A theoretical study of electrostatic field wave shapes from lightning leaders

Abstract

Electrostatic dE/dt field wave shapes are calculated for various lightning leader models over a perfectly conducting ground plane. These provide an improved theoretical basis for the characterization and interpretation of observed leader wave shapes for close lightning. Since dE/dt at a particular time is a function of how the leader tip is propagating, whereas the total electric field change at the same time is a function of the aggregate behavior of the leader up to this time, dE/dt is the preferable parameter for leader characterization. In particular, whether or not dE/dt changes polarity in the course of the leader is independent of the channel charge distribution, unlike the polarity of the net field change. The dE/dt wave shape is also more easily interpreted in terms of channel geometry than the electric field wave shape for leader channels that have branches or are not vertical. Features of dE/dt are derived for a vertical, one‐dimensional leader channel assuming an electrostatic relation, and deviations from this model are studied for both inclined channels and three‐dimensional charge distributions. The existence of a turning point (dE/dt = 0) in the electric field wave shape is investigated, and the distance dependence of the leader tip height corresponding to an electric field turning point is presented. For a vertical channel the final leader current IL0 is shown to be related to the final dE/dt, (dE/dt)0, by IL0 = −2πε0[H2 + D2]3/2 (dE/dt)0/H, where H is the height above ground level and D is the horizontal distance for the charge center which is the origin of the leader charge. The physical validity of the leader models used is discussed, and some applications of the derived plots are considered.