Spinor Bose-Einstein Condensates and Topological Defects

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.

Ring Dark Solitons in Toroidal Bose-Einstein Condensates

In this Thesis, we study various aspects of ring dark solitons (RDSs) in quasi-two-dimensional toroidally trapped Bose-Einstein condensates, focussing on atomic realisations thereof. Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments. It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition.

Spin-Dynamics in Cold Gases of 87Rb and Atomic Hydrogen. The spins they are a-changin’

In this thesis the dynamics of cold gaseous atoms is studied. Two different atomic species and two different experimental techniques have been used. In the first part of the thesis experiments with Bose-Einstein condensates of Rb-87 are presented. In these experiments the methods of laser cooling and magnetic trapping of atoms were utilized. An atom chip was used as the experimental technique for implementation of magnetic trapping. The atom chip is a small integrated instrument allowing accurate and detailed manipulation of the atoms. The experiments with Rb-87 probed the behaviour of a falling beam of atoms outcoupled from the Bose-Einstein condensate by electromagnetic field induced spin flips. In the experiments a correspondence between the phases of the outcoupling radio frequency field and the falling beam of atoms was found. In the second part of the thesis experiments of spin dynamics in cold atomic hydrogen gas are discussed. The experiments with atomic hydrogen are conducted in a cryostat using a dilution refrigerator as the cooling method. These experiments concentrated on explaining and quantifying modulations in the electron spin resonance spectra of doubly polarized atomic hydrogen. The modifications to the previous experimental setup are described and the observation of electron spin waves is presented. The observed spin wave modes were caused by the identical spin rotation effect. These modes have a strong dependence on the spatial profile of the polarizing magnetic field. We also demonstrated confinement of these modes in regions of strong magnetic field and manipulated their spatial distribution by changing the position of the field maximum.

CFD Modelling of Direct Contact Condensation in Suppression Pools by Applying Condensation Models of Separated Flow

The condensation rate has to be high in the safety pressure suppression pool systems of Boiling Water Reactors (BWR) in order to fulfill their safety function. The phenomena due to such a high direct contact condensation (DCC) rate turn out to be very challenging to be analysed either with experiments or numerical simulations. In this thesis, the suppression pool experiments carried out in the POOLEX facility of Lappeenranta University of Technology were simulated. Two different condensation modes were modelled by using the 2-phase CFD codes NEPTUNE CFD and TransAT. The DCC models applied were the typical ones to be used for separated flows in channels, and their applicability to the rapidly condensing flow in the condensation pool context had not been tested earlier. A low Reynolds number case was the first to be simulated. The POOLEX experiment STB-31 was operated near the conditions between the ’quasi-steady oscillatory interface condensation’ mode and the ’condensation within the blowdown pipe’ mode. The condensation models of Lakehal et al. and Coste & Lavi´eville predicted the condensation rate quite accurately, while the other tested ones overestimated it. It was possible to get the direct phase change solution to settle near to the measured values, but a very high resolution of calculation grid was needed. Secondly, a high Reynolds number case corresponding to the ’chugging’ mode was simulated. The POOLEX experiment STB-28 was chosen, because various standard and highspeed video samples of bubbles were recorded during it. In order to extract numerical information from the video material, a pattern recognition procedure was programmed. The bubble size distributions and the frequencies of chugging were calculated with this procedure. With the statistical data of the bubble sizes and temporal data of the bubble/jet appearance, it was possible to compare the condensation rates between the experiment and the CFD simulations. In the chugging simulations, a spherically curvilinear calculation grid at the blowdown pipe exit improved the convergence and decreased the required cell count. The compressible flow solver with complete steam-tables was beneficial for the numerical success of the simulations. The Hughes-Duffey model and, to some extent, the Coste & Lavi´eville model produced realistic chugging behavior. The initial level of the steam/water interface was an important factor to determine the initiation of the chugging. If the interface was initialized with a water level high enough inside the blowdown pipe, the vigorous penetration of a water plug into the pool created a turbulent wake which invoked the chugging that was self-sustaining. A 3D simulation with a suitable DCC model produced qualitatively very realistic shapes of the chugging bubbles and jets. The comparative FFT analysis of the bubble size data and the pool bottom pressure data gave useful information to distinguish the eigenmodes of chugging, bubbling, and pool structure oscillations.

Elävä Einstein

Kirjallisuusarvostelu

Utilization of Particle Image velocimetry in PPOOLEX condensation experiments

Particle Image Velocimetry, PIV, is an optical measuring technique to obtain velocity information of a flow in interest. With PIV it is possible to achieve two or three dimensional velocity vector fields from a measurement area instead of a single point in a flow. Measured flow can be either in liquid or in gas form. PIV is nowadays widely applied to flow field studies. The need for PIV is to obtain validation data for Computational Fluid Dynamics calculation programs that has been used to model blow down experiments in PPOOLEX test facility in the Lappeenranta University of Technology. In this thesis PIV and its theoretical background are presented. All the subsystems that can be considered to be part of a PIV system are presented as well with detail. Emphasis is also put to the mathematics behind the image evaluation. The work also included selection and successful testing of a PIV system, as well as the planning of the installation to the PPOOLEX facility. Already in the preliminary testing PIV was found to be good addition to the measuring equipment for Nuclear Safety Research Unit of LUT. The installation to PPOOLEX facility was successful even though there were many restrictions considering it. All parts of the PIV system worked and they were found out to be appropriate for the planned use. Results and observations presented in this thesis are a good background to further PIV use.