Frozen plasma within the flow from a metal plate hit by an electron beam pulse

Abstract

When a pulsed electron beam hits a metal plate with sufficient energy a volume of the metal becomes hot fluid that subsequently sprays out of the plate. A portion of this flow is ionized. This report describes a fluid that expands so rapidly into a vacuum that the ionized portion of the flow departs from local thermodynamic equilibrium. This cold supersonic exhaust will have a much higher degree of ionization, and of higher electron temperature, than would be expected from a gas in thermodynamic equilibrium at the local temperature of the neutral flow. This report presents a continuation of the work described in reference (1). My aim is to develop as simple a model as will reasonably predict the speed and density of neutral flow, and the temperature and density of plasma. I use simplifying assumptions and mathematical approximations to develop convenient formulas, and I test them by comparing specific examples to experimental data and computations by DeVolder and other Los Alamos scientists (2). The phenomenon of sudden expansion of a gas cloud into vacuum is described in several sections of the two-volume work by ZelUdovich and Raizer (3). The criterion I use for estimating the point in the flow where plasma ceases to be in equilibrium is in principle that proposed by Bray (4), (5), and discussed extensively by Vincenti and Kruger (6). The immediate concern motivating this work is how to design a metal target that accurately converts an electron beam pulse train into a radiation pulse train for use in the high-speed radiography of implosion hydrodynamics experiments. In the radiography application, either the electron beam must be swept magnetically along the metal target more quickly than the spread of the debris plume, or the metal plate must move laterally past a fixed point of impact, carrying its plume with it. What is this speed, and how dense is this splash flow? Aside from its technological application, this problem has an intrinsic interest because it includes such a wide range of physical phenomena, and because it is an analog in miniature of supernova explosions. A small hot source created quickly propels an expanding flow into a vacuum, and this flow contains a remnant plasma that preserves information about the earliest moments of the flow. The plan of this report is as follows. The section ``Heat source and neutral flow`` reviews the physics of an electron beam pulse that generates enthalpy, which in turn propels a flow of neutral target material. The section ``Thermal plasma`` shows the Saha equation used to estimate the initial degree of ionization in the fluid and the collisional ionization rate coefficient used. The section ``Frozen flow`` describes the criterion that indicates when plasma has ceased to be in thermodynamic equilibrium with the neutral flow. The section ``An Example`` shows a specific case that was originally measured and calculated at Los Alamos, and described in reference (2).