This thesis will examine the interactions of a cloud of charged vortex rings (CVRs) in the low temperature limit in helium-II (0.2 < T < 0.8 K) in a cubic cell containing a quasi-uniform electric field. A model of geometric collisions between vortex rings is proposed to explain the observed critical density of CVRs given by nR^3 ~ 3 cm^{-1} R where n is the CVR number density and R is the average CVR radius. This model was simulated in a simplified situation where two perfectly circular parent CVRs collide geometrically to create two perfectly circular daughter CVRs, conserving momentum and charge and dissipating a random amount of energy. The simulations are in qualitative and quantitative agreement with experiment.For an intense injection of CVRs into a strong electric field the CVRs quickly reconnect with one another to form a tangle of charged vortex loops. These loops move as one quasi-connected unit, it was found that the charged tangle's response to forcing was given by a law of the form t3 ~ (QE)^{-1/3} where t3 is the charged tangle time of flight, Q is the charge of the tangle and E is the applied electric field. Simulations of the displacement current induced in two electrodes in the cell were run in order to glean some information as to the transverse distribution of charge in the tangle, which was found to be approximately constant with time of flight and injected charge.

No description available.

Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.

An apparatus for producing atomic-gas Bose-Einstein condensates (BECs) of 87-Rb atoms is described. The apparatus produces 87-Rb BECs in a dual-chamber vacuumsystem that incorporates magnetic transport of trapped atoms from the magneto-optical trapping cell to the BEC production cell via the operation of a series of overlapping magnet coils. The design, construction, and operation of the apparatus are described in detail.The apparatus is used to study the creation of quantized vortices in BECs by the merging and interference of multiple trapped condensates. In this experiment, a single harmonic potential well is partitioned into three sections by an optical barrier,enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either merge together during their growth, or, for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

Made available in DSpace on 2014-06-11T19:23:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-01Bitstream added on 2014-06-13T18:09:47Z : No. of bitstreams: 1 silva_ley_me_ift.pdf: 1027482 bytes, checksum: 33786f51e1c264a391590d7d9fd221a5 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho consideramos um gás diluído de átomos de Fermi a baixas temperaturas, com igual numero de átomos de espin para acima (↑) e espin para abaixo (↓) formando um conjunto de N pares de átomos fermiônicos prisioneiros pela ação de uma armadilha com diferentes simetrias, nos distintos limites: de interação fraca, no limite da unitariedade, e no chamado crossover BEC-unitariedade, empregando uma equação de funcional densidade cujas soluções descrevem adequadamente as características principais do superfluido, como são: a densidade de partículas, o tamanho médio, o potencial químico e a energia do sistema / In this work we considered a Fermi gas diluted at low temperatures, to equal number of atoms with spin up (↑) and spin down (↓) into a system of N fermion pairs prisoners for the action of a trap with different symmetries, in different limits: weak-coupling, unitarity limit, and the call crossover BEC-unitarity, using a densityfunctional equation whose solutions describe some characteristics of the superfluid appropriately, for example: density profiles of particles, radius, chemical potential and the energy of the system

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 < 100 mK, diffusive 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.

The presence of quantized vortices and a high level of control over trap geometries and other system parameters make dilute-gas Bose-Einstein condensates (BECs) a natural environment for studies of vortex dynamics and quantum turbulence in superfluids, primary interests of the BEC group at the University of Arizona. Such research may lead to deeper understanding of the nature of quantum fluid dynamics and far-from-equilbrium phenomena.Despite the importance of quantized vortex dynamics in the fields of superfluidity, superconductivity and quantum turbulence, direct imaging of vortices in trapped BECs remains a significant technical challenge. This is primarily due to the small size of the vortex core in a trapped gas, which is typically a few hundred nanometers in diameter. In this dissertation I present the design and construction of a new ^87Rb BEC apparatus with the goal of studying vortex dynamics in trapped BECs. The heart of the apparatus is a compact vacuum chamber with a custom, all-glass science cell designed to accommodate the use of commercial high-numerical-aperture microscope objectives for in situ imaging of vortices.The designs for the new system are, in part, based on prior work in our group on in situ imaging of vortices. Here I review aspects of our prior work and discuss some of the successes and limitations that are relevant to the new apparatus. The bulk of the thesis is used to described the major subsystems of the new apparatus which include the vacuum chamber, the laser systems, the magnetic transfer system and the final magnetic trap for the atoms. Finally, I demonstrate the creation of a BEC of ~2x10^6 ^87Rb atoms in our new system and show that the BEC can be transferred into a weak, spherical, magnetic trap with a well defined magnetic field axis that may be useful for future vortex imaging studies.

Abstract Helium is the second most abundant element in the Universe. It is the only known substance that can exist in liquid state at absolute zero. There are two stable isotopes of helium, fermionic ³He and bosonic ⁴He. At sufficiently low temperatures, both isotopes undergo a phase transition into a superfluid state. These superfluids are usually characterised by their ability to flow without resistance, but this is by no means their only remarkable property. In this thesis, we study theoretically superfluid ³He. The work consists of two separate projects. First, we study the effect of a quantised vortex line to spin dynamics of the superfluid. We find that the interplay between the vortex and the magnetisation of the liquid generates spin waves, dissipating energy. We find that the theoretically predicted energy dissipation is in agreement with experimental data, implying that spin-wave radiation can be an important mechanism of magnetic relaxation in superfluid ³He. Second, we study the drag force acting on an object moving through zero-temperature superfluid at a constant velocity. The drag arises if momentum is transferred from the object to the fluid. At low velocities, no such mechanism exist and thus the drag vanishes. If the velocity exceeds the Landau velocity \(v_L\), it becomes possible for the object to create quasiparticle excitations that could, in principle, transfer momentum away from the object. Thus, \(v_L\) has been generally assumed to be the critical velocity, that is, the velocity above which the drag force starts to increase rapidly towards the normal-state value. We find that this is not necessarily the case. Objects much larger than the superfluid coherence length modify the superfluid flow field around them. The spatial variation of the flow field can shield the object, preventing quasiparticles from transferring momentum away from the object. This leads to a critical velocity greater than \(v_L\). / Original papers The original publications are not included in the electronic version of the dissertation. Laine, S. M., &amp; Thuneberg, E. V. (2016). Calculation of Leggett–Takagi Relaxation in Vortices of Superfluid ³He-B. Journal of Low Temperature Physics, 183(3–4), 222–229. https://doi.org/10.1007/s10909-016-1516-x Kuorelahti, J. A., Laine, S. M., &amp; Thuneberg, E. V. (2018). Models for supercritical motion in a superfluid Fermi liquid. Physical Review B, 98(14). https://doi.org/10.1103/physrevb.98.144512 http://jultika.oulu.fi/Record/nbnfi-fe2018112148794 Laine, S. M., &amp; Thuneberg, E. V. (2018). Spin-wave radiation from vortices in ³He−B. Physical Review B, 98(17). https://doi.org/10.1103/PhysRevB.98.174516 http://jultika.oulu.fi/Record/nbnfi-fe2019092630083

We focus on studying laser-induced cavitation under widely different physical conditions, from superheated jets to superfluid liquid helium. We use ultra high-speed video imaging to track cavitation bubble dynamics at frame-rates of up to 7 million frames-per-second. Cavitation is induced by focusing a 532 nm pulsed Nd-YAG laser at a spot with a minimum spot size of 150 μm and pulse duration of six ns, which forms high-pressure plasma, leading to a rapidly expanding bubble/void, which subsequently collapses. We mainly study two configurations: (1) laser-induced cavitation in liquid helium inside an optical cryostat and (2) laser-induced cavitation in HCP solid helium. Moreover, we report preliminary results of two promising studies: (3) laser-induced cavitation inside a highly turbulent flow within a square channel and (4) laser-induced break-up inside a cylindrical liquid jet, leading to its atomization. (1) Inside the liquid helium-4, we reach widely different thermodynamic conditions when adjusting the temperature between 1.4 to 5.1 degrees Kelvin. Below the lambda point at T = 2.17 K, the liquid is superfluid, with viscosity appr zero, while above this temperature, regular liquid helium approaches the critical point at ≃ 5.1 K. This greatly changes the cavitation dynamics with different amounts of vapor appearing during cavity growth and collapse, and revealed four regimes of cavitation bubble behavior. We also measure shock velocities and analyze their characteristics. (2) At pressures of roughly 25 atmospheres, superfluid helium (He-II) solidifies. With wavy time-evolving oscillations on its surface when disturbed, the interface between the solid and the superfluid exhibits fascinating behavior with wavy time-evolving oscillations on its surface when disturbed. The interface between liquid and solid can consequently behave similarly to a free surface. Here, we experimentally investigate laser-induced interfacial dynamics at temperatures between 1.2 K and 2 K and at pressures ranging from the melting pressure of approximately 25 atm to a maximum of 39 atm, which covers both the HCP and BCC structure of the solid, using ultra-high-speed imaging at frame rates up to 7 million frames per second. (3) The cavitation inside the turbulent flow; this study aims to investigate the mutual effect of the rapid straining outside the bubble on the coherent vortices within the liquid and the feedback from the modified turbulence on the shape of the vapor cavity, and to include time-resolved particle image velocimetry. (4) The cavitation inside a liquid jet helps break it up into fine spray, which is of interest for injectors in combustion engines.

In this thesis we study a variety of problems in superfluid turbulence, princi-pally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these. In Chapter 1, we provide an overview of several problems in superfluid turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give: (a) a brief introduction of fluid turbulence; (b) an overview of superfluidity and the phenomenological two-fluid model; (c) a brief overview of experiments on superfluid turbulence; (d) an introductory accounts of the phenomenological models used in the study of superfluid turbulence. We end with a summary of the problems we study in subsequent Chapters of this thesis. In Chapter 2, we present a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power- law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc ; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other. In Chapter 3, we present the first calculation of the mutual-friction coefficients α and α (which are parameters in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model that we study in chapter 5) as a function of temperature in a homogeneous Bose gas in two-dimensions by using the Galerkin-truncated Gross-Pitaevskii equation, with very special initial conditions, which we obtain by using the advective, real, Ginzburg-Landau equation (ARGLE) and an equilibration procedure that uses a stochastic Ginzburg-Landau equation (SGLE). We also calculate the normal-fluid density as a function of temperature. In Chapter 4, we elucidate the interplay of particles and fields in superfluids, in both simple and turbulent flows. We carry out extensive direct numerical simulations (DNSs) of this interplay for the two-dimensional (2D) Gross-Pitaevskii (GP) equation. We obtain the following results: (1) the motion of a particle can be chaotic even if the superfluid shows no sign of turbulence; (2) vortex motion depends sensitively on particle charateristics; (3) there is an effective, superfluid-mediated, attractive interaction between particles; (4) we introduce a short-range repulsion between particles, with range rSR, and study two- and many-particle collisions; in the case of two-particle, head-on collisions, we find that, at low values of rSR, the particle collisions are inelastic with coefficient of restitution e = 0; and, as we in-crease rSR, e becomes nonzero at a critical point, and finally attains values close to 1; (5) assemblies of particles and vortices show rich, turbulent, spatio-temporal evolution. In Chapter 5, we present results from our direct numerical simulations (DNSs) of the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model in two dimensions. We have designed these DNSs to study the statistical properties of inverse and forward cascades in the HVBK model. We obtain several interesting results that have not been anticipated hitherto: (1) Both normal-fluid and superfluid energy spectra, En(k) and Es(k), respectively, show inverse- and forward-cascade regimes; the former is characterized by a power law Es(k) En(k) kα whose exponent is consistent with α 5/3. (2) The forward-cascade power law depends on (a) the friction coefficient, as in 2D fluid turbulence, and, in addition, on (b) the coefficient B of mutual friction, which couples normal and superfluid compo-nents. (3) As B increases, the normal and superfluid velocities, un and us, re-spectively, get locked to each other, and, therefore, Es(k) En(k), especially in the inverse-cascade regime. (4) We quantify this locking tendency by calculating the probability distribution functions (PDFs) P(cos(θ)) and P(γ), where the angle θ ≡ (un • us)/( |un||us|) and the amplitude ratio γ = |un|/|us |; the former has a peak at cos(θ) = 1; and the latter exhibits a peak at γ = 1 and power-law tails on both sides of this peak. (4) This locking increases as we increase B, but the power-law exponents for the tails of P(γ) are universal, in so far as they do not depend on B, ρn/ρ, and the details of the energy-injection method. (5) We characterize the energy and enstrophy cascades by computing the energy and enstrophy fluxes and the mutual-friction transfer functions for all wave-number scales k. In Chapter 6, we examine the multiscaling of structure functions in three-dimensional superfluid turbulence by using a shell-model for the three-dimensional HVBK equations. Our HVBK shell model is based on the GOY shell model. In particular, we examine the dependence of multiscaling on the normal-fluid fraction and the mutual-friction coefficients. We hope our in silico studies of 2D and 3D superfluid turbulence will stimulate new experimental, numerical, and theoretical studies.