Stepped Leader Progression and Speed Evolution in a Thunderstorm: Theoretical Model

Abstract

This paper presents a theoretical model to describe the progression of leading (falling) lightnings in storms (stepped leaders). Stepped leaders move down from the thundercloud base to the encounter point with an upward streamer. First, the existing models, related to the advance of leading lightnings, are analyzed. Then, a novel theory is presented. The proposed model describes both the leader progression and speed. It aims at explaining the leader progression as a succession of several steps, or branches, that form the well-known tree-like shape. The speed of advance per step is described as a function of various parameters: the charge concentration surface diameter and the step length, among others. The derived formulas include two new parameter named ( χ ) and G. χ is the ratio between the guide beam length ( L ) and the diameter of the circle, inside the cloud, where the charges are concentrated ( D ) . G relates density of charges, as explained herein.