Griffiths and Phelps Lightning Initiation Model, Revisited

Abstract

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.

Modeling Compact Intracloud Discharge (CID) as a Streamer Burst

“…In the present paper, we will also model and simulate the CID as a streamer burst. However, our study differs in several aspects from the work described in [27,28]. In contrast to the work done by Attanasio et al [27], we will attempt to connect the growth parameters of the streamer burst to the signature of the NBP and from that we will attempt to evaluate the temporal and spatial development of the streamer burst.…”

“…Recently, several attempts were made to model CID's as streamer bursts [25][26][27][28]. In [25,26], the CID is modeled as an interaction between two (or more) bipolar streamer structures formed in a strong large-scale electric field of a thundercloud and the features of the electromagnetic emission resulting from this interaction between streamer structures were examined.…”

“…In [25,26], the CID is modeled as an interaction between two (or more) bipolar streamer structures formed in a strong large-scale electric field of a thundercloud and the features of the electromagnetic emission resulting from this interaction between streamer structures were examined. In the two publications [27,28], the idea of CIDs as a streamer burst was explored to study their physical parameters. In [27], the concept of propagating streamer systems inside the cloud environment as proposed by Griffith and Phelps [29] was utilized.…”

“…In the two publications [27,28], the idea of CIDs as a streamer burst was explored to study their physical parameters. In [27], the concept of propagating streamer systems inside the cloud environment as proposed by Griffith and Phelps [29] was utilized. Assuming that the streamer channel is of zero conductivity, the authors of [27] showed how the streamer system exhibits an initial exponential growth followed by a quadratic steady state.…”

“…In [27], the concept of propagating streamer systems inside the cloud environment as proposed by Griffith and Phelps [29] was utilized. Assuming that the streamer channel is of zero conductivity, the authors of [27] showed how the streamer system exhibits an initial exponential growth followed by a quadratic steady state. In [28], the radio spectrum of NBPs was investigated by modelling the CID as a burst of streamers.…”