Conductivity of a Lightning-Channel Corona Sheath During Return Stroke

A generalized lightning traveling current source (GTCS) return-stroke model has been used to examine the conductivity of the lightning-channel corona sheath surrounding a thin channel core. A model of lightning channel consisting of the charged corona sheath and the narrow high-conducting central core conducting the main current flow is assumed. A strong electric field, in a prevalent radial direction, has been created during the return stroke between the channel core and the outer channel sheath containing the negative channel charge. The return-stroke process is modeled with the positive charge coming from the channel core discharging the negative leader charge. The channel corona-sheath model that predicts the charge motion in the corona sheath is used to derive the expressions of the channel sheath conductivity during the return stroke. This model can be viewed as the generalization of the corona-sheath model proposed by Maslowski and Rakov in 2006. According to this model, the corona sheath consists of two zones, zone 1 (inner zone containing a net positive charge) and zone 2 (outer zone containing negative charge), respectively. Gauss' law, the charge conservation law, and the point form of Ohm's law are combined to form the differential equation which is analytically solved, yielding the expression for the sheath conductivity in zones 1 and 2. The expressions of the radial electric fields, the current densities, and the conductivities in zones 1 and 2 are derived using the GTCS return-stroke model. The measurements of the electric field in the immediate vicinity of the lightning channel by Miki in 2002 enabled the calculation of the channel sheath parameters. It is shown that the maximum radii of zones 1 and 2 at 2 m above ground are less than 1.5 and 6 cm, respectively. The minimum value of the channel sheath conductivity, about 10 muS/m , is obtained between zones 1 and 2 during the return stroke. The theoretical considerations given in this paper can be also applied to other types of ldquoengineeringrdquo return-stroke models.