Generation possibility of gamma-ray glows induced by photonuclear reactions
Gabriel Sousa Diniz, Ivan Soares Ferreira, Yuuki Wada, Teruaki Enoto
GGeneration possibility of gamma-ray glows induced byphotonuclear reactions
G. Diniz , I.S. Ferreira , Y. Wada , T. Enoto , • Photonuclear reactions triggered by a TGF will sustain a gamma-rayemission level that can promote new RREAs. • Both photonuclear reactions and their induced RREA can extend TGFeffects to minute timescale. • We evaluate the possibility of gamma-ray glows promoted by RREAsoriginating from photonuclear-induced nuclides decays. • An edited version of this paper was published by AGU. Copyright 2021American Geophysical Union, Diniz et al. [2021].
Abstract
Relativistic runaway electron avalanches (RREAs) imply a largemultiplication of high energy electrons ( ∼ a r X i v : . [ phy s i c s . a o - ph ] J a n Introduction
High-energy atmospheric phenomena (HEAP) [Babich, 2003], although thelate discovery with terrestrial gamma-ray flashes (TGFs: Fishman et al.[1994]), have been studied since much earlier as in Wilson [1924, 1925], Libbyand Lukens [1973]. Different HEAP have been observed over the decadesas; spatial distribution and energy spectrum of TGFs [Briggs et al., 2010,Smith et al., 2005, Tavani et al., 2011]), particle production – in particularneutrons [Shah et al., 1985, Babich et al., 2007, Shyam and Kaushik, 1999,Bratolyubova-Tsulukidze et al., 2004, Martin and Alves, 2010, Rutjes andEbert, 2017, Chilingarian et al., 2012a,b] with the detections reviewed byBabich [2019a] , as well as extended gamma-ray emissions so-called gamma-ray glows, thunderstorm ground enhancements (TGEs) or long bursts [Toriiet al., 2002, Tsuchiya et al., 2007, Tsuchiya et al., 2012, Chilingarian, 2013,Kelley et al., 2015, Wada et al., 2019]. Although Libby and Lukens [1973]thought the neutron production as a result from nuclear fusion, photonuclearreactions has been proved to be the generation mechanism [Babich, 2006,Babich et al., 2007, Babich and Roussel-Dupr´e, 2007].It has been recently predicted that a TGF can extend its duration [Rutjeset al., 2017] and confirmed as TGF afterglows which are due to capturesof neutrons produced by a TGF in the air [Enoto et al., 2017], an earliergamma generation mechanism by neutrons was proposed by Paiva et al.[2013] but through fusion channels. These neutrons, as they are generated,leave unstable atoms as a byproduct which leads to β -decay [Bowers et al.,2017, Enoto et al., 2017, Enoto, 2019] and proton emissions [Babich, 2017a,b,2019b]. The current whole set of HEAP can then be extended from µs timescales with TGFs [Fishman et al., 1994] up to minutes or hours with thegamma-ray glows [Tsuchiya et al., 2012], which are summarized in Figure 1.Although the connection from TGFs to neutron emissions and TGF af-terglows has recently become clear, there is no record of TGFs followedby gamma-ray glows while Wada et al. [2019] reported the latter preced-ing the former. Both events are thought to be generated by relativisticrunaway electron avalanches (RREAs), the feedback mechanism [Gurevichet al., 1992, Dwyer, 2003, Dwyer et al., 2012], and their subsequent brem-strahlung [Babich et al., 2004a]. However, they are still seen as separateevents.Nevertheless, the recent β -decay observations by Umemoto et al. [2016],Enoto et al. [2017] provides high-energy particles that may serve as seedsfor RREA, thus generate gamma-ray glows as the atomic-decay emissionscontinue for a timescale of minutes, and provide a bridge between the phe-nomena as they are indistinctly correlated with TGF emissions. The possi-ble products and byproducts by nuclear interactions of HEAP are exploredfurther on. 2igure 1: A distribution of HEAP durations. There are several photonuclear byproducts [Ortega, 2020, Babich, 2017a,b,2019b]; some of them are stable and others are unstable [Varlamov et al.,1999, Dietrich and Berman, 1988]. We focus on the main atmospheric com-ponents. Nuclear reactions of our interests are basically the giant dipoleresonance (GDR) and neutron capture. Proton-related captures are notconsidered here since the cross-section of proton captures with nitrogen N( p, γ ) O peaks at ∼
260 keV with ∼ − barns [Daigle, 2013]: theminimum cross-section of neutron captures N( n, γ ) N is above 10 − barnsat ∼
20 MeV and, that at 260 keV is ∼ − barns . Also as the protonthermalizes, it can recombine into hydrogen with the available electrons.Table 1 summarizes all interested photonuclear products and byproductstogether with the possibility of β -decay and Q being the available energyfor the decay byproducts. The present paper investigates the minute-lasting effects of a TGF. It isfurther divided into three sections; Section 2 presents theoretical calcula-tions that shows minute-long TGF effects through its byproducts and chain N N β + ∼ .
965 1.203 O O β + ∼ .
037 1.732 Ar Ar β − ¿ years 0.054Proton emission N C Stable - - O N Stable - - Ar C β − ∼ . N N Stable - - O O Stable - - Ar Ar β − ∼ . N C β − > years 0.146 O N β − ∼ .
12 10.420 Ar Cl β − ∼ .
35 7.482reactions. Section 3 shows that the β + particles have an RREA-generatingcapability given their isotropic emission. Section 4 discusses the require-ments for gamma-ray glows driven by unstable nuclei decay to exist afterTGFs. Currently, two mechanisms are thought of as gamma-ray glow sources: theRREA [Gurevich et al., 1992] and Modification Of the energy Spectra (MOS)[Chilingarian et al., 2012c]. RREA depends on electric fields higher than285 kVm − [Dwyer, 2003, Babich et al., 2004b] and an arbitrary seed source(which can be cosmic-rays), while MOS is the cosmic ray energy spectrachanged by thunderstorm electric fields and it can occur in lower electricfields and is easier to sustain than RREA. Since MOS is strictly connectedto cosmic-rays, TGF-induced glows should happen through the RREA mech-anism started by TGF byproducts. Therefore, the byproducts’ effects musthave minute-long duration and energy enough to trigger an avalanche. Alongwith these requirements on the source, there is also ambient conditions thatmust be matched, explored in Section 4.This section focuses on phenomena durations and models accordinglyto the creation and destruction mechanisms. The timescale analysis showsthat TGF products continue for tens of minutes with energies around MeV4ange, i.e., capable of generating high-energy photon emissions throughoutthe characteristic time of gamma-ray glows. The following subsections con-sider rates at standard temperature and pressure (STP) in the atmosphereas is done by Rutjes et al. [2017] for simplicity because of all the processfrequencies scale in the same fashion with density [Choi et al., 2007]. Thelast subsection characterizes the β + particles emitted by the unstable nucleias possible RREA seeds.The TGF pulse shape is modeled as a gaussian, following Briggs et al.[2010], with values to match their observations while we emulate the eventsafter the TGF as non-gaussian pulses in the form P ( t ) = n p (1 − e − tκ xr ) e − tκ xd .The latter form is characterized by growth and decay rates κ x , where thesub-index designates the physical process. Hence, the number of particles ina given time depends on creation rate, κ xr , decreasing rate of, κ xd , and theparent particle number n p . Thus if κ xr >> κ xd , the particles are createdtoo quickly in comparison to their sink process and would generate a longemission behavior. The TGF spectrum is modeled as Equation 1 [Dwyer et al., 2012], with ε th as 7.33 MeV [Briggs et al., 2010] and allows energies up to tens of MeV.One issue is that the spectrum diverges by approaching zero energy. Thus,it is impossible to normalize it without a lower energy cutoff ε cut . There isphysically no problem with this divergence because there is no sense of zeroenergy photons. This energy cutoff needs to be low in comparison with thecontext and simulations usually implement it as tens of keV [Rutjes et al.,2016].The interesting energies for neutron production are above 10.5 MeV,range in which the photonuclear reactions are relevant [Baldwin and Klaiber,1947]. The number of photons n γ , for our purposes on probability, in thefollowing calculations is taken as 1 so our calculations are per photon. But,for particle number calculation, Gjesteland et al. [2015] estimates 10 -10 photons with energy above 1 MeV, F tgf ( ε ) = n γ e − εε th ε , (1) (cid:82) ∞ . F tgf ( ε ) dε (cid:82) ∞ ε cut F tgf ( ε ) dε = Υ; (2)considering Gjesteland et al. [2015] and ε cut as 1 MeV, Υ ≈
7% and the totalamount of gammas above 10.5 MeV will be 7 × -7 × . According toBabich et al. [2010] results of 4.3 × − produced neutrons per photon above10.5 MeV, there will be approximately 3 × - 3 × neutrons producedin a TGF. 5he TGF gaussian (Equation 3) parameters are µ tgf = 130 µs and σ tgf = 100 µs to emulate both the rise time and duration. P tgf ( t ) = n γ e − ( t − µ tgf)22 σ (cid:113) πσ (3) As soon as the TGF starts, the photons may interact with the air particlesaccordingly based on the process probability within their energy range [K¨ohnet al., 2017]. Consequently, the time scale of neutron bursts is basicallydefined by the frequency of photonuclear reactions κ ph − nuc as well as thatof neutron captures κ capt which is taken to be constant since σ capture ∝ ( (cid:112) ε neutron ) − ∝ ( v neutron ) − and κ capt = v neutron σ capture n air ∝ nn as we areusing homogeneous density [Rutjes et al., 2017, Blatt and Weisskopf, 1979].Both collision frequencies model the neutron pulse shown in Equation 4, P neut ( t ) ≈ n γ Υ κ ph − nuc κ ph − absp (1 − e − κ ph − nuc t ) e − κ capt t , (4)here n γ Υ takes into account only TGF photons with energy above 10.5 eV.But these photons may undergo other interactions such as Compton scatter-ing and pair production. Photonuclear reactions are rarer than those [K¨ohnand Ebert, 2015]. Such factor agrees with the rate between the photonuclearreaction frequency ( κ ph − nuc ) and the photo-absorption frequency ( κ ph − absp )[Rutjes et al., 2017] with respective values at STP of ≈ × s − and ≈ × s − while the neutron capture frequency is ≈ . − [Rutjeset al., 2017, Choi et al., 2007]. As the neutrons are captured, gamma-rays will be emitted during the cap-ture, the so-called TGF afterglow [Rutjes et al., 2017, Enoto et al., 2017,Diniz et al., 2018]. Thus, the photon number will increase accordinglywith both photonuclear and neutron-capture processes. Since κ ph − absp (cid:29) κ ph − nuc > κ capt , the photons will be rapidly absorbed by atmospheric parti-cles as they are being created, hence the afterglow time pulse has the samebehavior as the neutron’s one, but its intensity decreases by a factor 10 dueto their absorption, resulting in the factor κ ph − nuc κ n − γ κ − absp , in which the radiativecapture rate is κ n − γ = 0 . − since it is not only possible capture process[Rutjes et al., 2017, Choi et al., 2007] resulting in Equation 5, P aft ( t ) ≈ n γ Υ κ ph − nuc κ n − γ κ − absp (1 − e − κ ph − nuc t ) e − κ capt t . (5)6 .4 Atomic decay Another photonuclear effect is its unstable byproducts confirmed by [Dwyeret al., 2015, Enoto et al., 2017, Babich, 2017a,b, Kochkin et al., 2018, Babich,2019a]. Both nitrogen and oxygen leave, by neutron emission, unstableatoms that will undergo β + decay, as indicated in Table 1. Each unstableatom has the probability to decay with κ − , a characteristic time from themoment when it is generated. In consequence of this fact, the decay timepulse (Equation 6) will start by following the neutron creation and sustainthe positron emission during the decay timescale, P decay ( t ) ≈ n γ Υ ρ rel κ ph − nuc κ ph − absp (1 − e − κ ph − nuc t ) e − tκ dc . (6)There are different contributions from nitrogen, oxygen, and even argon.To take this into account in Equation 6, the relative density ρ rel is intro-duced. As shown in Table 1, argon will contribute with β − emissions butwith a short characteristic rate κ dc ; for this reason and its low relative den-sity together with lower photonuclear cross-section [Varlamov et al., 1999],we do not proceed with argon contribution in our estimates.Although there is no record, found in the literature, of TGFs generatinggamma-ray glows, the equation analysis and Figure 2 show that TGF effectsreach the time scale of gamma-ray glows as illustrated in Figure 1. β + -decay emitted positrons The temporal estimate makes clear the gamma emission maintenance of atime scale from a TGF to a gamma-ray glow. Depending on the energy, thereis the possibility of RREA generation, possibly together with the feedbackmechanism [Dwyer, 2003, 2012]. It may be one possible source of gamma-rayglows.The spectral shape of β -decay particles can be described by equations7–9 [Wilson, 1968, Krane, 1988], following the assumption of massless neu-trinos and high positron energies for simplicity. This simplification does notundermine our estimations since the spectral correction due to the neutrinomass have impact mostly at the extreme spectrum points, F β ( ε ) = (cid:112) ε + 2 εm e ( Q − ε ) ( ε + m e ) F Fermi ( ε, Z ) , (7) S ( Z ) = (cid:112) − αZ − , (8) F F ermi ( ε, Z ) = 2 πν ( ε, Z )1 − e − πν ( ε,Z ) ( α Z ω ( ε ) + 0 . ω ( ε ) − S ( Z ) , (9)here, F Fermi ( ε, Z ) is the Fermi function [Krane, 1988], Z is the daughter (orproduct) atomic number, α is the fine structure constant, Q is the availableenergy displayed in Table 1; ω and ν are defined respectively as,7 Time (s)10 R e l a t i v e i n t e n s i t y p e r a s i n g l e T G F p h o t o n Extended TGF effects
TGFNeutron burstTGF afterglowNitrogen decayOxygen decay
Figure 2: Particle pulses according to equations 1–6. Following the TGFtimeline, up until the nitrogen decay. All curves are thought as per TGFphoton with energy between 10 and 30 MeV. ω ( ε ) = εm e c + 1 , (10) ν ( ε, Z ) = αZ ( ε + m e c ) √ ε + 2 εm e c , (11)where m e c = 511 keV, is the positron rest energy. It is important tonote that Equation 11 diverges as energy decreases, stressing the equationvalidity only at higher energies.Equation 7 shows the possibilities of kinetic energy for the releasedpositron; and, by energy conservation, during the following electron-positronannihilation the two generated photons will share energy given by 2 m e c + K [ e + ] with K [ e + ] as the positron kinetic energy and considering the elec-trons at rest.As the β decay spectrum and its decay in time are statistically indepen-dent and normalized, the composed function is the product of both functions.For such, since Equation 7 is invalid for lower energies, we normalize it be-tween 2 keV and its maximum value Q. Figure 3 displays the spectrum (top8eft panel), decay pulse (top right panel), and the combined information asa function of time and energy for the N and O decay. E n e r g y ( M e V ) Runaway Threshold 15 minutes N O + ( MeV s ) . - . e - . e - . e - . e - . e - + ( M e V )
1e 3 Runaway Threshold N O + ( s )
15 minutes N O Figure 3: β + emission as a function of energy (top left panel) and time (topright panel) and the joint information in the bottom panel. The 15-minuteline indicates relevant emissions of energetic positron emissions already atthe gamma-ray glow time scale. All the e + created with higher energy thanthe runaway threshold can be an avalanche seed. The runaway thresholdline of 0.25 MeV requires an electric field of approximately 0.6 MVm − torunaway [Kutsyk et al., 2012]. β + decay as RREAseeds by simulations We have performed Monte-Carlo based simulations with GEANT4 softwarekit focused on the possibility of positron-generating RREAs. GEometryANd Tracking 4 (GEANT4) [Agostinelli et al., 2003, Allison et al., 2006,Allison et al., 2016] is an open-source toolkit to simulate the particle motionthrough matter, developed by a collaboration lead by the CERN. It is codedin C++, following an object-oriented methodology. It can simulate thetransport of almost all known particles and can include electromagneticfields. We use the version 10.6 released in December 2019. Referencesand details for these models are presented in the ”geant4 Physics referencemanual” available at http://geant4.web.cern.ch . In the present paper,we adapted Sarria et al. [2018] codes to be positron driven but following thesame parameters from their supplementary material (available at ).9 .1 Setup of simulations
The setup is described in detail on the supplementary material of Sarria et al.[2018]. Nevertheless, we implemented simulations with 10 positrons eachand electric fields between 0.2 and 1.5 MV m − . The energies of primarypositrons are between 0.02 and 1.73 MeV because the avalanche probabilityis nearly null for 0.01 MeV [Sarria et al., 2018] and the oxygen limitingQ value (see Table 1). For our purposes, we consider an avalanche as theproduction of 20 electrons with 1 MeV and use the O4 physics list. FollowingSarria et al. [2018], the avalanche threshold is sufficiently above one runawayelectron, a criteria used in earlier works [Lehtinen et al., 1999, Li et al.,2009, Liu et al., 2016, Chanrion et al., 2016a], but low enough to deal withcomputational limitations. It is important to highlight the difference between electron avalanche andrelativistic runaway electron avalanche. The former can be achieved in alower energy regime and with electric fields that sustain ionization energy( ∼
10 eV) producing thermal energy particles. The latter is related to therunaway threshold and, with charge carriers in this energy regime, can besustained producing relativistic particles [Gurevich et al., 1992].Even though runaway particles require sub-breakdown fields to keeptheir energy [Skeltved et al., 2014], high electric fields above the break-down threshold are required to transfer thermal particles into the runawayregime – the strong-field runaway [Babich, 1995] or cold runaway [Gurevich,1961]. This change in electric field requirement is explained by the frictioncurve behavior [Peterson and Green, 1968, Moss et al., 2006], which has apeak at 200 eV for atmospheric air and prevents the thermal particles fromtransferring to higher energy regimes [Diniz et al., 2019, Chanrion et al.,2016b, Chanrion et al., 2014].Our ¿1 keV energy regime thus requires sub-breakdown electric fieldsbut the field existence is still a necessity for RREAs as will be exploredsection 4.2. The electric field serves as an energy source and provides itenough to not only sustain the avalanche but also accelerate the producedparticles to keep them in the runaway regime. Figure 4 displays the proba-bility to reach RREA status, here defined as the production of 20 electronswith one MeV electron/positron, as a function of electric field and primaryparticle energy.Figure 4 demonstrates the differences between a positron RREA seedand an electron one. At low energies, the positron seed has a significantlyhigher chance of avalanche production because, after the seed thermalizes, itwill annihilate producing gamma-rays able to produce high-energy electronswhile low energy electrons always need to be accelerated to emit gamma-ray.10 .5 1.0 1.5Seed energy (MeV) 0.51.01.5 180180 ElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositronsElectronsPositrons0.51.01.5 00 E l e c t r i c f i e l d ( M V / m ) Figure 4: Probability (%) of an RREA induced by a positron (red) or anelectron (blue) with energy given by x-axis and in an electric field in they-axis. Each panel regards a different angle between the initial velocity andacceleration identified by the black number in degrees at each panel. Here,we consider RREA as the production of 20 electrons with 1 MeV.
It is important to notice that while high-energy positrons do not lose allenergy to annihilate, they also produce high-energy electrons. Both features,the electron production, and the annihilation make positron RREA seedsmore efficient than electron ones.The decay products will not be necessarily emitted aligned with theelectric field. This alignment modifies the RREA production chance, asshown by Figure 4. Nevertheless, the results display at least 20% probabilityof RREA generated by positrons with any considered energy for all simulatedinitial alignment with electric fields ≥ − .As RREA can promote multiple HEAP events, this possibility permits acyclic view on the phenomena as they can take origin through the byproductsof other events. There are limits for such a cycle [Dwyer, 2007]: the possiblechain reaction of the high-energy particle production is limited by the needfor an electric field, thus it is limited in time by the thunderstorm durationand in space by the electric field decreasing with distance.11 Gamma-ray glow requirements
Two conditions are necessary for gamma-ray glows: (1) enough seed numberand (2) strong and long electric fields. The former concerns the sourcecapability to provide a large number of energetic particles while the latterrestricts the ambient electric field to values and sizes capable of sustainingthe particle multiplication during the cascade motion through the air. β + decay versus cosmic-ray seed Cosmic rays are thought to be RREA seed providers [Wilson, 1925, Williams,2010] and related with gamma-ray glow source [Wada et al., 2019]. The fluxof energetic cosmic-ray electrons represents a reference quantity to comparephenomenological candidates to RREA and gamma-ray glow sources.Wada et al. [2019] measurements occurred at (36.5 ◦ N, 136.6 ◦ E) on 9January 2018, during a winter thunderstorm in Japan. The energetic cosmic-ray shower spectra (differential flux) can be retrieved for such coordinatesusing EXPACS [Sato, 2015, 2016] model in units of [/MeV/cm /s]. Wehave summed the differential flux of electrons and positrons to comparewith the β + -decay seed deposit.The radial density distribution of secondary cosmic-ray electrons canbe described by the well-known NKG empirical formulae which depend on acharacteristic radius scale (R ≈
115 m for air) [Gaisser et al., 2016, Gurevichet al., 1999]. We estimate the cosmic ray shower spectra integrated over thearea by multiplying EXPACS results by the orthogonal circular area with a115 m radius.This comparison is chosen because while the secondary cosmic ray par-ticles all reach the thunderstorm region from upwards and are distributedradially, the unstable nuclei are left from photonuclear reactions in a longi-tudinal developed fashion and the β particles are emitted isotropically, notallowing a direct flux comparison.To compare the cosmic ray secondary spectra in [MeV − s − ] with the β -emission from unstable nuclei, we considered the normalized β -decay spectramultiplied by the rate of decayed particles. For such, we are considering thatall neutrons are produced by the same channel, i.e., single neutron outgoingfrom the nuclei and leaving unstable N or O.Using the total neutron number, 3 × , estimated in section 2.1 andfollowing our approximations, there will be approximately 2.3 ×
13 13
N and6.2 ×
12 15
O to decay. Figure 5 compares cosmic ray shower of electronsand positrons with the β -decay spectra.The higher number of avalanche seed particles from unstable nuclei thancosmic ray shower background yield for the comparable energy range, hence, http://phits.jaea.go.jp/expacs/ .25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Energy (MeV)10 Sp e c t r a ( M e V s ) Seed source ± from CRS at 0.1 km ± from CRS at 4.0 km + from N initially + from O initially + from N after 5 min + from O after 5 min Figure 5: Cosmic-ray secondary spectra compared (electrons and positronscombined) with the β + -decay spectrum at different moments. The blue (red)lines regards emissions from N ( O) right after the neutrons generation(solid line) and after five minutes (dashed lines). The black lines are thesummed electron and positron spectra from cosmic ray secondaries at thetime and geographic location of Wada et al. [2019] detections for two differentaltitudes: 100 m (solid line) and 4 km (dashed line).making the β + emitters a viable enhancer of energetic particle flux forminute-scale after the TGF.Although the cosmic-ray secondaries cover a wider energy range than the β -decay, the total rate of particles from the latter is greater than from theformer. Integrating the Figure 5 spectra over the energy, the rate of electronsand positrons from cosmic rays is approximately 1.8 × and 1.8 × persecond at 4 km and 0.1 km altitude respectively while the rate of decayedunstable nuclei is, initially, 3.9 × decayed N and 5.1 × decayed Oper second; after 5 minutes the rates will be 2.1 × decayed N and4.4 × decayed O per second.
During the motion through the air, energetic particles will lose their energydue to stochastic collisions. Thus, there is a need for a constant energy13ain to sustain the avalanche capability of generating gamma-rays. Thedynamic friction implements a minimal value for runaway-causing electricfields of 216 kVm − [Gurevich et al., 1992, Gurevich and Zybin, 2001] whilethe threshold for RREA is approximately 285 kVm − [Dwyer, 2003, Babichet al., 2004b] due to stochastic Coulomb scattering that prevents an optimalenergy gain from the electric field.TGFs are correlated with lightning discharges which will remove chargedregions, from the thundercloud, changing the ambient electric field and pro-moting an abrupt end to high energy radiation [Parks et al., 1981, McCarthyand Parks, 1985, Tsuchiya et al., 2007, Kelley et al., 2015]. Such effect im-poses a challenge for a gamma-ray glow following the TGF although thelatter produce possible avalanche seed particles. Nevertheless, observationsalso show long bursts despite lightning occurrence [Chilingarian et al., 2017]suggesting that not always the discharge will interrupt a long gamma emis-sion; moreover, Chilingarian et al. [2020] reports intermittent TGE thatends with lightning discharge and continuously recover the count rate inminute-scale.The unstable leftovers from neutron-generating photonuclear reactionshave a long duration following the characteristic decay time and will bedistributed over the elongated photon path. These two features allow themto feed the ambient with avalanche seeds while the electric field recoversfrom the lightning discharge and reach different cloud regions that may stillhave a charge configuration. We have shown an extended TGF timescale up to tens of minutes via itsparticles byproducts. Moreover, the possibility of the TGF particle chainproduction results in new RREA that can be sustained to gamma-ray glowsduration. Although the decay emission is isotropic, our simulations displaypositrons are capable of inducing RREA efficiently despite their initial ori-entation regarding the electric field. Due to the β decay nature, long-lastingextra supply of energetic particles is available thus, if the thundercloud elec-tric field recovers in minute-scale after the TGF. There will be a chance fora follow up gamma-ray glow despite the associated lightning charge removal.Such conditions allow HEAP a cyclic nature as they keep producing RREAand there are multiple possible outcomes from it. The need for an electricfield introduces the actual limitation to this chain-reaction process as it islimited both in time and space, i.e., the electric field variations can stop thecycle. This new perspective on HEAP connection explains how a TGF mayprovide a possibility for a gamma-ray glow to take place and even generatethe gamma-ray glow itself depending mostly on the ambient electric fielddynamics since, as it is shown, parallel to the constant cosmic ray. The14GF itself provides a long-lasting supply of avalanche seed particles. Acknowledgement
This work and G.D. is supported by MEXT/JSPS KAKENHI Grant No.19H00683; T.E. and Y.W. are supported by Hakubi Research Project andSpecial Postdoctoral Researcher fellowship program of RIKEN, respectively;I.F. is supported by CAPES. The simulation results are available online(doi: 10.17632/kv3bnscc8b.4). The codes for the simulations presentedhere can be found at the supplementary material of Sarria et al. [2018]:https://gmd.copernicus.org/articles/11/4515/2018/gmd-11-4515-2018.html.We sadly inform the community that our coauthor Dr. Ivan Soares Ferreirapassed away in October. He was an incredible friend, scientist, and pro-fessor. Although not everyone knew him, his decease is a tremendous lossfor all the academic community. The two last songs he sent singing were:”S˜ao Murungar” by Bezerra da Silva, in his profound love for samba; and,ironically, ”My way” popularized in the voice of Frank Sinatra. May Ivanbe always remembered as the great person he was and may we be capableof honor his memory.
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