1.1.1 Beginnings

Studies of air breakdown began in the eighteenth century. Two names are pre-eminent: Franklin [1] and Lichtenberg [2], although contemporaries were active. Franklin's work grew out of his interest in lightning - a long spark - while Lichtenberg drew tree-like discharges, now called corona, across the surface of a large cake of resin. These two men defined two broad approaches to the study of breakdown which are perpetuated to this day in experimental and theoretical work. In the late 19th century, the emergence of modern physics, exemplified by the work of Townsend [3] and his successors, permitted knowledge of the process of ionisation to be applied to these phenomena. The two approaches were thus linked and another concept from the 18th century, the electric field, became established as paramount in all discussions of the subject.

Indeed, many of the quantities used in discussion of the processes in discharge physics, such as ionisation and attachment coefficients, electron and ion temperatures, diffusion coefficients and so on, have been measured and are quoted in terms of electric field. Usually, it is assumed that the electric fields being considered are uniform. In fact, this is very rarely true in practice and the use of these quantities is always subject to such modifications as are dictated by non-uniform electric field conditions. This was true in the times of Franklin and Lichtenberg, and it will be assumed in most of the discussion in this chapter since practical engineers rarely enjoy...