Positive and negative streamers in ambient air: measuring diameter,   velocity and dissipated energy
  Positive and negative streamers are studied in ambient air at 1 bar; they emerge from a needle electrode placed 40 mm above a planar electrode. The amplitudes of the applied voltage pulses range from 5 to 96 kV; most pulses have rise times of 30 ns or shorter. Diameters, velocities and energies of the streamers are measured. Two regimes are identified; a low voltage regime where only positive streamers appear and a high voltage regime where both positive and negative streamers exist. Below 5 kV, no streamers emerge. In the range from 5 to 40 kV, positive streamers form, while the negative discharges only form a glowing cloud at the electrode tip, but no streamers. For 5 to 20 kV, diameters and velocities of the positive streamers have the minimal values of d=0.2 mm and v \approx 10^5 m/s. For 20 to 40 kV, their diameters increase by a factor 6 while the voltage increases only by a factor 2. Above the transition value of 40 kV, streamers of both polarities form; they strongly resemble each other, though the positive ones propagate further; their diameters continue to increase with applied voltage. For 96 kV, positive streamers attain diameters of 3 mm and velocities of 4*10^6 m/s, negative streamers are about 20 % slower and thinner. An empirical fit formula for the relation between velocity v and diameter d is v=0.5 d^2/(mm ns) for both polarities. Streamers of both polarities dissipate energies of the order of several mJ per streamer while crossing the gap. 
T.M.P. Briels, J. Kos, G.J.J. Winands, E.M. van Veldhuizen and Ute   Ebert