Positive streamers in air and nitrogen of varying density: experiments   on similarity laws
  Positive streamers in ambient air at pressures from 0.013 to 1 bar are investigated experimentally. The voltage applied to the anode needle ranges from 5 to 45 kV, the discharge gap from 1 to 16 cm. Using a "slow" voltage rise time of 100 to 180 ns, the streamers are intentionally kept thin. For each pressure p, we find a minimal diameter d_{min}. To test whether streamers at different pressures are similar, the minimal streamer diameter d_{min} is multiplied by its pressure p; we find this product to be well approximated by p*d_{min}=0.20 \pm 0.02 mm*bar over two decades of air pressure at room temperature. The value also fits diameters of sprite discharges above thunderclouds at an altitude of 80 km when extrapolated to room temperature (as air density rather than pressure determines the physical behavior). The minimal velocity of streamers in our measurements is approximately 0.1 mm/ns = 10^5 m/s. The same minimal velocity has been reported for tendrils in sprites. We also investigate the size of the initial ionization cloud at the electrode tip from which the streamers emerge, and the streamer length between branching events. The same quantities are also measured in nitrogen with a purity of approximately 99.9 %. We characterize the essential differences with streamers in air and find a minimal diameter of p*d_{min}=0.12 \pm 0.02 mm*bar in our nitrogen. 
T.M.P. Briels, E.M. van Veldhuizen, Ute Ebert