A Comprehensive Analytical Model of the Dynamic Z-Pinch

TL;DR

This paper introduces an analytical 1D model for the dynamic z-pinch that predicts key physical profiles and stages of implosion, aiding the design of pulsed-power experiments.

Contribution

It provides a novel analytical framework capable of modeling the evolution of the z-pinch with variable current and initial conditions, validated against experimental data.

Findings

Model accurately predicts magnetic piston and shock front trajectories.

Good agreement with COBRA experimental data.

Useful for designing future pulsed-power experiments.

Abstract

We present an analytical 1D axisymmetric model describing the evolution of the dynamic z-pinch. This model is capable of predicting the trajectories of the imploding sheath's magnetic piston and preceding shock front, along with the velocity, pressure, density, and magnetic field profiles, for any time-dependent current, spatially-varying initial density profile, and weak initial axial field. The implosion is divided into stages, with each stage described by a set of coupled ordinary differential equations derived from the ideal MHD equations. Comparison with experimental data from the COBRA pulsed-power facility is quite promising and implies this model could prove useful in designing and analyzing future pulsed-power experiments.