The inception of pulsed discharges in air: simulations in background   fields above and below breakdown
  We investigate discharge inception in air, in uniform background electric fields above and below the breakdown threshold. We perform 3D particle simulations that include a natural level of background ionization in the form of positive and O$_{2}^-$ ions. When the electric field rises above the breakdown and the detachment threshold, which are similar in air, electrons can detach from O$_{2}^-$ and start ionization avalanches. These avalanches together create one large discharge, in contrast to the `double-headed' streamers found in many fluid simulations.   On the other hand, in background fields below breakdown, something must enhance the field sufficiently for a streamer to form. We use a strongly ionized seed of electrons and positive ions for this, with which we observe the growth of positive streamers. Negative streamers were not observed. Below breakdown, the inclusion of electron detachment does not change the results much, and we observe similar discharge development as in fluid simulations. 
Anbang Sun, Jannis Teunissen, Ute Ebert
physics.plasm-ph