Simulation of Z-pinch dynamics in a high-current plasma lens with a new one-dimensional model including finite plasma conductivity

Abstract

The dynamics of a fast Z-pinch plasma lens was simulated with a one-dimensional model for the phase of constriction. The calculation resulted in a realistic description—compared to experiment—of pinch dynamics and current density distribution up to the time of minimum plasma radius, which is important to evaluate the focus quality of the lens. Equations of the inverse skin effect and the momentum conservation equation of magnetohydrodynamics were used. Due to the consideration of a finite plasma conductivity a finite current density distribution was computed, reaching 16 kA/cm2 at its maximum, which corresponds to a total current of about 280 kA at pinch time. The plasma is compressed from an initial radius of 100 mm to a pinch radius of about 14 mm within 3.33 μs. Thus, an ion density of 1.6×1018 cm−3 and a temperature of 30 eV is calculated. Although no shock wave is implemented in the model explicitly, a sharp radial density increase appears in the contraction phase and moves toward the axis with a velocity of up to 8×104 m/s.