Diffusion correction to the avalanche--to--streamer transition
  Space-charge dominated streamer discharges can emerge in free space from single electrons. We reinvestigate the Raether-Meek criterion and show that streamer emergence depends not only on ionization and attachment rates and gap length, but also on electron diffusion. Motivated by simulation results, we derive an explicit quantitative criterion for the avalanche-to-streamer transition both for pure non-attaching gases and for air, under the assumption that the avalanche emerges from a single free electron and evolves in a homogenous field. 
C. Montijn and U.Ebert