Some generalised characteristics of the electro-dynamics of the plasma focus in its axial phase: illustrated by an application to independantly determine the drive current fraction and the mass swept-up fraction

Abstract

We describe the axial phase of the Mather plasma focus by two coupled equations of motion and circuit. We non-dimensionalised these equations resulting in two coupled equations which are characterised by only three scaling parameters α, β and δ which are ratios of electrical to transit times, inductances and impedances respectively. The normalised current waveform, trajectory and speed profile are unique for each combination of α, β, δ which are the ratios of characteristic times (electrical discharge vs. axial transit), inductances (tube inductance vs. static inductance) and impedances (stray resistance vs. electrical surge impedance). This leads to important information and insight into various aspects of the axial phase. In the present work we show that in a time-matched plasma focus shot we deduce the value of axial phase current fraction fc simply by measuring the calibrated voltage waveform and the uncalibrated current waveform. The scaling parameters β and δ are fixed; and by form-fitting the measured current waveform to the normalised current waveform using the value of α of the shot is determined uniquely; from which the peak current and the ratio of peak to average speed [the speed form factor (SFF)] are obtained. The average transit speed is measured by time-of-flight using the voltage upturn as indicator of end of axial phase. Then the SFF yields the peak speed. The measured voltage (back EMF), peak current and peak axial speed (all at the end of axial phase) allows the unambiguous measurement of fc. The value of the mass swept-up fraction fm is deduced from α which is the ratio of the characteristic discharge and the characteristic transit times, both deduced during the non-dimensionalisation of the equations. Analysis of a time-matched shot in the INTI PF at 15 kV, 3 Torr D2 gave fc = 0.68 and fm = 0.05.