Dynamics of a lightning corona sheath—A constant field approach using the generalized traveling current source return stroke model

Abstract

A generalized lightning traveling current source return stroke model has been used to examine the characteristics of the lightning channel corona sheath surrounding a thin channel core. A model of the lightning channel consisting of a charged corona sheath and a narrow, highly conducting central core that conducts the main current flow is assumed. Strong electric field, with a predominant radial direction, has been created during the return stroke between the channel core and the outer channel sheath containing the negative charge. The return stroke process is modeled with the positive charge coming from the channel core discharging the negative leader charge in the corona sheath. The corona sheath model that predicts the charge motion in the sheath is used to derive the expressions of the sheath radius vs. time during the return stroke. According to the corona sheath model proposed earlier by Maslowski and Rakov (2006) and Maslowski et al. (2009), it consists of three zones, zone 1 (surrounding channel core with net positive charge), zone 2 (surrounding zone 1 with negative charge) and zone 3 (outer zone representing the virgin air without charges). We adopted the assumption of a constant electric field inside zone 1 of the corona sheath observed in the experimental research of corona discharges in a coaxial geometry by Cooray (2000). This assumption seems to be more realistic than the assumption of a uniform corona space charge density used previously in the study of Maslowski and Rakov (2006), Marjanovic and Cvetic (2009), and Tausanovic et al. (2010). Applying the Gauss’ law on the infinitesimally small cylindrical section of the channel the expressions for time-dependence of the radii of zones 1 and 2 during the return stroke are derived. The calculations have shown that the overall channel dynamics concerning electrical discharge is roughly 50% slower and the maximum radius of zone 1 is about 33% smaller compared to the corresponding values calculated in the study of Tausanovic et al. (2010).