Modeling heat dominated electric breakdown in air, with adaptivity to electron or ion time scales

We model heat dominated electrical breakdown in air in a short planar gap. We couple the discharge dynamics in fluid approximation with the hydrodynamic motion of the air heated by the discharge. To be computationally efficient, we derive a reduced model on the ion time scale, and we switch between the full model on the electron time scale and the reduced model. We observe an ion pulse reaching the cathode, releasing electrons by secondary emission, and these electrons create another ion pulse. These cycles of ion pulses might lead to electrical breakdown. This breakdown is driven by Ohmic heating, thermal shocks and induced pressure waves, rather than by the streamer mechanism of local field enhancement at the streamer tip.