Capabilities and Limits of Deep Learning-Assisted E-FISH Diagnostics in Nanosecond Corona Discharges

Accurately resolving the electric field in nanosecond discharges is essential for understanding transient plasma behavior, particularly in streamer-based corona discharges where field localization governs ionization and wavefront propagation. In this work, we investigate a pin-to-pin nanosecond corona discharge in atmospheric air using a combination of time-resolved emission imaging and Electric Field Induced Second Harmonic Generation (E-FISH) diagnostics. The discharge exhibits a dual morphology: a steady, highly reproducible bulk region near the high-voltage electrode, and a stochastic, filamentary streamer region extending radially outward. To reconstruct the axial electric field profile, we applied a convolutional neural network (CNN)-based inverse method trained on synthetic E-FISH data. Calibration of the E-FISH signal was performed using both high-voltage probe measurements under non-discharging conditions and electrostatic simulations based on realistic electrode geometries. These independent methods allowed us to estimate an uncertainty range for the reconstructed field amplitude. Time-resolved ICCD imaging confirmed that the E-FISH laser probe was confined to the stable discharge region during early times (<5 ns), validating the field reconstruction under those conditions. Beyond this regime, the influence of streamer variability introduces uncertainty in the E-FISH interpretation. This study highlights both the capabilities and limitations of deep-learning-assisted E-field diagnostics in partially stochastic discharges.