Systematic 1D electric field induced second harmonic measurement on primary-to-secondary transition phase of positive streamer discharge in atmospheric-pressure air

Abstract The electric field induced second harmonic generation (E-FISH) technique has been widely utilized for the electric field measurement of atmospheric-pressure nonthermal plasmas. However, the measurement accuracy has not been quantified. Further, the E-FISH signal generation that is necessary to the evaluation of the measurement accuracy has been formulated only for the probe laser beam focused by a spherical lens and not for the cylindrical lens. Here, the E-FISH method utilizing the focusing cylindrical lens was studied for accurate one-dimensional (1D) electric field measurement of the primary-to-secondary transition phase of a single-filament positive streamer discharge generated in atmospheric-pressure air. A combination of numerical analysis and the E-FISH signal measurement was used to establish the radial distribution of the electric field vectors and the accompanying measurement accuracy. The E-FISH methodology captured a distinct evolution in the 1D electric field varying over timescales of ∼ 1 ns and length scales of 100 µ m. At the instant when the primary streamer arrived at the cathode, the electric field at 3 mm above the cathode surface was found to be as high as 225 Td, while the field at 10 mm above the cathode surface was as low as 5 Td. At the final stage of the primary-to-secondary transition phase completed in 3 ns from the primary streamer arrival at the cathode, the electric field at 3 mm above the cathode was found to be lower than that observed at 10 mm from the cathode; this finding is consistent with predictions made based on a previous model describing the initiation of the secondary streamer discharge and previously published electron density measurement.