Experimental testing of least-square procedure for determining railgun plasma current distribution

Abstract

The plasma current distribution (initial length, velocity, amplitude versus x, and expansion rate) was determined by simultaneously fitting (using the method of least squares) the measured voltages of multiple B-dot probes to a function model. The model for the probe voltage was derived using the Biot-Savart equation and some simplifying assumptions, one of which was to divide the current into segments and then sum for the total voltage. The computer model contains selectable form functions which give the amplitude of the current for each segment. The procedure was tested by comparing multiple fits of symmetrically positioned probes on opposite sides of the bore, comparing fits using different form functions and different numbers of segments, comparing fits of different-size probes located at different distances from the bore, and comparing the fitted parameters of the plasma current distribution with other sensors. As far as could be determined, the current distribution determination gives meaningful data which correlate well with other measurements. >