The formation of small sparks

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Abstract
The formation of a small incendiary spark at atmospheric pressure is identified with the transition from a weakly to a strongly ionized plasma. It is shown that initial gaseous ionization produced by avalanches and/or streamers always creates a high‐temperature ideal electron gas that can shield the applied voltage difference and reduce ionization in the volume of the gas. The electron gas is collision dominated but able to maintain its high temperature, for times long compared to discharge events, through long‐range Coulomb forces. In fact, electrons in the weakly ionized plasma constitute a collisionless independent fluid with a thermodynamic state that can be affected directly by field or density changes. Accordingly, with metal electrodes, cathode spot emission is always associated with the transition to a strongly ionized plasma. Neutral heating can be accomplished in two different ways. Effective dispersal of the electrons from the cathode leads to electron heating dominated by diffusion effects. Conversely, a fast rate of emission or rapid field changes can produce nonlinear wave propagation. It is shown that solitary waves are possible, and it is suggested that some spark transitions are associated with shock waves in the collisionless electron gas. In either the diffuse or nonlinear regime, neutral gas heating is controlled by collisions of ions with isotropic thermal electrons. This interaction is always subsequent to changes in state of the electron gas population. The basic results obtained should apply to all sparks.