A one and one-half-dimensional simulation of the streamer breakdown in long
high-temperature air gaps is performed by using a detailed kinetic model f
or the ionization processes in heated air in a strong electric field, The b
reakdown threshold is calculated as a function of the initial gas temperatu
re under the assumption of the "frozen" number of NO and under the assumpti
on of the local-thermodynamic-equilibrium content of NO. The first assumpti
on corresponds to rebreakdown within a post-arc channel cooled down to the
temperatures T < 3500 K whereas the second one corresponds to the breakdown
of slowly heated air. A hysteresis effect in the breakdown threshold that
can attain 35% is obtained.