The influence of the breakdown electric field in the configuration of lightning corona sheath on charge distribution in the channel

Abstract

A model of corona sheath that surrounds the thin core of the lightning channel has been investigated by using a generalized traveling current source return stroke model. The lightning channel is modeled by a charged corona sheath that stretches around a highly conductive central core through which the main current flows. The channel core with the negatively charged outer channel sheath forms a strong electric field, with an overall radial orientation. The return stroke process is modeled as the negative leader charge in the corona sheath being discharged by the positive charge coming from the channel core. Expressions that describe how the corona sheath radius evolves during the return stroke are obtained from the corona sheath model, which predicts charge motion within the sheath. The corona sheath model, set forth by Maslowski and Rakov (2006), Tausanovic et al. (2010), Marjanovic and Cvetic (2009), Cvetic et al. (2011) and Cvetic et al. (2012), divides the sheath onto three zones: zone 1 (surrounding the channel core with net positive charge), zone 2 (surrounding zone 1 with negative charge) and zone 3 (the outer zone, representing uncharged virgin air). In the present study, we have assumed a constant electric field inside zone 1, as suggested by experimental research of corona discharges in coaxial geometry conducted by Cooray (2000). The present investigation builds upon previous studies by Tausanovic et al. (2010) and Cvetic et al. (2012) in several ways. The value of the breakdown electric field has been varied for probing its effect on channel charge distribution prior and during the return stroke. With the aim of investigating initial space charge distribution along the channel, total electric field at the outer surface of the channel corona sheath, just before the return stroke, is calculated and compared for various return stroke models. A self-consistent algorithm is applied to the generalized traveling current source return stroke model, so that the boundary condition for total electric field is fulfilled. The new density of space charge and the new radius of channel corona envelope, immediately before the return stroke stage, are calculated. The obtained results indicate a strong dependence of channel charge distribution on the breakdown electric field value. Among the compared return stroke models, transmission-line-type models have exhibited a good agreement with the predictions of the Gauss' law regarding total breakdown electric field on the corona sheath's outer surface. The generalized lightning traveling current source return stroke model gives similar results if the adjustment of the space charge density inside the corona sheath is performed.