Toward Quantitative Electric-Field Measurements of Inception Clouds in Nanosecond Discharges Using E-FISH Assisted by Machine Learning

TL;DR

This paper addresses the challenge of measuring electric fields during the inception of nanosecond atmospheric corona discharges. It combines time-resolved E-FISH with a neural-operator-based inversion (DDON) and iCCD imaging to reconstruct $E$-field profiles near the HV electrode with nanosecond resolution. The authors find peak reduced fields around $E/N \approx 230$--$270$ Td near 6–7 ns, corresponding to shell formation and onset of streamer destabilization, and show that beyond about 7 ns the inversion becomes dominated by averaging due to stochastic streamer branching. The work provides a framework for quantitatively diagnosing inception-phase fields in nanosecond discharges and informs applications relying on precise electric-field diagnostics.

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 E-FISH measurements, machine-learning-assisted field inversion (based on a recently developed operator-learning model), and iCCD optical emission imaging. The objective is to quantitatively characterize the electric field in the vicinity of the high-voltage electrode during inception and the transition toward streamer formation. 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 extending electric-field diagnostics to the inception phase of nanosecond atmospheric discharges.

Figures (12)

• Figure 1: Schematic of E-FISH Experimental setup. HV=High-voltage; Gen.=Generator.
• Figure 2: A) Magnified schematic of the reactor and electrode configuration together with B) Scanning electron microscope images of the electrode tips.
• Figure 3: Schematic illustrating the E-FISH spatial scan methodology: A), B), and C), different z positions (location of beam focus is represented by a bright red spot) and D) corresponding colored E-FISH signal in the complete scan.
• Figure 4: Plot of calibration curves generated from A) experiments versus simulation results following the procedure depicted in figure \ref{['fig:calibration']} and B) regular calibration procedure typically adopted in the literature. C) Comparison of the e-field magnitudes obtained using the E-FISH signals corrected for the profile shapes using the DDON model versus the uncorrected values.
• Figure 5: Diagram illustrating the details and flow of the calibration procedure, taking into account the effect of electric the field profile.