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.
Narrow bipolar events (NBEs) are high power intracloud discharges that produce a characteristic bipolar electric field change waveform and are either isolated in time or occur at the beginning of lightning flashes. Observations of NBEs suggest they are produced by a streamer-based type of discharge referred to as fast breakdown (Rison et al., 2016). Fast breakdown can be either positive or negative in polarity (Tilles et al., 2019), propagates at velocities comparable to or faster than laboratory-produced streamers, and have complicated behavior producing opposite polarity breakdown that travels backward along the same path as the original discharge. According to Rison et al. (2016), fast breakdown (FB) has a role in initiating at least some if not all lightning flashes. The more energetic FB events produce high power NBEs, which initiate about 1 out of 6 lightning flashes in storms (Wu et al., 2014). FB occurs with a wide range of VHF source powers and durations, and is responsible for initiating other flashes and precursor events (Lyu et al., 2019;Rison et al., 2016). Recent attempts at modeling FB have tried to explain the NBE radio spectra as an ensemble of non-interacting streamers (Liu et al., 2019) and to reproduce NBE sferics using branching streamers (Cooray et al., 2020). Other works argue that cosmic ray air showers play a key role in igniting the initial streamers that produce lightning (Kostinskiy et al., 2020;Shao et al., 2020). Here we use an improved version of the Griffiths and Phelps (1976) lightning initiation model to address the problem from the stance of hydrometeor-initiated streamers. The model simulates the cumulative charge growth of a system of streamers based on energy considerations and basic electrostatics (Attanasio et al., 2019). We use the model to determine the electrical conditions required to produce powerful FB events that match observed NBE waveforms, and to determine the threshold conditions for producing the different types of FB observed to date. Methods Modeling the Collective Dynamics of a Streamer SystemThe Griffiths and Phelps lightning initiation model, hereafter referred to as the G&P model, was among the earliest attempts to model how lightning initiation can result from streamer phenomena (Griffiths & Phelps, 1976). The model expanded upon the idea that repeated positive streamers systems (i.e., coronae or coronas) would concentrate the charge at their starting point within the cloud, increasing the local electric field to the point where dielectric breakdown would occur (Loeb, 1966(Loeb, , 1968. As the positive streamers propagate in an electric field above their stability threshold, their charge increases, resulting in branching and additional streamer growth, and leaving negatively charged ionized channels in their wake (Figure 1a). The G&P model simplifies the description by representing the streamer charge as a conical system Abstract Fast breakdown (FB), a breakdown process composed of systems of high-velocity streamers, has been observed to precede lightning...
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