  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.
