One-dimensional theory and simulations of the dynamic Z-pinch

The dynamical formation of a Z-pinch in the strong-shock limit is studied in this paper using one-dimensional (1D) simulations of a two-temperature magnetohydrodynamic model. The classic 1D picture consists of three stages: run-in, reflected-shock, and expansion. The special case of a constant current I and uniform gas fill, which are approximate conditions of the pinch-formation stage in a dense plasma focus, is examined in detail. Time-profiles for the shock-front and piston positions during the run-in stage are compared with some of the commonly used 0D models from the literature. Some practical improvements to these models are presented here and it is shown that this model gives the best agreement with results from the simulations. Maximum compression of the plasma is achieved when the reflected shock from the axis meets the incoming current layer. The ratio of the plasma radius at this time with respect to its initial radius is found from the simulations to be r p / R ≈ 1 / 8 using 5/3 for the adiabatic coefficient γ. The pressure and temperature of the compressed plasma are found to peak a short time after maximum compression due to the inability of the reflected shock to completely stagnate the incoming plasma driven by the converging current layer. The variation of the results with a finite dI/dt and for different values of γ is presented.The dynamical formation of a Z-pinch in the strong-shock limit is studied in this paper using one-dimensional (1D) simulations of a two-temperature magnetohydrodynamic model. The classic 1D picture consists of three stages: run-in, reflected-shock, and expansion. The special case of a constant current I and uniform gas fill, which are approximate conditions of the pinch-formation stage in a dense plasma focus, is examined in detail. Time-profiles for the shock-front and piston positions during the run-in stage are compared with some of the commonly used 0D models from the literature. Some practical improvements to these models are presented here and it is shown that this model gives the best agreement with results from the simulations. Maximum compression of the plasma is achieved when the reflected shock from the axis meets the incoming current layer. The ratio of the plasma radius at this time with respect to its initial radius is found from the simulations to be r p / R ≈ 1 / 8 using 5/3 for the ad...