DANTAS, Davi Soares. Estruturas de confinamento de baixa dimensionalidade em superfícies de hélio líquido suspensas. 2012. 73 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2012. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-21T21:20:12Z No. of bitstreams: 1 2012_dis_dsdantas.pdf: 7266499 bytes, checksum: 9ac270f80eddaf4378a655a66bd0d2e6 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-22T21:33:49Z (GMT) No. of bitstreams: 1 2012_dis_dsdantas.pdf: 7266499 bytes, checksum: 9ac270f80eddaf4378a655a66bd0d2e6 (MD5) / Made available in DSpace on 2015-10-22T21:33:49Z (GMT). No. of bitstreams: 1 2012_dis_dsdantas.pdf: 7266499 bytes, checksum: 9ac270f80eddaf4378a655a66bd0d2e6 (MD5) Previous issue date: 2012 / The system of electrons on liquid helium (EoH) is one of the most ideal objects for investigating the fundamental principles of the physics of low dimensionality, since they do not have the inhomogeneities and impurities generally found on semiconductors. Besisdes, these systems are expected to have future technological applications as quantum bits, which are of fundamental importance as building blocks of future quantum computers. Usually, the low-dimensional confinements structures for EoH suggested in the literature are based on a planar surface, where the lateral confinement is induced by an external potential controlled by electrodes. In this work, we suggest an alternative way to produce lateral confinement in liquid helium surfaces, namely, we demonstrate that the shape of the surface can be designed to produce single and double quantum dots by adjusting the shape of a cavity in the substrate. The surface was calculated for four different shapes of substrate cavity: i) a cilyndrical cavity, generating a single quantum dot; ii) a ring-shaped cavity, generating a quantum ring; iii) two cubic cavities connected by a channel, creating a coupled double-dot structure; and iv) two channel-shaped cavities that intersect perpendicularly to each other, where a single dot is formed in the intersection point. The electron is then deposited and confined to move on each surface by an external electric field. Our results show that the electron energy levels in these systems can be tuned by varying the electric field and the bulk level, which are easily adjustably. The effect of an external magnetic field on the energy spectrum in one of these systems is also investigated. / O sistema de elétrons na superfície de hélio líquido é considerado um dos melhores objetos na investigação de príncipios fundamentais da Física de baixa dimensionalidade, uma vez que estes não apresentam heterogeneidades e impurezas geralmente encontradas em heteroestruturas semicondutoras. Além disso, espera-se que estes sistemas tenham uma aplicação tecnológica futura como extit{bits} quânticos, que são fundamentais na construção de blocos dos futuros computadores quânticos. Geralmente, as estruturas de confinamento de baixa dimensionalidade sugeridas para elétrons na superfície de hélio líquido na literatura são baseadas em superfícies planas, onde o confinamento lateral é induzido por um potencial externo controlado por eletrodos. No presente trabalho, é sugerida uma forma alternativa de produzir o confinamento lateral em superfícies de hélio líquido, isto é, é demonstrado que a forma da superfície pode ser projetada para produzir anéis, fios e pontos quânticos apenas variando a forma da cavidade do substrato no qual o hélio líquido se encontra suspenso. A superfície foi calculada para quatro formas diferentes de cavidade: i) uma cavidade cilíndrica, gerando um ponto quântico simples; ii) uma cavidade em forma de anel circular, gerando um anel quântico; iii) duas cavidades em forma de canais que se interceptam perpendicularmente, formando um ponto quântico simples no ponto de interceptação; e iv) duas cavidades retangulares conectadas por um canal estreito, gerando um ponto duplo. O elétron é então depositado sobre a superfície e confinado a se mover em cada superfície devido à ação de um campo elétrico externo. Os resultados apresentados aqui mostram que os níveis de energia para estes sistemas podem ser alterados através da variação do campo elétrico e do banho de hélio, que são facilmente ajustáveis. O efeito de um campo magnético externo é também investigado em um destes sistemas.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O sistema de elÃtrons na superfÃcie de hÃlio lÃquido à considerado um dos melhores objetos na investigaÃÃo de prÃncipios fundamentais da FÃsica de baixa dimensionalidade, uma vez que estes nÃo apresentam heterogeneidades e impurezas geralmente encontradas em heteroestruturas semicondutoras. AlÃm disso, espera-se que estes sistemas tenham uma aplicaÃÃo tecnolÃgica futura como extit{bits} quÃnticos, que sÃo fundamentais na construÃÃo de blocos dos futuros computadores quÃnticos. Geralmente, as estruturas de confinamento de baixa dimensionalidade sugeridas para elÃtrons na superfÃcie de hÃlio lÃquido na literatura sÃo baseadas em superfÃcies planas, onde o confinamento lateral à induzido por um potencial externo controlado por eletrodos. No presente trabalho, à sugerida uma forma alternativa de produzir o confinamento lateral em superfÃcies de hÃlio lÃquido, isto Ã, à demonstrado que a forma da superfÃcie pode ser projetada para produzir anÃis, fios e pontos quÃnticos apenas variando a forma da cavidade do substrato no qual o hÃlio lÃquido se encontra suspenso. A superfÃcie foi calculada para quatro formas diferentes de cavidade: i) uma cavidade cilÃndrica, gerando um ponto quÃntico simples; ii) uma cavidade em forma de anel circular, gerando um anel quÃntico; iii) duas cavidades em forma de canais que se interceptam perpendicularmente, formando um ponto quÃntico simples no ponto de interceptaÃÃo; e iv) duas cavidades retangulares conectadas por um canal estreito, gerando um ponto duplo. O elÃtron à entÃo depositado sobre a superfÃcie e confinado a se mover em cada superfÃcie devido à aÃÃo de um campo elÃtrico externo. Os resultados apresentados aqui mostram que os nÃveis de energia para estes sistemas podem ser alterados atravÃs da variaÃÃo do campo elÃtrico e do banho de hÃlio, que sÃo facilmente ajustÃveis. O efeito de um campo magnÃtico externo à tambÃm investigado em um destes sistemas. / The system of electrons on liquid helium (EoH) is one of the most ideal objects for investigating the fundamental principles of the physics of low dimensionality, since they do not have the inhomogeneities and impurities generally found on semiconductors. Besisdes, these systems are expected to have future technological applications as quantum bits, which are of fundamental importance as building blocks of future quantum computers. Usually, the low-dimensional confinements structures for EoH suggested in the literature are based on a planar surface, where the lateral confinement is induced by an external potential controlled by electrodes. In this work, we suggest an alternative way to produce lateral confinement in liquid helium surfaces, namely, we demonstrate that the shape of the surface can be designed to produce single and double quantum dots by adjusting the shape of a cavity in the substrate. The surface was calculated for four different shapes of substrate cavity: i) a cilyndrical cavity, generating a single quantum dot; ii) a ring-shaped cavity, generating a quantum ring; iii) two cubic cavities connected by a channel, creating a coupled double-dot structure; and iv) two channel-shaped cavities that intersect perpendicularly to each other, where a single dot is formed in the intersection point. The electron is then deposited and confined to move on each surface by an external electric field. Our results show that the electron energy levels in these systems can be tuned by varying the electric field and the bulk level, which are easily adjustably. The effect of an external magnetic field on the energy spectrum in one of these systems is also investigated.

The density amplitude of an isolated quantum vortex line in superfluid 4He is calculated using a generalized Gross-Pitaevskii (G-P) equation. The generalized G-P equation for the order parameter extends the usual mean-field approach by replacing the interatomic potential in the ordinary G-P equation by a local, static T matrix, which takes correlations between the particles into account. The T matrix is a sum of ladder diagrams appearing in a diagrammatic expansion of the mean field term in an exact equation for the order parameter. It is an effective interaction which is much softer than the realistic interatomic Morse dipole-dipole potential from which it is calculated. A numerical solution of the generalized G-P equation is required since it is a nonlinear integro-differential equation with infinite limits. For the energy denominator in the T matrix equation, a free-particle spectrum and the observed phonon-roton spectrum are each used. For the fraction of particles in the zero-momentum state (Bose-Einstein dondensate) which enters the equation, both a theoretical value of 0.1 and an experimental value of 0.024 are used. The chemical potential is adjusted so that the density as a function of distance from the vortex core approaches the bulk density asymptotically. Solutions of the generalized G-P equation are not very dependent on the choice of energy denominator or condensate fraction. The density profile is a monotonically increasing function of the distance from the vortex core. The core radius, defined to be the distance to half the bulk density, varies from 3.7 A to 4.7 A, which is over three times the experimental value of 1.14 A at absolute zero.

Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.

Cette thèse de doctorat à été réalisée au sein du Laboratoire des Écoulements Géophysiques et Industriels (LEGI) et du Service des Basses Températures du CEA de Grenoble. Ce travail expérimental a porté sur l'étude comparative de la turbulence classique et quantique à très grand nombre de Reynolds d'un écoulement turbulent de jet d'hélium liquide normal (HeI) et superfluide (HeII) entre 2.3K et 1.78K. Le travail s’est en premier lieu concentré sur le développement des moyens d'essais (une soufflerie cryogénique à boucle fermée pressurisée et régulée en température) et sur l'adaptation de la technique de l'anémomètrie à fil chaud aux basses températures. L’étude s’est poursuivie par l'analyse statistique du champ de vitesse en He I et, plus particulièrement, des incréments spatiaux de vitesse en fluide normal montrant un bon accord avec la littérature et fournissant un véritable point de départ pour la mise en évidence de comportements différents en HeII. Les résultats obtenus en superfluide montrent d'une part un comportement classique à grande échelle et, d’autre part, des écarts aux petites échelles qui dépendent de la température du fluide (i.e. de la fraction variable de superfluide). L'effet le plus évident se manifeste par un changement du signe de la fonction de structure d'ordre 3 des incréments de vitesse. / This experimental work is focused on the the statistical study of the high Reynolds number turbulent velocity field in an inertially driven liquid helium axis-symmetric round jet at temperatures above and below the lambda transition (between 2.3 K and 1.78 K) in a cryogenic wind tunnel. The possibility to finely tune the fluid temperature allows us to perform a comparative study of the quantum HeII turbulence within the classical framework of the Kolmogorov turbulent cascade in order to have a better understanding of the energy cascade process in a superfluid. In particular we focused our attention on the intermittency phenomena, in both He I and He II phases, by measuring the high order statistics of the longitudinal velocity increments by means of the flatness and the skewness statistical estimators.A first phase consisted in developing the cryogenic facility, a closed loop pressurized and temperature regulated wind tunnel, and adapting the classic hot-wire anemometry technique in order to be able to work in such a challenging low temperature environment. A detailed calibration procedure of the fully developed turbulent flow was the carried out at 2.3 K at Reynolds numbers based on the Taylor length scale up to 2600 in order to qualify our testing set-up and to identify possible facility-related spurious phenomena. This procedure showed that the statistical properties of the longitudinal velocity increments are in good agreement with respect to previous results.By further reducing the temperature of the working fluid (at a constant pressure) below the lambda point down to 1.78K local velocity measurements were performed at different superfluid density fractions. The results show a classic behaviour of the He II energy cascade at large scales while, at smaller scales, a deviation has been observed. The occurence of this phenomenon, which requires further investigation and modelling, is highlighted by the observed changing sign of the third order structure function of the longitudinal velocity increments. The intermittency phenomena is also observed and a quantitative analysis is carried out by measuring the scaling behaviour of the velocity increments flatness which is consistent with results obtained in Navier-Stokes fluids. This Ph.D. thesis has been carried out at the LEGI (Laboratoire des Écoulement Géophysiques et Industriels) laboratory in Grenoble and at the CEA Low Temperature Department (SBT) in Grenoble.

Die thermodynamischen Eigenschaften von Flüssighelium erfordern einen hohen technischen Aufwand zu dessen Lagerung und Transfer. Aufgrund der extrem niedrigen Normalsiedetemperatur von 4,2 K ist die Verflüssigung des unter Normbedingungen gasförmigen Heliums sehr energieintensiv. Darüber hinaus besitzt Helium eine sehr niedrige Verdampfungsenthalpie, weshalb bereits geringe Wärmeeinträge signifikante Verdampfungsverluste verursachen. Infolge der räumlichen Trennung von Heliumverflüssigungsanlagen und Verbrauchern ist ein Flüssigheliumtransfer in der Regel unvermeidlich. Beim Transfervorgang durch Wärmeeintrag und Druckverluste generiertes Heliumkaltgas muss erneut dem energieaufwändigen Verflüssigungsprozess zugeführt werden, bevor es als Kältemittel verwendet werden kann. Zur Etablierung eines verlustarmen Flüssigheliumtransfers mit einflutigen flexiblen Transferleitungen sind daher die Verdampfungsverluste im Rahmen der thermohydraulischen Optimierung zu reduzieren. Die Optimierung erfolgt dabei durch die Kopplung von systematischen Messungen mit thermohydraulischen Berechnungen. Untersuchungen mit instrumentierten Versuchstransferleitungen erfolgen an einem an der Heliumverflüssigungsanlage der Technischen Universität Dresden neu eingerichteten Versuchsstand. Dabei stellt sich heraus, dass der Gesamtdruckverlust vorwiegend durch das im flexiblen Abschnitt eingesetzte Wellrohr verursacht wird. Mittels eines gesonderten Messaufbaus werden verschiedene Wellrohrtypen hinsichtlich der resultierenden Reibungsdruckverluste untersucht und eine verlustarme Wellrohrgeometrie identifiziert. Neben den Druckverlusten wird auch der Wärmeeintrag durch Modifikationen des Isolationsaufbaus reduziert. Im Zuge der thermohydraulischen Optimierung vermindern sich die Verdampfungsverluste, wodurch die pro Zeiteinheit in der Transportkanne deponierte Flüssigheliummenge zunimmt. Zusätzliche Messungen während des Stillstands der Transferleitung liefern Rückschlüsse auf das Verhalten der Transferleitung, wenn kein Flüssighelium transferiert wird. Im Stillstand neigen die betrachteten Transferleitungsgeometrien zu thermisch angetriebenen Druckschwingungen, sogenannten thermoakustischen Oszillationen. Diese beeinflussen die Betriebssicherheit und die Lagergüte des stationären Speichers negativ, weshalb geeignete Methoden zur Dämpfung der thermoakustischen Oszillationen vorgeschlagen werden.

An equilibrium multielectron bubble (MEB) in liquid helium is a fascinating object with a spherical two-dimensional electron gas on its surface. After it was first observed a few decades ago, a plethora of physical properties of MEBs, for example, a tunable surface electron density, have been predicted. In this thesis, we will discuss two new methods to create MEBs in liquid helium. Before the discussion, the way to generate a large number of electrons in a low temperature system will be discussed, including thermionic emission and field emission in helium. In the first new method to make MEBs, we used a dome-shaped cell filled with superfluid helium in which an MEB was created and confined at the dome. The lifetime of the MEB was substantially longer than the previously reported observations of MEBs. In the second method, MEBs were extracted from the vapor sheath around an electrically heated tungsten filament submerged in liquid helium, either by a high electric field (up to 15 kV/cm) or by a sudden increase of a negative pressure in liquid helium. High-speed photography was used to capture the MEB's motion. A method to determine the number of electrons was developed by monitoring the oscillations of the MEBs. Finally, an electromagnetic trap was designed to localize the MEBs created using the second method, which was important for future studies of the properties of MEBs. / Physics

Electrons are weakly attracted to liquid helium due to the small but finite polarizability of helium atoms. However, they cannot enter the liquid unless their energy is more than 1 eV, due to the Pauli exclusion principle. As a result, electrons are bound perpendicular to the surface but are free to move parallel to the surface i.e., they form a two-dimensional electron system (2DES). If the electron density of the 2DES is increased above a critical value ( 1013 per m2) the surface becomes un-stable leading to the formation of charged bubbles known as multielectron bubbles (MEBs). In MEBs the electrons are confined to the inner bubble surface and hence we have a 2DES on a curved surface. The critical density of electrons on the bulk surface is too low to study the quantum dominated phases of the 2DES. In contrast, due to the enormous surface defects and impurities, the electronic density of 2DES in semiconductors cannot be lowered below 1015 per m2, which is high enough such that the 2DES is always in a quantum liquid phase. Alternatively, the possibility of varying the electron density over a wide range and the effects of curvature implies that MEBs can be used to probe new phases of 2DES like Wigner crystallization with strong electron-ripplon coupling, quantum melting, superconductivity etc. In this thesis the experiments done on MEBs in liquid helium are described. In the initial experiments we generated MEBs which were observed to shrink in size. We saw a difference in their collapse behaviour: MEBs in super fluid helium though initially bigger in size collapse much faster than MEBs generated in normal fluid. The vapour present in the MEBs cannot condense fast in normal fluid due to the lower thermal conductivity. In subsequent experiments, we could trap these MEBs, generated in normal fluid and stabilised by their vapour content, in a linear Paul trap. We measured the charge and radius of these trapped MEBs by analysing their dynamics. Interestingly, the stably trapped MEBs were found not to lose charge as they shrink and disappear in hundreds of milliseconds, implying that the charge density inside increases at least two orders of magnitude from the initial value. MEBs so trapped can be used to study the properties of 2DES in the high electron density limit where the quantum confinement energy dominates. Later, we measured the charge of the MEB with respect to time when it was held on a solid substrate. We propose a charge loss mechanism as the tunneling of electrons across a thin lm of helium formed between the MEB and the substrate. We estimated the density of electrons on this thin lm by using a numerical model. We found that the maximum electron density (about a few 1015 per m2) which could be held on a thin lm is limited by tunneling. Moreover, the substrate surface roughness did not affect the charge loss due to the microscopic contact of MEBs with the substrate, resolving the complications in charge loss observed in previous experiments on macroscopic thin films on metallic substrates. Finally, we describe the experiments and the results on the stability of MEBs generated in super fluid helium. Highly charged MEBs (with more than 104 electrons which have an equilibrium radius that is easily visible) are found to be unstable against fission into smaller bubble showing a type of electro-hydrodynamic instability. However, the stability of bubbles with radius less than our detection limit ( 1 m) is still an open question.

Multielectron bubbles (MEBs) are micron sized cavities in liquid helium that contain electrons confined within a nanometer thick layer on the inner surface of a bubble. These objects present a rich platform to study the behavior of a two dimensional electron gas (2DES) on a curved surface. Most crucially, the surface electron densities in MEBs can vary over a wide range, making it a suitable candidate for studying classical Wigner crystallization and quantum melting in a single system. So far, there has been only limited experimental study of MEBs, with most of the previous investigation transient in nature. As we discuss in our presentation, we have built a cryogenic system for performing transport and optical measurements of MEBs down to 1.3 K. We have developed a new technique of generating MEBs, and trapping them using two different methods. In the first method, we trapped MEBs using a Paul trap for more than hundreds of milliseconds. This allows the MEBs to be further manipulated with buoyant and electric forces, such as to obtain reliable measurements of their physical properties. As we observe experimentally, the surface charge density of a single MEB can vary by orders of magnitude during the course of one measurement, thereby covering a previously unexplored section of the 2DES phase diagram. In the second method, we trapped MEBs using a dielectric coated metal electrode over many seconds. This also allowed the properties of MEBs to be measured in a non-destructive manner. Since MEBs are charged bubbles, their motion can be controlled by electric fields, which allowed us to measure the drag of MEBs as a function of Reynolds number by analysing the trajectories. Due to the low viscosity and surface tension of helium compared to other liquids, these measurements could be performed at Morton Numbers that have never been explored. We also show that how the shape of a single MEB evolves from spherical to ellipsoidal as their speeds vary. During the course of experiments, we observed number of interesting phenomena, such as coalescence of similarly charged bubbles, as well as their splitting into secondary bubbles at high speeds. Most interestingly, we have imaged their dynamics in the presence of static, as well as oscillating electric fields, which may provide insight into the phase of the electronic system present inside the bubbles.

Die thermodynamischen Eigenschaften von Flüssighelium erfordern einen hohen technischen Aufwand zu dessen Lagerung und Transfer. Aufgrund der extrem niedrigen Normalsiedetemperatur von 4,2 K ist die Verflüssigung des unter Normbedingungen gasförmigen Heliums sehr energieintensiv. Darüber hinaus besitzt Helium eine sehr niedrige Verdampfungsenthalpie, weshalb bereits geringe Wärmeeinträge signifikante Verdampfungsverluste verursachen. Infolge der räumlichen Trennung von Heliumverflüssigungsanlagen und Verbrauchern ist ein Flüssigheliumtransfer in der Regel unvermeidlich. Beim Transfervorgang durch Wärmeeintrag und Druckverluste generiertes Heliumkaltgas muss erneut dem energieaufwändigen Verflüssigungsprozess zugeführt werden, bevor es als Kältemittel verwendet werden kann. Zur Etablierung eines verlustarmen Flüssigheliumtransfers mit einflutigen flexiblen Transferleitungen sind daher die Verdampfungsverluste im Rahmen der thermohydraulischen Optimierung zu reduzieren. Die Optimierung erfolgt dabei durch die Kopplung von systematischen Messungen mit thermohydraulischen Berechnungen. Untersuchungen mit instrumentierten Versuchstransferleitungen erfolgen an einem an der Heliumverflüssigungsanlage der Technischen Universität Dresden neu eingerichteten Versuchsstand. Dabei stellt sich heraus, dass der Gesamtdruckverlust vorwiegend durch das im flexiblen Abschnitt eingesetzte Wellrohr verursacht wird. Mittels eines gesonderten Messaufbaus werden verschiedene Wellrohrtypen hinsichtlich der resultierenden Reibungsdruckverluste untersucht und eine verlustarme Wellrohrgeometrie identifiziert. Neben den Druckverlusten wird auch der Wärmeeintrag durch Modifikationen des Isolationsaufbaus reduziert. Im Zuge der thermohydraulischen Optimierung vermindern sich die Verdampfungsverluste, wodurch die pro Zeiteinheit in der Transportkanne deponierte Flüssigheliummenge zunimmt. Zusätzliche Messungen während des Stillstands der Transferleitung liefern Rückschlüsse auf das Verhalten der Transferleitung, wenn kein Flüssighelium transferiert wird. Im Stillstand neigen die betrachteten Transferleitungsgeometrien zu thermisch angetriebenen Druckschwingungen, sogenannten thermoakustischen Oszillationen. Diese beeinflussen die Betriebssicherheit und die Lagergüte des stationären Speichers negativ, weshalb geeignete Methoden zur Dämpfung der thermoakustischen Oszillationen vorgeschlagen werden.:1 Einleitung 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Stand der Wissenschaft . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Gegenstand und Aufbau der Arbeit . . . . . . . . . . . . . . . . . . . . . 3 2 Helium als Kälteträger 6 2.1 Grundlegende Stoffeigenschaften von Helium . . . . . . . . . . . . . . . . 6 2.2 Vorkommen, Gewinnung und Verwendung von Helium . . . . . . . . . . . 7 2.3 Bereitstellung von Flüssighelium . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Aufbau einer flexiblen Transferleitung für Flüssighelium . . . . . . . . . . . 12 3 Berechnungsgrundlagen 14 3.1 Druckverlust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.1.1 Gesamtdruckverlust . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.1.2 Reibungsdruckverlust im Glattrohr . . . . . . . . . . . . . . . . . . 14 3.1.3 Reibungsdruckverlust im Rohr mit parallelen Wellen . . . . . . . . 15 3.1.4 Zweiphasenmultiplikator . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.5 Druckverlust durch Höhenänderung . . . . . . . . . . . . . . . . . 19 3.1.6 Beschleunigungsdruckverlust . . . . . . . . . . . . . . . . . . . . . 19 3.1.7 Druckverlust durch Einzelwiderstände . . . . . . . . . . . . . . . . 19 3.2 Gesamtwärmeeintrag der Transferleitung . . . . . . . . . . . . . . . . . . 20 3.3 Lokaler Wärmestrom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.1 Strahlungswärmestrom . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.2 Wärmetransport durch die MLI . . . . . . . . . . . . . . . . . . . 23 3.3.3 Wärmetransport durch die Rohrwand . . . . . . . . . . . . . . . . 24 3.3.4 Wärmetransport entlang der Konstruktionselemente . . . . . . . . 25 3.3.5 Konvektiver Wärmeübergang bei einphasiger Strömung . . . . . . . 25 3.3.6 Wärmeübergang beim Sieden einer erzwungenen Strömung . . . . 26 3.4 Thermoakustische Oszillation . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4.1 Definition und Entstehung einer thermoakustischen Oszillation . . . 28 3.4.2 Abschätzung von Amplitude und Frequenz . . . . . . . . . . . . . 31 4 Messaufbau und Versuchsdurchführung 34 4.1 Charakterisierung der Transferleitung . . . . . . . . . . . . . . . . . . . . 34 4.1.1 Messaufbau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.1.2 Versuchsdurchführung . . . . . . . . . . . . . . . . . . . . . . . . 36 4.1.3 Untersuchte Transferleitungskonfigurationen . . . . . . . . . . . . 37 4.2 Druckverlust in parallel gewellten Rohren . . . . . . . . . . . . . . . . . . 38 4.2.1 Messaufbau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2.2 Versuchsdurchführung . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2.3 Untersuchte Wellrohrgeometrien . . . . . . . . . . . . . . . . . . . 40 4.3 Messmittel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3.1 Druckmessung . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3.2 Temperaturmessung . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3.3 Volumenstrommessung . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3.4 Wägeeinrichtung . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3.5 Supraleitende Füllstandssonde . . . . . . . . . . . . . . . . . . . . 43 4.3.6 Datenaufnahme . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5 Thermohydraulisches Berechnungsmodell 44 5.1 Aufbau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.2 Validierung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3 Ergebnisse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.3.1 Wärmeeintrag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.3.2 Druckverlust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.3.3 Transferrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6 Ergebnisse der messtechnischen Untersuchung 59 6.1 Wärmeeintrag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.2 Druckverlust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.3 Austrittsdampfgehalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.4 Transferrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.5 Einkühl- und Aufwärmverhalten . . . . . . . . . . . . . . . . . . . . . . . 70 6.6 Schwingungsneigung der Transferleitung im Stillstand . . . . . . . . . .72 6.6.1 Auftreten thermoakustischer Oszillationen . . . . . . . . . . . . . . 72 6.6.2 Ermittlung des Temperaturprofils . . . . . . . . . . . . . . . . . . 74 6.6.3 Berechnung von Druckamplitude und Frequenz . . . . . . . . . . . 76 6.6.4 Resultierender Wärmeeintrag in den Heliumspeicher . . . . . . . . 79 6.6.5 Dämpfung thermoakustischer Oszillationen . . . . . . . . . . . . . 79 6.7 Reibungsdruckverlust in parallel gewellten Rohren . . . . . . . . . . . . 81 7 Design- und Anwendungsempfehlungen 87 8 Zusammenfassung 91 Literatur 94 Anhang 100 A Messwerte von Druck, Volumenstrom und Massenänderung für HeTra 1 . . 100 B Messwerte von Druck, Volumenstrom und Massenänderung für HeTra 2 . . 101 C Messwerte von Druck, Volumenstrom und Massenänderung für HeTra 3 . . 103 D Messwerte des Kannendrucks für alle untersuchten Transferleitungen . . . 105 E Reibungsbeiwerte der Wellrohre . . . . . . . . . . . . . . . . . . . . . . . 106 F Berechnung des Wärmeeintrags durch thermoakustische Oszillationen . . . 107