Toward quantitative electric-field measurements of inception clouds in nanosecond discharges using E-FISH assisted by machine learning

Abstract This study investigates the spatio-temporal evolution of the electric field during the early stages of a nanosecond positive corona discharge in atmospheric-pressure air by combining time-resolved electric field induced second harmonic measurements, machine-learning-assisted field inversion (based on a recently developed operator-learning model), and iCCD optical emission imaging. The objective is to characterize the electric field, with quantitative interpretation limited to the early, quasi-axisymmetric phase of the discharge. By averaging over a large number of discharge events and operating in a regime where the discharge remains statistically axisymmetric, the proposed approach enables reconstruction of the electric-field profiles with nanosecond resolution. The results show a rapid increase of the field during the first nanoseconds, followed by the formation of a shell-like structure exhibiting the highest reduced fields prior to destabilization. The reconstructed reduced electric-field magnitude reaches peak values in the range of approximately 230–270 Td, with an estimated uncertainty of about 20%–30% associated with calibration and profile-shape effects. These values correspond to the regime where electron-impact excitation and photoionization processes become highly efficient, consistent with the observed transition from a stable inception cloud to streamer destabilization. After the onset of streamer branching, increasing asymmetry limits the applicability of the inversion, and the reconstructed fields represent averaged contributions rather than the local field at individual streamer heads. The methodology thus identifies the conditions under which quantitative E-field mapping is reliable and establishes a framework for machine learning-assisted electric-field diagnostics in axisymmetric discharges.