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

Transition to turbulence for a quartz tuning fork in superfluid He-4

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 "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

Quartz Tuning Fork: Thermometer, Pressure- and Viscometer for Helium Liquids

Commercial quartz oscillators of the tuning-fork type with a resonant frequency of ∼ 32 kHz have been investigated in helium liquids. The oscillators are found to have at best Q values in the range 10⁵–10⁶, when measured in vacuum below 1.5 K. However, the variability is large and for very low temperature operation the sensor has to be preselected. We explore their properties in the regime of linear viscous hydrodynamic response in normal and superfluid ³He and ⁴He, by comparing measurements to the hydrodynamic model of the sensor

Vibrating Quartz Fork – A Tool for Cryogenic Helium Research

Oscillating objects such as discs, piles of discs, spheres, grids and wires have been widely used in cryogenic fluid dynamics and in quantum fluids research since the discovery of superfluidity. A new addition are quartz tuning forks, commercially available frequency standards. We review their use as thermometers, pressure- and viscometers as well as their potential as generators and detectors of cavitation and turbulence in viscous and superfluid He liquids

Thermometry in Normal Liquid He-3 Using a Quartz Tuning Fork Viscometer

We have developed the use of quartz tuning forks for thermometry in normal liquid He-3. We have used a standard 32 kHz tuning fork to measure the viscosity of liquid He-3 over a wide temperature range, 6 mK <T <1.8 K, at SVP. For thermometry above 40 mK we used a calibrated ruthenium oxide resistor. At lower temperatures we used vibrating wire thermometry. Our data compare well with previous viscosity measurements, and we give a simple empirical formula which fits the viscosity data over the full temperature range. We discuss how tuning forks can be used as convenient thermometers in this range of temperatures with just a single parameter needed for calibration

The damping of a quartz tuning fork in superfluid He-3-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