ESTIMATING RATIO OF PEAK TO UNIFORM VALUES OF VARIOUS PROFILES OF RELEVANCE TO PLASMA FOCUS PINCH COLUMNS

In the Lee Model code for radiative plasma focus computation, both the density profile and the temperature profile (versus anode radius) of the pinch column are approximated by step functions with uniform values across the column radius. This means that the computed density and temperatures will be lower than the physical situation where the density and temperature profiles will certainly have peak values higher than the uniform (with radius) values of the step function. It has been shown that the density profile is side-peaked (somewhat shell-shaped or like the shape of a volcanic crater) with the assumption of no reflected shock wave; whereas the temperature profile is centre-peaked somewhat like a Gaussian shape. The aim of this paper is to investigate the use of higher degree mathematical function, where the crater-shaped profile can be well represented, to pproximate the plasma focus density profile. Two different approximated functions will be discussed: namely Gaussian distribution function and Bézier function. From these profiles we obtain the likely ratio of the profiled peak temperature to the step function uniform temperature and the peak density to the step function uniform density. In this manner we are able to suggest correction factors to the temperature and density computed by the Lee Model code.