Simplified Magnetohydrodynamic Models of a Dynamic Z-Pinch

Studies in Z-pinch have focused on improving existing models to provide details on the separate trajectories for the magnetic piston and the shock. The Ordinary Differential Equation (ODE) methods used have focused on consistent improvement to include terms that were previously ignored. Further development has solved the Magnetohydrodynamics (MHD), Partial Differential Equations (PDE) of the dynamic Z-pinch. This work provides a simplified ODE model of the dynamic Z-pinch by using MHD magnetostatic equilibrium to address limitations in a recent model. Additionally, this work simplifies the existing PDE approach by not separating the ions and electron constituents, but model expected to retain the plasma flow behavior. The Z-Pinch phenomenon is then modelled in a cylindrical geometry, one dimensional (1D) space coordinate using the governing Equations. Numerical approaches to solving ODEs and PDEs are used to provide solutions and comparative analysis of models is performed.