A 3D Self-consistent Propagation Model of the Lightning Leader

The research on simulation of lightning discharge and propagation is one of key issues nowadays in the knowledge of lightning physics. To study propagation characteristics of the lightning leader and the interaction between the lightning leader and structures, a 3D self-consistent propagation model of lightning leader is proposed considering the limitation of the 2D random model that cannot describe physical features of lightning discharge three-dimension well. This model proposed can properly simulate the downward stepped leader in 3D space based on the initial conditions, such as the background electric field and the geometry of ground installations. Also, the upward continuous progression of positive connecting leaders from its inception to the final jump as the downward negative stepped leader approaches the ground can be simulated. Meanwhile, this model can self-consistently calculate physical parameters of the leader while it develops in three dimensional space based on the transient electric field under the influence of the downward stepped leader and the geometry of ground structures, such as tip location every step, leader velocity, current density, charge per unit length and the length every step moved. Compared with the optical and electrical data of the natural and artificially triggered lightning detected in Guangzhou experiment base, as well as research results available in literature, simulation results of the self-consistent propagation model show that the initiation of the positive upward leader mainly depends on the electric field intensity and the geometry of the structure in the simulated domain. As the upward leader initiates and propagates towards the downward stepped leader, its velocity increases from 10⁴ m·s^-1 to 10⁵ m·s^-1 order of magnitude gradually along with time during the first 0-600 μs, and then its velocity obviously increases to 10⁶ m·s^-1 order of magnitude when the upward positive leader connects to the downward stepped leader, during which the average velocity reaches about 5×10⁵ m·s^-1. Furthermore, the current intensity in the channel also increases with the upward positive leader moving forward, and the trend has a good coherence with the variation of the relative brightness of the leader, which is consistent with the optical data and existing research. Through simulation results of lightning flashes striking on high structure, it is also derived that the charge per unit length in the propagation channel of upward positive leader initiated from high structure reaches about 50.0-108.0 μC·m^-1, with an average value of 64.3 μC·m^-1. In addition, the average length of upward positive leader is approximately 417 m. The research of 3D self-consistent propagation model of lightning leader can provide reference for further study of characteristics of lightning flashes striking on structures.