Electric field determination in streamer discharges in air at atmospheric pressure

The electric field in streamer discharges in air can be easily determined by the ratio of luminous intensities emitted by N(2)(C(3) Pi(u)) and N(2)(+) (B(2) Sigma(+)(u)) if the steady-state assumption of the emitting states is fully justified. At ground pressure, the steady-state condition is not fulfilled and it is demonstrated that its direct use to determine the local and instantaneous peak electric field in the streamer head may overestimate this field by a factor of 2. However, when spatial and time-integrated optical emissions (OEs) are considered, the reported results show that it is possible to formulate a correction factor in the framework of the steady-state approximation and to accurately determine the peak electric field in an air discharge at atmospheric pressure. A correction factor is defined as Gamma = E(s)/ E(e), where E(e) is the estimated electric field and E(s) is the true peak electric field in the streamer head. It is shown that this correction stems from (i) the shift between the location of the peak electric field and the maximum excitation rate for N(2)(C(3) Pi(u)) and N(2)(+) (B(2) Sigma(+)(u)) as proposed by Naidis (2009 Phys. Rev. E 79 057401) and (ii) from the cylindrical geometry of the streamers as stated by Celestin and Pasko (2010 Geophys. Res. Lett. 37 L07804). For instantaneous OEs integrated over the whole radiating plasma volume, a correction factor of Gamma similar to 1.4 has to be used. For time-integrated OEs, the reported results show that the ratio of intensities can be used to derive the electric field in discharges if the time of integration is sufficiently long (i.e. at least longer than the longest characteristic lifetime of excited species) to have the time to collect all the light from the emitting zones of the streamer. For OEs recorded using slits (i.e. a window with a small width but a sufficiently large radial extension to contain the total radial extension of the discharge) the calculated correction factor is Gamma similar to 1.4. As for OEs observed through pinholes, the reported results demonstrate that for local OEs, the Gamma coefficient depends slightly on the radial position and is in a range [1.24, 1.28]. For line-integrated OEs, the radial variation of Gamma is more significant and Gamma is in the range [1.24, 1.38]. Finally, it is noted that the use of different sets of Einstein coefficients and quenching rates of excited states has negligible influence on the value of Gamma.