Dynamics of a lightning corona sheath - a constant field approach using the GTCS model

A generalized lightning traveling current source return stroke model (GTCS) has been used to examine the characteristics of the lightning channel corona sheath surrounding a thin channel core. A model of lightning channel consisting of a charged corona sheath and a narrow, high conducting central core conducting the main current flow is assumed. Strong electric field, in prevalent 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, it consists of two zones, zone 1 (inner zone containing net positive charge) and zone 2 (outer zone containing negative charge), respectively. We adopted the assumption of a constant electric field inside zone 1 of the corona sheath proved in the experimental research of the corona discharges in a coaxial geometry of 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.