Abstract

A lightning flash is initiated by electrical breakdown of 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 dart leaders propagating from cloud to the Earth down the channel made by the stepped leader. This chapter is concerned with the mathematical modelling of first and subsequent return strokes.

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