Modeling the development of the stepped leader of a lightning discharge

A stochastic-deterministic model is presented for the propagation of a downward-moving leader. Lightning formation is described by a stochastic growth of branching discharge channels which is determined by the electrostatic field. The dynamics of the electric field and of the charge distribution over the lightning structure are calculated deterministically. The model includes the initiation of lightning, a preliminary discharge in a cloud, the propagation of a downward-moving stepped leader toward the earth, and the initiation and upward motion of a return stroke from the earth's surface. Numerical execution of the model yields a dynamic picture of the development of the downward-moving leader and of the intracloud discharge structure. The effect of the charge density in the cloud and the parameters of the developing channels on the spatial-temporal, current, and charge characteristics of the stepped leader's propagation are studied. The effect of free-standing structures on the distribution of points on the earth's surface where lightning strikes is examined.