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A cryostat has been constructed for the determination of the latent heat of evaporation of liquid helium-4 from 1.8°K to the critical point. It has not yet proved possible to stabilize the cryostat behaviour sufficiently and thermal oscillations of the type reported by Taconis are strongly suspected as being the source of the difficulty. Modifications that were carried out in the design of the equipment to improve its behaviour were limited in their success so that two conclusions were reached. Firstly, a separate investigation of the problem of Taconis resonate® is necessary before reliable results can be obtained, Secondly, the existing cryostat could in the meantime readily be converted to other cryogenic uses. / Thesis / Master of Science (MS)

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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.