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 ns and length scales of 100 µm. 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.