Circuit Model for Driving Three-Dimensional Resistive MHD Wire Array $Z$-Pinch Calculations

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Compact tungsten wire array <formula formulatype="inline"><tex Notation="TeX">$Z$</tex></formula>-pinches imploded on the Z generator at Sandia National Laboratories have proven to be a powerful reproducible X-ray source. Wire arrays have also been used in dynamic hohlraum radiation flow experiments and as an intense K-shell source, while the generator has been used extensively for isentropic compression experiments. A problem shared by all these applications is current loss, preventing the <formula formulatype="inline"><tex Notation="TeX">$\sim$</tex></formula>20-MA drive current from being reliably coupled to the load. This potentially degrades performance, while uncertainties in how this loss is described limit our predictive capability. We present details of a transmission line equivalent circuit model of the Z generator for use in driving 3-D resistive MHD simulations of wire array loads. We describe how power delivery to these loads is affected by multiple current losses and demonstrate how these may be calculated or reconstructed from available electrical data for inclusion in the circuit model. We then demonstrate how the circuit model and MHD load calculation may be combined to infer an additional current loss that has not been directly diagnosed for wire arrays. </para>