On the birth of spark channels

The breakdown stage of a spark discharge in air is analyzed. This short duration stage (< 1 μs) has been divided into two phases. In the first, the electrical energy is introduced in a constant volume process. In the second, a sudden expansion occurs which is associated with the generation of a shock wave. The thermodynamic properties of the plasma were calculated by using concepts of statistical thermodynamics, in which molecular dissociation, ionization (up to the 3rd ionization) and the various modes of energy storage in a molecule were considered. The transport coefficients (thermal and electrical conductivities) were evaluated from molecular theory, as modified for partially ionized gas. The plasma conditions at the end of the second phase are expressed in terms of the breakdown energy and the maximum temperature of the plasma. The initial conditions for the arc stage have therefore been established. It is shown that owing to the drastic changes in the gas composition at high temperatures, the relationship between the input energy and the plasma temperature and its dimensions is quite complicated. The total thermal energy of the kernel at the end of the breakdown stage, as predicted by a simple model, was found to be four times higher than predicted by the present rigorous model.