Sub-nanosecond delays of light emitted by streamer in atmospheric pressure air: Analysis of N₂(⁠$C3Πu$⁠) and $N2+$(⁠$B2Σu+$⁠) emissions and fundamental streamer structure

Theoretical analysis of ultra-short phenomena occurring during the positive streamer propagation in atmospheric pressure air is presented. Motivated by experimental results obtained with tens-of-picoseconds and tens-of-microns precision, it is shown that when the streamer head passes a spatial coordinate, emission maxima from N₂ and $N2+$ radiative states follow with different delays. These different delays are caused by differences in the dynamics of populating the radiative states, due to different excitation and quenching rates. Associating the position of the streamer head with the maximum value of the self-enhanced electric field, a delay of 160 ps was experimentally found for the peak emission of the first negative system of $N2+$⁠. A delay dilatation was observed experimentally on early-stage streamers and the general mechanism of this phenomenon is clarified theoretically. In the case of the second positive system of N₂, the delay can reach as much as 400 ps. In contrast to the highly nonlinear behavior of streamer events, it is shown theoretically that emission maximum delays linearly depend on the ratio of the streamer radius and its velocity. This is found to be one of the fundamental streamer features and its use in streamer head diagnostics is proposed. Moreover, radially resolved spectra are synthesized for selected subsequent picosecond moments in order to visualize spectrometric fingerprints of radial structures of N₂(⁠$C3Πu$⁠) and $N2+$(⁠$B2Σu+$⁠) populations created by streamer-head electrons.