Modeling of the Dynamic Plasma Pinch in Plasma Focus Discharges Based in Von Karman Approximations

Abstract

Dynamic plasma pinches occur in a variety of devices, as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinches and plasma focus. In this paper, a lumped parameter model of a dynamic plasma pinch produced in a plasma focus discharge is presented. The model is based in Von Karman approximations of the radial density and velocity profiles, which leads to the reduction to a system of ordinary differential equations describing the dynamic evolution of the pinch compression and expansion. The model was coupled with a fusion kernel to produce an estimate of the neutron yield per pulse. The calculations were tested against available data of the pressure-yield curve of seven experimental devices ranging from 1 to 250 kJ, showing excellent agreement, particularly regarding the curvature of the pressure-yield curve.