Growing discharge trees with self-consistent charge transport: The collective dynamics of streamers

We introduce the generic structure of a growth model for branched discharge trees that consistently combines a finite channel conductivity with the physical law of charge conservation. It is applicable, e.g., to streamer coronas near tip or wire electrodes and ahead of lightning leaders, to leaders themselves and to the complex breakdown structures of sprite discharges high above thunderclouds. Then we implement and solve the simplest model for positive streamers in ambient air with self-consistent charge transport. We demonstrate that charge conservation contradicts the common assumption of dielectric breakdown models that the electric fields inside all streamers are equal to the so-called stability field and we even find cases of local field inversion. We also find that, counter-intuitively, the inner branches of a positive-streamer tree are negatively charged, which provides a natural explanation for the observed reconnections of streamers in laboratory experiments and in sprites. Our simulations show the structure of an overall 'streamer of streamers' that we name collective streamer front, and predict effective streamer branching angles, the charge structure within streamer trees and streamer reconnection.