Analysis of the Spatial Nonuniformity of the Electric Field in Spectroscopic Diagnostic Methods of Atmospheric Electricity Phenomena

The spatial nonuniformity of the electric field in air discharges, such as streamers, can influence the accuracy of spectroscopic diagnostic methods and hence the estimation of the peak electric field. In this work, we use a self-consistent streamer discharge model to investigate the spatial nonuniformity in streamer heads and streamer glows. We focus our analysis on air discharges at atmospheric pressure and at the low pressure of the mesosphere. This approach is useful to investigate the spatial nonuniformity of laboratory discharges as well as sprite streamers and blue jet streamers, two types of transient luminous events taking place above thunderclouds. This characterization of the spatial nonuniformity of the electric field in air discharges allows us to develop two different spectroscopic diagnostic methods to estimate the peak electric field in cold plasmas. The commonly employed method to derive the peak electric field in streamer heads underestimates the electric field by about 40-50% as a consequence of the high spatial nonuniformity of the electric field. Our diagnostic methods reduce this underestimation to about 10-20%. However, our methods are less accurate than previous methods for streamer glows, where the electric field is uniformly distributed in space. Finally, we apply our diagnostic methods to the measured optical signals in the second positive system of N₂ and the first negative system of $N_2^{+}$ of sprites recorded by Armstrong et al. (1998, https://doi.org/10.1016/S1364-6826(98)00026-1) during the SPRITE's 1995 and 1996 campaigns.