A predictive model of the positive discharge in long air gaps under pure and oscillating impulse shapes

This paper presents a general model allowing the prediction of the behaviour of given gap submitted to a given voltage. The only input data are the electrode geometry, the applied voltage waveform and the atmospheric pressure and temperature. The model also allows for various conditions for arrest or instability of the discharge. By assuming the discharge channel to be a long conductor and using a typical single LCR conductor line (L, C and R being respectively the line inductance, capacitance and resistance), we derive a predictive model for a positive discharge in long air gaps. This allows one to describe the evolution of the entire discharge, with the parameters L, C and R varying with time according to the channel characteristics and discharge geometry. The model allows us to determine the time histories of the current both during the leader and during the return stroke, the charge, the potential gradient in the leader channel, the power and energy injected into the gap and the channel's thermal radius. It also permits the simulation of an image converter working in streak or frame mode and the leader propagation velocities. Furthermore, it allows the trajectory of the discharge, which is obtained from a probability distribution, to be plotted in real time. Good agreement between computed and experimental results was obtained for various test configurations.