Variability in fluence and spectrum of high‐energy photon bursts produced by lightning leaders

Abstract

In this paper, we model the production and acceleration of thermal runaway electrons during negative corona flash stages of stepping lightning leaders and the corresponding terrestrial gamma ray flashes (TGFs) or negative cloud‐to‐ground (−CG) lightning‐produced X‐ray bursts in a unified fashion. We show how the source photon spectrum and fluence depend on the potential drop formed in the lightning leader tip region during corona flash and how the X‐ray burst spectrum progressively converges toward typical TGF spectrum as the potential drop increases. Additionally, we show that the number of streamers produced in a negative corona flash, the source electron energy distribution function, the corresponding number of photons, and the photon energy distribution and transport through the atmosphere up to low‐orbit satellite altitudes exhibit a very strong dependence on this potential drop. This leads to a threshold effect causing X‐rays produced by leaders with potentials lower than those producing typical TGFs extremely unlikely to be detected by low‐orbit satellites. Moreover, from the number of photons in X‐ray bursts produced by −CGs estimated from ground observations, we show that the proportionality between the number of thermal runaway electrons and the square of the potential drop in the leader tip region during negative corona flash proposed earlier leads to typical photon fluences on the order of 1 ph/cm2 at an altitude of 500 km and a radial distance of 200 km for intracloud lightning discharges producing 300 MV potential drops, which is consistent with observations of TGF fluences and spectra from satellites.

Analysis of Individual Terrestrial Gamma‐Ray Flashes With Lightning Leader Models and Fermi Gamma‐Ray Burst Monitor Data

“…First, we derive the true fluxes of gamma-rays incident on Fermi detectors by taking the instrumental effects into account, for example, pulse pileup, dead time, and effective detection area. Note that this number is generally higher than the theoretical value suggested by Celestin et al (2015), which is derived using ground-based measurements of X-ray bursts (Schaal et al, 2012) by approximately 1 order of magnitude. Finally, this number of source photons is converted into seed electrons using a conversion factor.…”

“…The modeling procedure is similar to that used in, for example, Celestin et al (2012) and Xu et al (2015), specifically in three steps. We emphasize that the maximum electric field of 50 kV/cm (at ground level) is used in order to avoid the acceleration of runaway electrons in the extremely strong electric field obtained by the static vacuum solution (method of moments) at locations close to the leader tip (see discussion in Celestin & Pasko, 2011;Celestin et al, 2015). Second, using the Monte Carlo model for electrons, we simulate the acceleration of thermal runaway electrons in this leader field and the production of bremsstrahlung photons.…”

“…Specifically, this factor describes the total number of bremsstrahlung photons (>10 keV) produced per electron injected in Monte Carlo simulations and is calculated explicitly following the procedure described in Celestin et al (2015). In the present paper, using satellite-measured photon fluence and corresponding best fit leader model, we have estimated this number in three steps.…”

“…Not accounting for these effects may lead to erroneous interpretation of the data (see discussion in Mailyan et al, 2016, and references therein). Primarily focusing on the lightning leader model of the TGF production, we study the beaming geometry issues discussed in Mailyan et al (2016) and spectra variability effects discussed in Celestin et al (2015) using the Fermi GBM TGF data. The best fit with narrow beams, where wider beams are excluded, would seem to reject lightning leader scenario.…”

VHF and UHF Electromagnetic Radiation Produced by Streamers in Lightning

“…Similarly, with the same assumption for cases II, III and IV, the required numbers of streamers are ∼ 3.5 × 10 5 , ∼ 5 × 10 4 and ∼ 2.5 × 10 6 , respectively, and thus the UHF radiation energy would be ∼3 ×10 −4 J, ∼1 × 10 −5 J, and ∼2 × 10 −5 J, respectively. from the electrostatic consideration of the streamer zone (e.g., Celestin et al, 2015), 10 5 -10 7 streamers are required to give a potential drop of 2-20 MV near the lightning leader tip, which is commonly accepted for typical lightning leaders and also consistent with analysis of ground-based observation of X-rays produced by lightning (e.g., Xu et al, 2014). Specifically, the blue curve corresponds to the parameters: = 1.7 × 10 9 s −1 , = 7.5 × 10 7 s −1 , I CM0 = 0.44 A⋅m, and T 0 = 6 ns.…”