Griffiths and Phelps Lightning Initiation Model, Revisited

In this paper we reconstruct Griffiths and Phelps' seminal model of streamer systems to test if it can reproduce the key observational features of fast positive breakdown. We first confirm that our implementation is accurate by reproducing the original results. The model describes how a system of positive streamers exhibits an initial exponential charge growth, as a function of position or time, which rapidly transitions into a quadratic steady state. The charge growth is accompanied by substantial electric field enhancement near the onset location, creating favorable conditions for lightning initiation. Due to the relatively low conductivity of streamers (effectively zero in this model), the electric field enhancement is created by the charge deposited in the first few meters of propagation, in the scale length where the charge growth transitions from exponential to quadratic. The quadratic growth of charge, combined with conical system expansion, makes the surface charge density of the moving front constant. The resulting electric field ahead of the streamer system remains nearly constant during its propagation, consistent with the observations of fast breakdown, which reveal a nearly constant propagation velocity, independently of discharge polarity. Minimal changes to the model allow for simulation of narrow bipolar events, reproducing very well their characteristic bipolar electric field change waveform. Despite its simplicity, the Griffiths and Phelps model provides valuable physical insights in the relationship between fast positive breakdown and lightning initiation. Key Points The seminal Griffiths and Phelps model of lightning initiation provides valuable insights into the physics of fast positive breakdown The predicted constant electric field ahead of the moving streamer‐system front agrees with the constant velocity seen in observations With few upgrades the model can reproduce the classical electric field change waveform of narrow bipolar events