6.1 Introduction

A lightning flash is initiated by electrical breakdown of the air in a cloud. This process, commonly known as the preliminary breakdown, signifies the initiation of a stepped leader. Such a stepped leader propagates towards the earth, in a succession of nearly discontinuous surges or steps. The stepped leader leaves a charged, conducting channel in its wake. When the leader reaches the ground, the current flowing in the channel increases abruptly, marking the beginning of the return stroke. After the first return stroke, several subsequent return strokes may occur, each of which is preceded by a fast, continuously moving leader the dart leader which propagates from cloud to earth down the channel made by the stepped leader. This Chapter is concerned with the mathematical modelling of return strokes.

From the point of view of an electrical engineer, the return stroke is the most important event in a lightning flash; it is the return stroke that causes most of the destruction and disturbance in electrical and telecommunication networks. In their attempts to provide protection, engineers seek the aid of return stroke models for three reasons. First, they would like to characterise and quantify the electromagnetic fields produced by return strokes at various distances to provide them with the input for mathematical routines that analyse the transient voltages and currents induced in electrical networks by these fields. This calls for return stroke models that are capable of generating electromagnetic fields similar to those created by natural...