Transition Criteria and Scaling Law of Streamer-Spark Pulsed Discharges

Once the electrodes are not isolated by dielectrics, the spark discharge occurs when the discharge connects the electrodes. The transition from a streamer to a spark can be widely seen in the applications of pulsed discharges. In this chapter, the condition for the transition in a pin to plane configuration is investigated. A two-dimensional fluid and a zero-dimensional global are combined to reveal the spark transition at different temperatures. A conservative criterion to determine the condition for the streamer-to-spark transition of the first pulse is proposed. The conditions of spark formation in subsequent pulses in repetitive discharges when the field is lower than the ionization threshold are derived quantitatively taking into consideration the “knocking off” effects of long-life O atoms and negative ions. An analytical solution is formulated to scale the spark discharges to different pressures, energy depositions and discharge durations for hydrodynamics applications.