Simulation of positive streamers in atmospheric air by a macroscopic model with a new branching criterion

Streamers are the initial stage of electric breakdown in a long air gap. The modelling of streamers in atmospheric air can lay the foundation for the modelling of long sparks and help the insulation design in ultra-high voltage projects. In this paper, a 3D macroscopic model is built to describe the development of positive streamers. This model is based on a discharge tree model, first implemented by Luque and Ebert, which describes the self-consistent charge transport in streamers. The modified model considers the multiple initial streamers, streamer width variation after branching and improved streamer head mobility. More importantly, a new practical branching criterion of positive streamers is proposed. A higher branching possibility is shown if the average photoionization rate ahead of a streamer decreases to a certain critical value. In atmospheric air this critical value is estimated to be 4.5×10
¹⁹
cm
^-3
S
^-1
from experimental results. We performed a simulation on the development of streamers with tens of centimeters. The calculated results of streamer branching ratio agrees well with the experimental data. The influences of the critical photoionization rate and channel electrical conductance are discussed.