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Experiments on quantum turbulence within superfluid 3He-B

Michael Robert Lowe

Published Jan 1, 2003• 0 citations
Publisher

Abstract

This thesis describes experiments conducted on B phase 3He in the μK temperature regime to investigate the turbulent properties of quantised vortices created by driving a vibrating wire resonator above its superfluid pair breaking critical velocity. By operating several resonators as highly sensitive vortex detectors the localised effects of vortex lines have been measured. The results have shown the vortices being of greater density in the directions of the generating wire motion and the rate of production being dependent upon the generator wire velocity. The rate at which the vortices decay spatially has been shown to approximate to a simple exponential and the decay length of this exponential has been measured. Using a thermal quasiparticle beam emitted by a black body radiator, the temperature dependence of the vorticity has been investigated for several quasiparticle beam temperatures between 177μK and 275μK and several bulk superfluid temperatures between 171μK and 236μK. The vortex line density of the turbulence has been calculated using a mathematical model developed here at Lancaster and shows some dependence on the temperature of the superfluid. The method of using a quasiparticle beam emitted from a black body radiator may be developed to allow a higher resolution of investigation of vortex creation and decay.

DOI
10.17635/lancaster/thesis/667

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This thesis describes experiments conducted on B phase 3He in the μK temperature regime to investigate the turbulent properties of quantised vortices created by driving a vibrating wire resonator above its superfluid pair breaking critical velocity. By operating several resonators as highly sensitive vortex detectors the localised effects of vortex lines have been measured. The results have shown the vortices being of greater density in the directions of the generating wire motion and the rate of production being dependent upon the generator wire velocity. The rate at which the vortices decay spatially has been shown to approximate to a simple exponential and the decay length of this exponential has been measured. Using a thermal quasiparticle beam emitted by a black body radiator, the temperature dependence of the vorticity has been investigated for several quasiparticle beam temperatures between 177μK and 275μK and several bulk superfluid temperatures between 171μK and 236μK. The vortex line density of the turbulence has been calculated using a mathematical model developed here at Lancaster and shows some dependence on the temperature of the superfluid. The method of using a quasiparticle beam emitted from a black body radiator may be developed to allow a higher resolution of investigation of vortex creation and decay.
Quantum turbulence is a conceptually simple form of turbulence, consisting of a tangle of quantised vortex lines. It provides a model system, through which it may be possible to understand features of the complex and not yet fully understood classical turbulence. A novel detector made from arrays of custom-designed tuning forks was developed and used to investigate properties of excitation beams and quantum turbulence in superfluid 3He-B at temperatures below 200 µK. The detector was constructed from 5 arrays of 5 tuning forks mounted in a copper block to create a 25 pixel square detector of excitation flux. The detector was situated in a cell such that it could be illuminated with a beam of thermal excitations, and that turbulence could be generated in the path of the beam, which will cast a shadow on the face. Characterisation of the detector response to beams generated by the black-body radiator and source wire were performed. We observe that the beam generated by a black-body radiator appears approximately symmetric, consistent with being emitted from a point-source of excitations. In addition to this we find that the profile of the beam generated by the black-body radiator was independent of the power applied to it, an important assumption of the properties of the black-body radiator that had not been previously observed. The beam emitted from a vibrating wire was found to be much narrower and has a angular profile that changes as the velocity of the wire is increased. Probing a turbulent tangle generated by a vibrating wire with this beam showed that the turbulence appears to fill all of the volume in between the radiator and detector. The vortex line density of the tangle appeared the be greatest in the vicinity of the wire, consistent with previous measurements of the vortex tangle generated by vibrating wires. In addition, we find that there are reproducible features in the development of the shadow as a function of the wire velocity, indicating that there is some structure in the development. The shadow is independent of the power of the beam used to probe the tangle. Measurements of fluctuations in the shadow cast by the vortex tangle show that the turbulence has a spectrum reminiscent of the Kolmogorov spectrum. In addition to this the resolution of the detector is such that it is possible in principle to measure the shadow cast by a single vortex line, and we examine candidate events for such a measurement. This represents the first such measurement of the motion of vortex lines in 3He-B.
This thesis details experiments in the ballistic regime of superfluid 3He-B at temperatures around 100 ➭K. In this thesis, the quasiparticle beam profile from a Black-Body radiator and a vibrating wire resonator is measured using a quasiparticle camera which consists of 25 tuning forks. The vibrating wire resonator is found to have a very thinly spread beam at velocities slightly higher than the pair-breaking critical velocity which spreads out at higher velocities. At 21 mm/s the vibrating resonator is found to have a more focused beam than the Black-Body radiator where both beam profiles are found to be focused around the centre of the quasiparticle camera. A theoretical model is created in order to model the spread and intensity of the experimental beam profile from the Black-Body radiator. In this thesis, the response of some of the probes to thermal damping is measured in the form of the geometrical constants γ and λ. The geometrical constant λ is related to the velocity dependence of the probe to thermal damping and is found for two wires of varying diameter, a tuning fork and its overtone mode in which all the values of λ were close to unity. The geometrical constant γ is related to the sensitivity of a probe to thermal damping. This is found for a Black-Body radiator and then used to derive the sensitivity for other wires in the cell in thermal equilibrium with it. Two resonant modes of a small tuning fork are used to do a Black-Body radiator calibration on the area around the tuning fork which is used to find the sensitivity of 25 tuning forks (pixels) in the quasiparticle camera.
An oscillating object can stretch quantized vortices attached to it in superfluids due to the relative superflow, steadily generating quantum turbulence, even in the zero-temperature limit. We report the emission and propagation of quantized vortices from quantum turbulence generated in superfluid 4{}^{4}4He at low temperatures. A vortex-free vibrating wire enables us to detect the first collision of vortex rings and therefore to measure the time-of-flight of a vortex emitted from a generator to a detector. The detection times from the start of turbulence generation exhibit an exponential distribution, suggesting that the detection is a Poisson process. Vortices are emitted continuously, but each vortex has a random flight velocity and direction. We estimated the nondetection time and mean detection period from the distribution for two flight distances. By estimating the flight velocity, we find that only vortices with velocities lower than the detector velocity can be detected, even if the sizes of the emitted vortices are smaller than the wire thickness or the vibration amplitude. The ratio of the detection rate as a function of vortex velocity suggests anisotropic emission of vortices from the quantum turbulence.
In this thesis we use quartz tuning fork resonators to probe properties of normal and superfluid 4He and 3He. Our main goal is to study both quantum turbulence and acoustic emission of tuning forks in liquid helium. By employing a multi-frequency lock-in amplifier we contrast single and multi- frequency methods of measuring tuning forks in the linear regime. In the non-linear response of tuning forks during turbulence we create multi-frequency excitations called intermodulation products which are used to find the non-linear forces that created them. We apply this technique to quantum turbulence in superfluid 4He-II and find that the retarding in-phase force on the fork increases at a critical velocity for turbulence nucleation. We also observe that the out-of-phase non-linear force increases, which we attribute to energy loss via vortex ring emission by the fork. Superfluid 3He is a fermionic condensate of Cooper pairs of 3He atoms. At ultra-low temperatures of 120 μK thermally excited unpaired quasiparticles travel ballistically through the condensate. We beam quasiparticles from a black body source towards a 5 × 5-pixel camera and observe that the excitations follow photonic-like trajectories. We apply the source-camera configuration to non-invasively detect and even image quantum vortices, that are topological defects in the superfluid. Lastly, we explore the frequency dependent damping of quartz tuning forks in liquid 3He. We find that at high frequencies the fork damping is governed by acoustic emission. Furthermore, we show that existing models developed for sound emission in 4He can be used to predict observed acoustic damping in 3He. The results also suggest that devices for 3He experiments should be placed in cavities or designed to operate at low frequencies.
Motions of vortices are fundamental characteristics of quantum turbulence. These motions are expected to be governed only by quantized circulations in superfluids at the zero temperature limit. In the present paper, we report the motions of vortex rings emitted from a quantum turbulence in superfluid 4 He, by detecting vortex rings using a vortex-free vibrating wire as a detector. The time of flights of vortex rings are distributed, because vortex rings are emitted in any direction from a turbulent region and the detector can respond only to a reachable vortex ring. By measuring time-of-flights many times, we find an exponential distribution of time-of-flights with a non-detection period, which corresponds to the fastest time of flights of vortex rings. For a larger generation power of vortex rings, a distribution of time-of-flights still shows a single exponential distribution, but a non-detection period becomes shorter. This result implies that sizes of emitted vortex rings are distributed dependently on the generation power of turbulence. The observed exponential distributions are confirmed by numerical simulations of the dynamics of vortex rings.
The decay of quantum turbulence in superfluid (_^4)He in the zero temperature limit wasinvestigated. Quantum turbulence was created by impulsive spin-down from a specific angular velocity to rest. A measurement of the vortex line density was performed using the scattering of charged vortex rings. The vortex line density decayed as L ? t^(-3/2) which is the characteristic of quasiclassical turbulence forced at large length scales. The interaction of metastable spin-triplet ?He?_2^* molecules with quantized vortex lines in superfluid (_^4)He at temperatures below 200 mK was studied too. The molecules were generated during an injection of electrons from a sharp metal tip at high voltage. They were detected as a current into a metal collector after ionization upon colliding with the collector surface. The detected current was suppressed by even a small rotation indicating the trapping of the molecules on quantized vortices. The presence of (_^3)He impurities at the level of 0.3 ppb strongly suppressed the detected signal. The temperature dependence of the detected signal showed a sharp peak, most probably associated with the condensation of (_^3)He atoms on vortex cores. The time of flight of the molecules as a function of temperature was measured. It was observed that there are three regimes for ?He?_2^* molecules transportation in superfluid (_^4)He : ballistic regime for T 200 mK, and an intermediate regime between them. The vortex lines were created by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96 � 6 nm at pressure of 0.1 bar and 27 � 5 nm at 5.0 bar. It was also demonstrated that a tangle of vortices moving in superfluid (_^4)He are capable of conveying the ?He?_2^* molecules through the drift region.