluid 3He-B due to Vortex Shielding

We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid 3He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.

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.

History Dependence of Turbulence Generated by a Vibrating Wire in Superfluid 4He at 1.5 K

We report on the onset of turbulence in normal and superfluid 4He using several 13.5 μm diameter vibrating wire resonators placed in a cell, filtered from the surrounding helium bath. We measured the force-velocity characteristics of the wires in normal and superfluid helium over a velocity range up to several meters per second. The transition from laminar to turbulent behavior can be clearly identified. Surprisingly we find that, depending on the cooling history, turbulence in the superfluid does not always develop fully.

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 He-3 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 He-3-B and in superfluid He-4 at low temperatures. In superfluid He-4 the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid He-3 the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid He-3-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid He-4.

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 He-4, 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 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.

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.

Bolometric calibration of a superfluid 3He detector for Dark Matter search: Direct measurement of the scintillated energy fraction for neutron, electron and muon events

We report on the calibration of a superfluid 3He bolometer developed for the search of non-baryonic Dark Matter. Precise thermometry is achieved by the direct measurement of thermal excitations using Vibrating Wire Resonators (VWRs). The heating pulses for calibration were produced by the direct quantum process of quasiparticle generation by other VWRs present. The bolometric calibration factor is analyzed as a function of temperature and excitation level of the sensing VWR. The calibration is compared to bolometric measurements of the nuclear neutron capture reaction and heat depositions by cosmic muons and low energy electrons. The comparison allows a quantitative estimation of the ultra-violet scintillation rate of irradiated helium, demonstrating the possibility of efficient electron recoil event rejection.

Probing “Cosmological” Defects in SuperfluidHe3−Bwith a Vibrating-Wire Resonator

We report on the observation of an anomalously high damping measured by a vibrating-wire resonator (VWR) immersed into superfluid at ultralow temperatures. The observed dissipation is orders of magnitude above that corresponding to friction with the dilute normal fraction and superfluid vortices. A clear pinning behavior is also observed, as well as a strong magnetic field dependence. Our analysis points to the interaction of the VWR with a planar topological defect, analogue to cosmological vacua defects, as proposed by Salomaa and Volovik.

Decay of Pure Quantum Turbulence in SuperfluidHe3−B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.

The Dynamic Texture of Superfluid 3He-B at Very Low Temperatures and in High Magnetic Fields

We report experiments using a pair of crossed vibrating wire resonators (VWRs) in the B phase of superfluid 3He in the zero temperature ballistic limit and in magnetic fields up to the B to A phase transition field of 340 mT. The VWRs are sensitive mechanical probes of energy gaps, textures and turbulent flow. In high magnetic fields the energy gap is no longer isotropic but significantly distorted, and the damping measured by the VWRs increases. With the crossed pair, we find that we can reduce the damping measured by one VWR when we increase the drive on the other one. We suggest that the reduction arises from the orientation of the surrounding texture by superflow and the screening of quasiparticles by the creation of superfluid turbulence.

Turbulence generated by vibrating wire resonators in superfluid 4He at low temperatures

We have measured responses of vibrating wire resonators in superfluid 4He at millikelvin temperatures. We find evidence for turbulence generation above a critical velocity on the order of a few cm/s. At the critical velocity for the onset of turbulence, the resonator velocity abruptly decreases and shows hysteretic behavior. Surprisingly we find that the resonant frequencies of the resonators increase in the turbulent regime. We also find that the critical velocity may be reduced by the presence of turbulence generated by a neighboring vibrating wire resonator, allowing the detection of existing turbulence in the low temperature regime.

The Thermal Damping of an Aerogel Resonator in Superfluid 3He-B at Ultra Low Temperatures

We present measurements of the thermal damping of a cylindrical aerogel sample oscillating in superfluid. 3He-B in the low temperature regime. The measurements are made at low pressures where the 3He confined in the aerogel is normal. As in the case of conventional vibrating wire resonators, the thermal damping arises from quasiparticle collisions at the wire surface and is enhanced by many orders of magnitude by Andreev scattering from the superfluid backflow around the resonator. However, in the case of aerogel, incoming quasiparticles must be absorbed and thermalised within the aerogel before being re-emilled.

Slip Corrections for Vibrating Wire Resonators

Vibrating wire resonators have long been used as probes of the helium liquids. They have been employed as viscometers or thermometers over a wide temperature range and a corresponding range of mean free paths, from the hydrodynamic regime to the ballistic regime. The scattering of helium quasiparticles from the surface of the wire may be diffuse or specular depending on the smoothness of the wire and the helium liquid through which it is moving. The scattering is characterized by a slip length which is of order the mean free path. Recent experiments by Perisanu and Vermeulen on 3He/4He mixtures show that the scattering appears to be mostly specular; in this case there is an enhancement of the slip length. However, they find that the existing theory of Hojgaard Jensen et al. does not fit well to their experiments. In this paper, we present new calculations of the force on the wire for a mean free path which is less than a tenth of the wire diameter. The boundary conditions have been modified from those of Hojgaard Jensen et al.: we include the effect of curvature of the wire and we no longer assume that the boundary condition is that the normal component of velocity in the rest frame of the wire is zero. Perisanu and Vermeulen find that the theory gives an impressive fit to their mixture data.

Vibrating Wire Thermometry in Superfluid3He

We report systematic measurements of the response of a Vibrating Wire Resonator (VWR) in normal and superfluid liquid 3He. Special attention has been paid to the hydrodynamic regime of the superfluid B-phase, where the response parameters of the VWR do not follow a simple law. We show that a simple interpolation between the region where first order slip-corrections can be applied and the ballistic regime is insufficient. Measuring an empirical effective viscosity, we propose a temperature calibration method which allows the use of VWRs as a secondary thermometer at intermediate and high pressures in the temperature range 0.2 T c < T < 50 mK.