Vertical electric field inside the lightning channel and the channel-core conductivity during discharge – Comparison of different return stroke models

Abstract The longitudinal electric field along the axis and the channel core conductivity of a straight, vertical lightning channel above ground has been calculated by using different return stroke models. The lightning channel is modeled by a negatively charged corona sheath that stretches around a thin, very conductive central core. It is commonly held that the majority of the leader charge is located within the corona sheath radius, which is of the order of meters, while the highly conductive channel core, with a diameter assessed at around 1 cm, in effect transports the whole of the axial current. An inhomogeneous channel line charge density generates as strong radial as well as vertical electric field inside the corona sheath. Transmission-line-type models and the generalized traveling current source model, representing the “engineering” return stroke models, are used for the calculation of the vertical field and the core conductivity in the channel. For the purpose of the present study only the influence of the charge in the corona sheath on the vertical electric field are taken into account while all other effects are neglected. For comparison purposes, the same channel-base current for all models is assumed. First, we calculated the vertical electric field along the axis on the channel. Knowing the axial current density profile along the channel determined by the particular return stroke model and the assumed channel core diameter, the core conductivity is calculated using simple scalar relationship. The conductivity is compared between the models and with the values found in the existing literature. It is concluded that all considered models give the maximum value of the core conductivity more or less in accordance with the predictions in the literature (of the order of 10 4  S/m). Some discrepancies (negative conductivity) are observed for two transmission-line-type models at the very bottom of the channel. They can be explained by the great amount of injected positive charge in zone 1 of the channel sheath and by the presence of the image charge, small changes in input parameters could diminished or avoid it. Due to the big charge accumulation near the ground the generalized traveling current source model gives greater discrepancies regarding negative conductivity at 25–35 m above ground. It is concluded that the removing of these discrepancies requires a more complex approach, the inclusion of the new physical mechanisms during the discharge (for example the magnetic field generated by the core current in the channel), that is a more accurate calculation of the channel discharge function. On the other hand our results are consistent with the 1 cm core diameter value found in the literature.