Curve fitting for electric-field measurements in twin point corona discharges in air

This paper is concerned with numerical work on the mathematical representation of the electric field on the earthed plane electrode directly below a pair of matched coronating point-electrodes in large-scale negative DC discharges in air. The theoretical representation of the measurements on the central line where the plane through the points intersects with the earthed electrode is taken a stage further. A previously derived three-parameter representation that has a physical basis has been extended to four parameters. This more accurately reflects the repulsion of the charge envelopes emanating from the points and the effect that this has on the space-charge field, and consequently on the full Poissonian field. Two numerical techniques are used: least-squares optimization (regression) and a minimax approach. The results are in good mutual agreement and they also resemble the experimental data. This gives confidence in the mathematical representation of the measurements developed here.