Plasma dynamics and stability of radial foil explosions on COBRA

Abstract

Summary form only given. Radial foil configurations can generate high energy density plasmas with pressures on the order of 1 Mbar on a 1MA, 100 ns rise time pulsed-power generator such as the COrnell Beam Research Accelerator (COBRA). In this experimental set-up, a thin metallic foil stretched on a circular anode connects to a very small “pin” cathode. Radially directed currents flow through the foil then down the pin cathode, thereby generating an axisymmetric toroidal magnetic field. The plasma current density J interacts with the magnetic field B and the resulting J×B force accelerates the foil vertically until a plasma cavity forms. Connecting to the cathode via a central plasma column (Z-pinch), this “bubble” contains most of the magnetic field produced by the current discharge. Using very simple considerations, the plasma force density f roughly follows a quadratic power law equation. As a result, it is possible to control the plasma dynamics by adjusting the foil thickness h and the pin radius r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pin</sub> . This level of control proved extremely efficient at improving plasma properties and limiting the growth of plasma instabilities. For instance, radial foil discharges using 5μm aluminum foils and 500 μm-diameter pin cathodes produce many hot spots with electron densities above 5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and electron temperatures above 1.5 keV. On the other hand, pin cathodes with diameter larger than 2 mm yielded plasmas with more modest properties: electron densities below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , temperatures below 300 eV and no hot spot. Instabilities tend to appear early in the discharge with smaller cathodes, before current peak. They are dominant inside the central plasma column and are responsible for generating most hot spots. By adjusting the foil thickness, the onset of instabilities can be delayed until the current peaks, de facto maximizing plasma radiation burst intensity. When possible, we will compare experimental data to computational results obtained with the newly developed PERSEUS code, which solves extended MHD equations, a model that goes beyond standard MHD and includes electron inertia, Hall effect and electron pressure.