The analytical solution presented in this thesis is based on the Liquid Metal Experiment (LEX) at Virginia Tech to determine the practicality of replacing a solid metal electrode with a liquid metal electrode wall. Replacing the solid metal with a liquid metal may improve the operational lifetime of Z-pinches. The LEX is based upon the University of Washington's High Energy Density Z-pinch (ZaP-HD) and Fusion Z-Pinch Experiments (FuZE) and replaces one solid metal electrode with a liquid metal electrode. During the operation of the ZaP-HD and FuZE, a plasma column exerts electromagnetic forces and pressure on a solid electrode wall. The pressure exerted by the plasma column is called the magnetic pressure. In the Virginia Tech device magnetic pressure is exerted by a wire onto the liquid metal electrode. The magnetic pressure in the LEX displaces the liquid metal electrode free surface, and subsequently creates a waveform. The initial free surface displacement and subsequent wave motion of the liquid metal is found by analyzing the geometry of the device, the electromagnetic forces generated during operation, and material properties of the tin-bismuth liquid metal mixture. The initial displacement for changing current, current pulse length, tin percentage, and applied pressure range are investigated. The results are compared for verification and validation. These methods are shown to be accurate to within an order of magnitude and are valid for an axisymmetric domain. The results presented here may inform further experimentation and aid in improving designs for newer devices. / Master of Science / This thesis presents analytical solutions for creating waveforms in liquid metal due to electromagnetic forces. The motivation for developing the analytical solutions is to aid in developing a device created by Virginia Polytechnic and State University (Virginia Tech). The Liquid Metal Experiment (LEX) at Virginia Tech investigates the practicality of incorporating a liquid metal into a Z-pinch fusion device under development at the University of Washington's High Energy Density Z-pinch (ZaP-HD) and Fusion Z-Pinch Experiments (FuZE). The ZaPHD and FuZE experiments are cylindrical and aim to investigate the viability of Z-pinches as fusion devices. An electric current passes between an internal electrode, the plasma column, and an external electrode along the z-axis of the Z-pinch. The time duration of the current is typically on the order of tens of microseconds. The plasma column and subsequent fusion events are generated only during this duration. During this duration, the interactions between the plasma column and the electrodes cause the electrodes to deteriorate. In standard Z-pinch devices, the electrodes are solid metal and deteriorate during the operation, limiting the device's lifespan. The liquid metal introduces other complexities to the system. During the time duration of the current, the electromagnetic forces produce a pressure gradient at the free surface of the liquid metal. The pressure created by the electromagnetic forces generates waveforms within the liquid metal. The analytical solutions presented in this thesis include electrodynamic solutions to find the pressure, kinematic solutions to determine the free surface displacement of the liquid metal due to the pressure, and fluid dynamic solutions of the waveform caused by the initial free surface displacement.

Zugl.: Clausthal, Techn. Univ., Diss., 2008

Universiẗat, Diss., 2002--Jena.

Depuis plusieurs décennies, les générateurs forts courants sont utilisés dans différents domaines comme l’étude des matériaux, la radiographie ou la fusion par confinement inertiel. Ces générateurs sont capables de délivrer des impulsions de courant de plusieurs millions d’ampères avec des fronts de montée inférieurs à la microseconde. Plusieurs projets à travers le monde ont, aujourd’hui, pour but d’améliorer encore et encore le gradient de courant des impulsions transmises à la charge. De nombreux schémas d’amplificateurs de puissance, dont le rôle est de jouer à la fois sur l’amplitude du courant de charge et sur son temps de montée, ont ainsi été testés. Le multiplicateur de courant dynamique (DLCM pour Dynamic Load Current Multiplier) fait partie de ces concepts novateurs permettant de contourner les limitations des générateurs de puissances pulsées actuels. Il est composé d’un réseau d’électrodes (servant d’autotransformateur), d’un extrudeur de flux dynamique (basé sur l’implosion d’un réseau de fils cylindrique) et d’un commutateur à fermeture sous vide. Dans la thèse, le principe de fonctionnement du DLCM est analysé d’un point de vue théorique par le biais de simulations de type circuits électriques et magnétohydrodynamiques. Une étude spécifique portant sur l’organe principal du DLCM est réalisée. Il s‘agit du commutateur à fermeture sous vide. Ainsi, après une phase de dimensionnement à l’aide d’outils de simulations électrostatiques, deux versions de commutateurs sont validées expérimentalement dans des conditions proches de celles d’un tir très fort courant. Enfin, des tirs sur le générateur SPHINX du CEA Gramat, capable de délivrer une impulsion de courant de 6MA en 800ns (sur charge Z-pinch), sont exposés pour retracer l’évolution du dispositif. Les résultats probants obtenus permettent, au final, de valider le concept DLCM connecté à une charge de type compression isentropique. / For several decades, high power generators are used in various fields such as materials research, radiography or inertial confinement fusion. These generators are capable of delivering current pulses of several millions of amperes with rise times below 1 microsecond. Several projects around the world are, today, trying to improve again and again the current gradient of pulses delivered to the load. Many concepts of power amplifiers, whose role is to optimize both the amplitude of the load current and its rise time, were tested. The Dynamic Load Current Multiplier (DLCM) is one of those innovating concepts used to overcome the existing pulsed power generators limitations. It is made up of concentric electrodes (for autotransformer), a dynamic flux extruder (based on the implosion of cylindrical wire array) and a vacuum closing switch. In this these, the operating principle of the DLCM is theoretically analyzed through electrical and magneto hydrodynamic simulations. A specific study of the DLCM key component is performed. This is the vacuum closing switch. Thus, after a design phase using electrostatic simulation tools, two versions of switches are experimentally validated in conditions similar to those of a very high current shot. Finally, shots on the SPHINX facility located at the CEA Gramat, capable of delivering a current pulse of 6MA in 800ns (on Z-pinch load), are exposed to trace the evolution of this device. The convincing results are used, ultimately, to validate the DLCM concept connected to an isentropic compression experiment load.

No description available.

Z-Pinch IFE (Inertial Fusion Energy) reactor designs will likely utilize high yield targets (~ 3 GJ) at low repetition rates (~ 0.1 Hz). Appropriately arranged thick liquid jets can protect the cavity walls from the target x-rays, ions, and neutrons. However, the shock waves and mechanical loadings produced by rapid heating and evaporation of incompressible liquid jets may be challenging to accommodate within a small reactor cavity. This investigation examines the possibility of using two-phase compressible (liquid/gas) jets to protect the cavity walls in high yield IFE systems, thereby mitigating the mechanical consequences of rapid energy deposition within the jets. Two-phase, free, vertical jets with different cross sections (planar, circular, and annular) were examined over wide ranges of liquid velocities and void fractions. The void fraction and bubble size distributions within the jets were measured; correlations to predict variations of the slip ratio and the Sauter mean diameter were developed. An exploding wire system was used to generate a shock wave at the center of the annular jets. Attenuation of the shock by the surrounding single- or two-phase medium was measured. The results show that stable coherent jets can be established and steadily maintained over a wide range of inlet void fractions and liquid velocities, and that significant attenuation in shock strength can be attained with relatively modest void fractions (~ 1%); the compressible two-phase jets effectively convert and dissipate mechanical energy into thermal energy within the gas bubbles. The experimental characteristics of single- and two-phase jets were compared against predictions of a state-of-art CFD code (FLUENT®). The data obtained in this investigation will allow reactor system designers to predict the behavior of single- and two-phase jets and quantify their effectiveness in mitigating the consequences of shock waves on the cavity walls in high yield IFE systems.

Ce travail estime le potentiel des plasmas de striction magnétique (Z-pinches) pour le chauffage de cavités radiatives à haute température (>200eV). Des modèles simples sont fournis pour calculer les performances atteignables avec des courants de 5 à 100 MA en 100 ns. La physique monodimensionnelle à l'échelle de l'épaisseur du plasma et les instabilités hydrodynamiques sont étudiées. Puis l'amélioration des performances des cavités avec une double coquille ou l'installation d'un champ magnétique axial est analysée. L'attaque directe par un Z-pinch d'une cible de fusion par confinement inertiel est enfin considérée. Tous les résultats présentés reposent sur une approche théorique et numérique (bidimensionnelle) et sur l'exploitation de résultats expérimentaux obtenus sur le générateur américain "Z". Les annexes rappellent les équations de la MHD radiative et vérifient leur validité pour les plasmas de striction magnétique.

The dissertation explores a framework for numerically simulating the deformation of the liquid metal wall's free surface in Z-pinch fusion devices. This research is conducted in the context of utilizing liquid metals as plasma-facing components in fusion reactors. In the Z-pinch fusion process, electric current travels through a plasma column and enters into a pool of liquid metal. The current flowing through the liquid metal generates Lorentz force, which deforms the free surface of the liquid metal. Modeling this phenomenon is essential as it offers insights into the feasibility of using liquid metal as an electrode wall in such fusion devices. The conventional magneto-hydrodynamic (MHD) formulation aims at modeling the situation where an external magnetic field is applied to flows involving electrically conducting liquids, with the initial magnetic field is known and then evolved over time through magnetic induction equation. However, in Z-pinch fusion devices, the electric current is directly injected into a conducting liquid. In these situations, an analytical expression for the magnetic field generated by the applied current is not readily available, necessitating numerical calculations. Moreover, the deformation of the liquid metal surface changes the geometry of the current path over time and the resulting magnetic field. By directly solving the Maxwell equations in combination with Navier-Stokes equations, it becomes possible to predict the magnetic field even when the fluid is in motion. In this dissertation, a numerical framework utilizing the Maxwell-Navier-Stokes system is explored to successfully capture the deformation of the liquid metal's free surface due to applied electric current. / Doctor of Philosophy / In this dissertation, a method is described that uses a computer to simulate how the initially stable, flat surface of liquid metal deforms when subjected to electrical currents in Z-pinch fusion devices, a specific type of nuclear fusion technology. Z-pinch fusion devices generate plasma, a hot fluid-like substance, through the nuclear fusion process, triggered and maintained by strong pulsated current. There's a growing interest in using liquid metal as the first layer of material to isolate the hot plasma from the rest of the nuclear fusion reactor body, rather than solid materials, due to its unique benefits. However, the Z-pinch fusion process, by introducing electric currents through the liquid metal layer, induces a Lorentz force that consequently deforms the surface of the liquid metal. Developing a tool to predict this deformation is vital as it aids in evaluating the potential of using liquid metal as a plasma-facing layer over solid materials in these fusion devices. The simulation tools presented in this dissertation are able to successfully captures the dynamics of how the liquid metal surface deforms under the impact of electrical currents.