Investigation of conditions necessary for inception of positive corona in air based on differential formulation of photoionization

Photoionization of molecular oxygen due to extreme ultraviolet emissions of molecular nitrogen in the wavelength range 98-102.5 nm [Zheleznyak et al., High Temperature, 20, 357, 1982] is a fundamental process in initiation of positive corona discharges [e.g., Naidis, Sov. J. Plasma Phys., 13, 645, 1987]. The mathematical formulation of the positive corona problem can be found in [e.g., Naidis, J. Phys. D: Appl. Phys., 38, 2211, 2005; Liu et al., JASTP, 80, 179, 2012; Benilov et al., J. Appl. Phys., 130, 121101, 2021]. Here we present a new approach to finding inception conditions of positive corona, which is based on differential formulation of the photoionization problem [Bourdon et al., PSST, 16, 656, 2007; Janalizadeh and Pasko, PSST, 28, 105006, 2019]. We compare results with (1) previous steady-state integral formulations [e.g., Naidis, 2005; Liu et al., 2012] and (2) a time-dynamic plasma fluid model originally developed for studying ignition of streamers in a system of two colliding hydrometeors [Jansky and Pasko, JGR, 125, e2019JD031337, 2020]. Results demonstrate significance of: (1) the increase in electron density due to reduction in discharge volume near sharp point in addition to electron avalanche multiplication included in the standard integral formulations [Naidis, 2005; Liu et al., 2012]; (2) accurate representation of photoionization in small discharge volumes; (3) inaccuracy of the approximation that most of photoionizing radiation originates next to surface of coronating electrode (especially in the case of large electrode dimensions ~1 m at low air pressures < 10% of atmospheric pressure).