An Improved Analytical Model of the Dynamic Z-Pinch

We present an analytical 1D axisymmetric model describing the implosion of the dynamic Z-pinch in the strong-shock limit. This model is capable of predicting the trajectories of the sheath's inner and outer radii, the shock and piston, along with density, temperature, and velocity profiles within the sheath for any arbitrary current, initial density profile, and axial field. Its implementation consists of simultaneously solving a pair of coupled ordinary differential equations, derived from the ideal MHD equations and Rankine-Hugoniot Jump Conditions, whose forms evolve throughout the different stages of the pinch: initialization, run-in, and reflected-shock, to best reflect the underlying physics. Comparison with experimental data from the COBRA pulsed-power facility after an MSE fit to determine the adiabatic index and starting radius is quite promising, and implies this model could prove useful in designing and analyzing future pulsed-power experiments.