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

TL;DR

This paper presents a new growth model for branched discharge trees that incorporates charge conservation, revealing complex internal charge structures and dynamics, including streamer reconnections and collective streamer fronts, applicable to natural and laboratory discharges.

Contribution

It introduces a self-consistent charge transport model for streamer growth, challenging previous assumptions and explaining streamer reconnections and collective behaviors.

Findings

Charge conservation contradicts the assumption of uniform internal electric fields.

The model predicts natural streamer reconnections observed in experiments.

Identification of a collective streamer front structure and its branching behavior.

Abstract

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 discuss the charge distribution inside discharge trees, 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.