A Comprehensive Analytical Model of the Dynamic Z-Pinch

Abstract: Here we discuss the development of an analytical 1D axisymmetric model describing the implosion story 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 axial magnetic field profiles, for any time-dependent current, spatially-varying initial density profile, and initial axial field. Its implementation consists of simultaneously solving a pair of coupled ordinary differential equations, derived from the ideal MHD equations, whose forms evolve throughout different stages of the implosion to best reflect the underlying physics. Comparison with experimental data from the COBRA pulsed-power installation is quite promising, and implies this model could prove useful in designing and analyzing future pulsed-power experiments.