The stepped nature of lightning, and the upward connecting streamer

We present numerical results that provide an explanation of the Finite steps of 20-50 m taken by lightning as it descends from the clouds, or as lightning rises from tall buildings towards the clouds. We also explain why positive streamers rise steadily from the ground to meet the descending lightning bolt at a distance of about 40 in above the ground, completing the discharge channel. Thus, the results define the limits of protection afforded by Franklin rods to buildings. Calculations for a 0.5 m positive point-plane gap show that the axial electric field of an ascending streamer has a remarkable structure comprised of a primary streamer head, followed by a secondary streamer head, and then a long plateau at a level greater than 30 kV cm(-1). This plateau in the electric field continues to elongate as the streamer propagates, maintaining the conductivity in the streamer channel. Once all the voltage is dropped along the channel plateau, streamer propagation must stop until heating modifies the channel properties. A limit is thus defined for the length of the streamer channel of around 20-50 in for typical lightning voltages. The step length must also reduce as the channel approaches the Earth, as observed, because of voltage dropped along the lengthening channel.