Theory of Wave Formation in Liquid Metal

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.