Study of the Variation of the β Factor and the Radius Through the Hollow Cathode Z-Pinch by Using Snowplow Model Simulation

Abstract

The Hollow cathode z-pinch is designed and operated to investigate the ejected plasma through the hollow cathode. The hollow cathode is simulated using the snow plow model. The model uses three phases: the radial inward phase, the reflected shock phase and expansion phase. The differential equation of plasma motion and its electric circuit equation are derived and solved numerically using the code. The snow plow model suggested that the plasma radius decreases to zero, so this problem was solved adding the effect of the internal kinetic pressure and the shock wave into the general equation of motion using β factor. The effect of β factor (ratio of the kinetic pressure of plasma to magnetic pressure) is studied on plasma temperature, plasma radii, plasma velocity, pinching time and plasma elongation distance. The simulated results illustrate that the β factor varies from 0 to 0.79. The data illustrate that the elongation velocity of plasma is increased by decreasing the β factor, while the elongation displacement of the plasma is increased by increasing of the ring radii of the hollow cathode. The code illustrates that a multi-pinch of the CS could be appeared at high energy.