Modeling of Sparkbreakdown of Short Non-Uniform Air Gaps

Summary form only given. The initial stage of discharge development at sufficiently high pd (where p is the gas pressure and d is the gap length) is the formation and propagation of ionization waves - streamers. Crossing the gap by the primary streamer does not necessary lead to breakdown. The next stage of discharge development evolution of the streamer channel is governed by the mean electric field inside the gap E_m=U/d, where U is the applied voltage. At E_m lower than the critical electric field E_c (corresponding to the equality of ionization and attachment coefficients) just after the bridging of the gap the mean net ionization rate is negative, so that the conductivity of streamer channel and, hence, the current decrease with time. However, in the initially decaying plasma some processes exist that tend to decelerate the decay and even to change the sign of the net ionization rate. As the result, after some time delay the decrease of current can be changed to an increase, resulting finally in spark breakdown. Two major factors lead to the growth of plasma conductivity. One, a thermal mechanism, is a lowering of the gas number density n inside the channel due to expansion of the heated plasma. It results in the growth of the mean reduced electric field E_m/n and, hence, in an increase of the net ionization coefficient. Another, a kinetic mechanism, is related to the accumulation of active particles (radicals and excited molecules) changing the balance between the rates of generation and loss of electrons due to the acceleration of the detachment, stepwise and associative ionization, etc. The time delay t _br between the bridging of the gap and spark formation is one of the main characteristics of the streamer-to-spark transition. Results of experiments have shown that the values of t_br in short non-uniform gaps in atmospheric-pressure air decrease steeply with growth of the mean electric field. Pre- ious simulations of the streamer-to-spark transition in short air gaps have been performed for relatively high values of E_m, when the breakdown occurs in the nanosecond time range and is governed by the kinetic mechanism only. At lower E_m the effect of channel expansion is essential. In the present work the results are presented of simulation of spark breakdown with account of both mentioned factors. The model is modified by inclusion of the gas dynamic equations describing gas motion in the radial direction (normal to that of streamer propagation). It is shown that an account of the channel expansion results in considerable shortening of the breakdown time t_br at low E_m. Calculated values of t_br versus the applied voltage agree with the experimental data