Uncertainty Analysis of Local and Integral Methods for Current Distribution Measurements

This paper provides an uncertainty analysis for current distribution measurements based on local magnetic field measurements (e.g., via Hall probes) or on magnetic flux measurements using large pick-up loops. The fundamental difference between the two approaches is first pointed out in the ideal case of an infinite straight wire. Then, a more complex geometry composed by parallel identical conductors connected between two bars is considered. The mathematical models employed for the current reconstruction according to the two approaches are derived, and their uncertainties are evaluated. An experimental validation of the model for pick-up loops is presented with application to an actual rail launcher prototype. From this analysis, the critical aspects of the two methods are highlighted, showing the different effect that the uncertainty of the sensor position has on the reconstructed current uncertainty. Finally, a case study aimed at evaluating the current distribution uncertainty under simplified hypotheses is described.