Observations of the Origin of Downward Terrestrial Gamma-Ray Flashes
J. W. Belz, P. R. Krehbiel, J. Remington, M. A. Stanley, R. U. Abbasi, R. LeVon, W. Rison, D. Rodeheffer, Telescope Array Scientific Collaboration, T. Abu-Zayyad, M. Allen, E. Barcikowski, D. R. Bergman, S. A. Blake, M. Byrne, R. Cady, B. G. Cheon, M. Chikawa, A. di Matteo, T. Fujii, K. Fujita, R. Fujiwara, M. Fukushima, G. Furlich, W. Hanlon, M. Hayashi, Y. Hayashi, N. Hayashida, K. Hibino, K. Honda, D. Ikeda, T. Inadomi, N. Inoue, T. Ishii, H. Ito, D. Ivanov, H. Iwakura, H. M. Jeong, S. Jeong, C. C. H. Jui, K. Kadota, F. Kakimoto, O. Kalashev, K. Kasahara, S. Kasami, H. Kawai, S. Kawakami, K. Kawata, E. Kido, H. B. Kim, J. H. Kim, J. H. Kim, V. Kuzmin, M. Kuznetsov, Y. J. Kwon, K. H. Lee, B. Lubsandorzhiev, J. P. Lundquist, K. Machida, H. Matsumiya, J. N. Matthews, T. Matuyama, R. Mayta, M. Minamino, K. Mukai, I. Myers, S. Nagataki, K. Nakai, R. Nakamura, T. Nakamura, Y. Nakamura, T. Nonaka, H. Oda, S. Ogio, M. Ohnishi, H. Ohoka, Y. Oku, T. Okuda, Y. Omura, M. Ono, A. Oshima, S. Ozawa, I. H. Park, M. Potts, M. S. Pshirkov, D. C. Rodriguez, G. Rubtsov, D. Ryu, H. Sagawa, R. Sahara, K. Saito, Y. Saito, N. Sakaki, T. Sako, N. Sakurai, K. Sano, T. Seki, K. Sekino, F. Shibata, T. Shibata, et al. (40 additional authors not shown)
mmanuscript submitted to
JGR: Atmospheres
Observations of the Origin of Downward TerrestrialGamma-Ray Flashes
J.W. Belz , P.R. Krehbiel , J. Remington , M.A. Stanley , R.U. Abbasi ,R. LeVon , W. Rison , D. Rodeheffer and the Telescope Array Scientific Collaboration T. Abu-Zayyad , M. Allen , E. Barcikowski , D.R. Bergman , S.A. Blake ,M. Byrne , R. Cady , B.G. Cheon , M. Chikawa , A. di Matteo ∗ , T. Fujii ,K. Fujita , R. Fujiwara , M. Fukushima , , G. Furlich , W. Hanlon ,M. Hayashi , Y. Hayashi , N. Hayashida , K. Hibino , K. Honda ,D. Ikeda , T. Inadomi , N. Inoue , T. Ishii , H. Ito , D. Ivanov ,H. Iwakura , H.M. Jeong , S. Jeong , C.C.H. Jui , K. Kadota ,F. Kakimoto , O. Kalashev , K.Kasahara , S. Kasami , H. Kawai ,S. Kawakami , K. Kawata , E. Kido , H.B. Kim , J.H. Kim , J.H. Kim ,V. Kuzmin † , M. Kuznetsov , , Y.J. Kwon , K.H. Lee ,B. Lubsandorzhiev , J.P. Lundquist , K. Machida , H. Matsumiya ,J.N. Matthews , T. Matuyama , R. Mayta , M. Minamino , K. Mukai ,I. Myers , S. Nagataki , K. Nakai , R. Nakamura , T. Nakamura ,Y. Nakamura , T. Nonaka , H. Oda , S. Ogio , , M.Ohnishi , H. Ohoka ,Y. Oku , T. Okuda , Y. Omura , M. Ono , A. Oshima , S. Ozawa ,I.H. Park ,M. Potts , M.S. Pshirkov , , D.C. Rodriguez , G. Rubtsov ,D. Ryu , H. Sagawa , R. Sahara , K. Saito , Y. Saito , N. Sakaki ,T. Sako , N. Sakurai , K. Sano , T. Seki , K. Sekino , F. Shibata ,T. Shibata , H. Shimodaira , B.K. Shin , H.S. Shin , J.D. Smith ,P. Sokolsky , N. Sone , B.T. Stokes , T.A. Stroman , Y. Takagi ,Y. Takahashi , M. Takeda , R. Takeishi , A. Taketa , M. Takita ,Y. Tameda , K. Tanaka , M. Tanaka , Y. Tanoue , S.B. Thomas ,G.B. Thomson , P. Tinyakov , , I. Tkachev , H. Tokuno , T. Tomida ,S. Troitsky , Y. Tsunesada , , Y. Uchihori , S. Udo , T. Uehama ,F. Urban , M. Wallace , T. Wong , M. Yamamoto , H. Yamaoka ,K. Yamazaki , K. Yashiro , M. Yosei , H. Yoshii , Y. Zhezher , ,Z. Zundel Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, USA Langmuir Laboratory for Atmospheric Research, New Mexico Institute of Mining and Technology,Socorro, NM, USA Department of Physics, Loyola University Chicago, Chicago, Illinois, USA The Graduate School of Science and Engineering, Saitama University, Saitama, Saitama, Japan Graduate School of Science and Engineering, Tokyo Institute of Technology, Meguro, Tokyo, Japan Department of Physics and The Research Institute of Natural Science, Hanyang University,Seongdong-gu, Seoul, Korea Department of Physics, Tokyo University of Science, Noda, Chiba, Japan Department of Physics, Kindai University, Higashi Osaka, Osaka, Japan Service de Physique Th´eorique, Universit´e Libre de Bruxelles, Brussels, Belgium The Hakubi Center for Advanced Research, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku,Kyoto, Japan Graduate School of Science, Osaka City University, Osaka, Osaka, Japan Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa,Chiba, Japan Information Engineering Graduate School of Science and Technology, Shinshu University, Nagano,Nagano, Japan Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, Japan Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, Kofu,Yamanashi, Japan Earthquake Research Institute, University of Tokyo, Bunkyo-ku, Tokyo, Japan Academic Assembly School of Science and Technology Institute of Engineering, Shinshu University,Nagano, Nagano, Japan Astrophysical Big Bang Laboratory, RIKEN, Wako, Saitama, Japan Department of Physics, Sungkyunkwan University, Jang-an-gu, Suwon, Korea –1– a r X i v : . [ phy s i c s . a o - ph ] O c t anuscript submitted to JGR: Atmospheres Department of Physics, Tokyo City University, Setagaya-ku, Tokyo, Japan Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo,Japan Department of Engineering Science, Faculty of Engineering, Osaka Electro-Communication University,Neyagawa-shi, Osaka, Japan Department of Physics, Chiba University, Chiba, Chiba, Japan Department of Physics, Yonsei University, Seodaemun-gu, Seoul, Korea Faculty of Science, Kochi University, Kochi, Kochi, Japan Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka City University, Osaka,Osaka, Japan Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga, Japan Sternberg Astronomical Institute, Moscow M.V. Lomonosov State University, Moscow, Russia Department of Physics, Ulsan National Institute of Science and Technology, UNIST-gil, Ulsan, Korea Graduate School of Information Sciences, Hiroshima City University, Hiroshima, Hiroshima, Japan Institute of Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki, Japan National Institute of Radiological Science, Chiba, Chiba, Japan CEICO, Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic Engineering Science Laboratory, Chubu University, Kasugai, Japan Department of Physics, Ehime University, Matsuyama, Ehime, Japan
Key Points: • Downward Terrestrial Gamma-ray Flashes occur during strong initial breakdownpulses of negative cloud-to-ground and cloud lightning. • The initial breakdown pulses consist of streamer-based fast negative breakdownhaving transient sub-pulse conducting events, or ‘sparks’. • The streamer to leader transition of negative stepping occurs during strong cur-rents in the final stage of initial breakdown pulses. ∗ Currently at INFN, sezione di Torino, Turin, Italy † Deceased
Corresponding author: Jackson Remington, [email protected] –2–anuscript submitted to
JGR: Atmospheres
Abstract
In this paper we report the first close, high-resolution observations of downward-directedterrestrial gamma-ray flashes (TGFs) detected by the large-area Telescope Array cos-mic ray observatory, obtained in conjunction with broadband VHF interferometer andfast electric field change measurements of the parent discharge. The results show thatthe TGFs occur during strong initial breakdown pulses (IBPs) in the first few millisec-onds of negative cloud-to-ground and low-altitude intracloud flashes, and that the IBPsare produced by a newly-identified streamer-based discharge process called fast negativebreakdown. The observations indicate the relativistic runaway electron avalanches (RREAs)responsible for producing the TGFs are initiated by embedded spark-like transient con-ducting events (TCEs) within the fast streamer system, and potentially also by individ-ual fast streamers themselves. The TCEs are inferred to be the cause of impulsive sub-pulses that are characteristic features of classic IBP sferics. Additional development ofthe avalanches would be facilitated by the enhanced electric field ahead of the advanc-ing front of the fast negative breakdown. In addition to showing the nature of IBPs andtheir enigmatic sub-pulses, the observations also provide a possible explanation for theunsolved question of how the streamer to leader transition occurs during the initial neg-ative breakdown, namely as a result of strong currents flowing in the final stage of suc-cessive IBPs, extending backward through both the IBP itself and the negative streamerbreakdown preceding the IBP.
The interplay between lightning and high-energy particle physics was realized overtwo decades ago with the serendipitous observation of gamma radiation emanating fromthe Earth. The BATSE (Burst and Transient Source Experiment) instrument aboardNASA’s Compton Gamma-Ray Observatory was designed to detect radiation from GammaRay Bursts (GRBs), deep-space events which are considered the most intense sourcesof electromagnetic radiation in the Universe. In 1994, BATSE unexpectedly recorded aseries of brief, intense flashes of gamma rays, which appeared to originate at high alti-tudes ( ≥
15 km above ground level) above thunderstorm regions (Carlson et al., 2007;Fishman et al., 1994). The terrestrial gamma-ray flashes (TGFs) lasted from hundredsof microseconds up to a millisecond or more, and their energy spectrum was consistentwith bremsstrahlung emission from electrons with energies of several million electron volts(MeV) or greater.Subsequent observations, now numbering in the thousands of events, aboard theRamaty High Energy Solar Spectroscopic Imager (RHESSI) satellite (Gjesteland et al.,2012; Grefenstette et al., 2009), NASA’s Fermi Gamma-ray Space Telescope (Briggs etal., 2013; Foley et al., 2014; Roberts et al., 2017), and the Astrorivelatore Gamma a Im-magini Leggero (AGILE) satellite (Marisaldi et al., 2014) have shown that, instead ofbeing produced at high altitude above storms, the TGFs originate at lower altitudes com-mensurate with being inside storms. In particular, it has been shown that the TGFs areproduced at the altitudes of intracloud (IC) lightning flashes, during upward negativebreakdown at the beginning of the flashes (Cummer et al., 2011, 2015; Lu et al., 2010;Lyu et al., 2016; Mailyan et al., 2016; Shao et al., 2010; Stanley et al., 2006). The earlyRHESSI observations were found to be associated with millisecond-duration initial break-down activity that occurs in the beginning stages of IC flashes. However, a direct con-nection with the initial breakdown events was uncertain due to a 1-3 ms timing uncer-tainty in the RHESSI data (Lu et al., 2011).In recent years, a small subset of TGFs has been associated with high-peak cur-rent (few hundred kiloampere) IC discharge events, called energetic in-cloud pulses (EIPs) (Lyuet al., 2015). EIPs are energetic versions of what are called preliminary or initial break-down pulses (Marshall et al., 2013), that are characteristic features of the beginning stages –3–anuscript submitted to
JGR: Atmospheres of IC and negative cloud-to-ground ( − CG) flashes. The EIP studies have utilized datafrom the Gamma-ray Burst Monitor (GBM) on Fermi (Briggs et al., 2010), which de-tects individual photons with microsecond timing accuracy, allowing more accurate cor-relation with ground-based low frequency (LF) radio atmospheric or “sferic” observa-tions. Although EIPs are infrequent and the number of documented cases is small (a dozenor so), TGFs have been detected for 100% of EIPs that occurred within view of the Fermisatellite and within range of ground-based sferic sensors. As a result of this predictabil-ity, EIPs are considered to be high-probability producers of at least a class of TGF-generatinglightning events (Cummer et al., 2017; Lyu et al., 2016, 2018). However, the detailed dis-charge processes that produce EIPs has not been understood, due to the lack of mea-surements of the parent flashes with ground-based instrumentation (such observationsof a close EIP by Tilles (2020), reported while this paper was in review, provides the firstdetailed information on the discharge processes and storm environment that led to itsoccurrence, as discussed later).As satellite-based observations of upward TGFs have accumulated, the questionhas been whether lightning produces downward TGFs that could be detected on the groundbelow or near thunderstorms. In particular, negative-polarity cloud-to-ground ( − CG)discharges begin with downward negative breakdown that would be expected to produceTGFs directed earthward. Until recently, only a few TGFs had been detected at groundlevel in association with overhead lightning. Instead of being produced in the early stagesof natural lightning, however, the gamma rays occurred either during the upward ascentof artificial trailing-wire, rocket-triggered lightning discharges (Dwyer, 2004; Hare et al.,2016), or at a later time in natural flashes, following high-current return strokes of − CGdischarges (Dwyer et al., 2012; Ringuette et al., 2013; Tran et al., 2015). Also, a partic-ularly strong downward TGF was recently reported during a winter thunderstorm by Wadaet al. (2019) at the time of lightning discharge in the storm that appeared to be producedat low altitude ( ’
400 m) above ground. Otherwise, significant impediments to detect-ing downward TGFs have been a) the increasingly strong attenuation of gamma radi-ation at low altitudes in the atmosphere, and b) the ground-based detectors being ei-ther too far below and/or not widespread enough to detect the forward-beamed radia-tion. Both issues have been addressed with observations from the large-area (700 km )Telescope Array Surface Detector (TASD) cosmic ray facility in central Utah.In data collected between 2008 and 2013 there were ten occasions in which the TASDwas triggered by multiple bursts of energetic particles — not arising from cosmic rays.The events occurred within a millisecond of being detected by the U.S. National Light-ning Detection Network (NLDN) (Abbasi et al., 2017), which identified them as beingproduced during − CG flashes. Follow-up observations with the TASD by the authorsof the present study, obtained between 2014 and 2016 in coordination with a 3-D light-ning mapping array (LMA) and a lightning electric field change sensor, detected ten ad-ditional events, each consisting of three to five lightning-initiated bursts (Abbasi et al.,2018). The bursts were typically ’ µ s or less in duration, and occurred over severalhundred µ s time intervals during the first millisecond of downward negative breakdownat the beginning of − CG flashes. Scintillator responses and simulation studies showedthat the bursts primarily resulted from gamma radiation and collectively comprised low-fluence TGFs. The LMA observations showed the bursts coincided with impulsive in-cloud VHF radiation events during energetic downward negative breakdown, 3-4 km aboveground level. Although the TASD and LMA observations had sub-microsecond time res-olution, the electric field change measurements recorded only the relatively slow electro-static field change, with insufficient bandwidth to detect the faster electric field changesof the initial breakdown activity.Here we report observations of downward TGFs produced by four additional flashes(three –CGs and one low-altitude IC flash) obtained in 2018 during continued studieswith the Telescope Array. For this study, the TASD and LMA observations were aug- –4–anuscript submitted to
JGR: Atmospheres mented with crucially important, high-resolution VHF interferometric and fast electricfield change measurements of the parent lightning discharges, obtained in relatively closeproximity (16–24 km) to the TGFs. Coupled with sub-microsecond TGF measurementsat TASD stations immediately below and near the flashes, the observations documentthe TGF occurrence with a high degree of temporal and spatial resolution not availablebefore now. In each of the four flashes, the TGFs show a clear correspondence with down-ward negative breakdown during strong initial breakdown pulse (IBP) events in the firstmillisecond or so of the flashes. The negative breakdown progresses at a fast average speed( ’ × m/s), indicative of a newly-recognized type of discharge process called fastnegative breakdown (FNB) (Tilles et al., 2019). Such breakdown is the negative analogof fast positive breakdown found in an earlier study to be the cause of high-power dis-charges called narrow bipolar events (NBEs) (Rison et al., 2016).For both polarities, the breakdown is produced by a propagating system of stream-ers that substantially enhance (up to 50% or more) the electric field ahead of the stream-ers’ advancing front (Attanasio et al., 2019). For the negative polarity version, electronavalanches produced within the streamer system would propagate through and aheadof the advancing front, producing downward-directed gamma radiation. Detailed anal-ysis of the observations indicate that the TGFs are often initiated at the time of char-acteristic “sub-pulses” that occur during large-amplitude, ‘classic’ sferics. From this, weinfer that the sub-pulses are produced by transient spark-like discharges embedded withinthe negative streamer system, the conducting tips of which would initiate relativistic elec-tron avalanches, whose further development is facilitated by the enhanced E field aheadof and beyond the streamer front. In other instances, TGFs appear to be initiated dur-ing brief episodes of accelerated-speed FNB.Although obtained for downward negative breakdown of –CG flashes, the resultsare expected to apply equally well to negative breakdown at the beginning of upwardIC flashes, for which the initial breakdown pulse activity is fundamentally the same asfor downward CG flashes. Together, the results establish that downward TGFs of –CGflashes and satellite-detected upward TGFs of IC flashes are variants of the same phe-nomenon, and are produced during fast negative breakdown early in the developing neg-ative leader stage of CG and IC flashes. Figure 1 shows the layout of the Telescope Array Surface Detector (TASD) and theLightning Mapping Array (LMA) used in both the earlier and present studies. The VHFinterferometer (INTF) and fast electric field change antenna (FA) were located 6 km eastof the TASD, and utilized three receiving antennas with 106–121 m baselines orientedto maximize angular resolution over the TASD (see Methods Appendix A1).On August 2, 2018, two small, localized storms occurred over the TASD that pro-duced three TGFs relatively close (17 km) to the INTF. The first TGF-producing dis-charge occurred at 14:17:20 UT and was a − CG flash that generated two TASD trig-gers ’ ’ ’ ’ × m/s, somewhat faster than the nor-mal stepped leader speeds of 1–2 × m/s. The two triggers recorded three gamma-raybursts, jointly called TGF A, when the breakdown was at ’ –5–anuscript submitted to JGR: Atmospheres . . ACB D a b
Figure 1.
Telescope Array Surface Detector. ( a ) View of a close and distant surface detec-tor stations on the desert plain west of Delta, Utah. Each detector unit consists of two 3 m by 1.2 cm thick scintillator planes separated by a 0.1 cm steel sheet (Abu-Zayyad et al., 2013).Photo by M. Fukushima. ( b ) Map of the TASD stations, showing the locations of TGFs A–D(dashed ellipses). A total of 512 surface detectors have been deployed over a 700 km area on a1.2 km grid since 2008. A nine-station 3-D lightning mapping array (LMA) has been operated atthe TASD since 2013 (blue dots). In July 2018, a VHF interferometer (INTF) and fast electricfield sferic sensor (FA) were deployed 6 km east of the TASD, only a few days prior to observingthe TGFs reported here. –6–anuscript submitted to JGR: Atmospheres
Figure 2.
TASD observations of TGF A.
Top left and right : Surface scintillator “footprints”for the three gamma-ray showers of TGF A. The grid spacing is in units of 1.2 km. The areaof each circle is proportional to the logarithm of the energy deposit, and color indicates timingin 4 µ s steps relative to the event trigger, corresponding to the approximate onset time of thegamma events at the ground. The yellow star shows the LMA-estimated plan location of theTGF, and is in close agreement with the location of its sferic by the National Lightning Detec-tor Network (NLDN, underlying magenta diamond) making it difficult to distinguish betweenthe two. The red lines denote the boundary of the TASD array, showing that a portion of bothshowers was likely undetected. Bottom left and right : Scintillator responses of the surface de-tector stations having the largest energy deposit during each of the gamma-ray showers. Theupper scintillator is represented by black traces and the lower scintillator by red traces. A singleVertical Equivalent Muon (VEM), or about 2 MeV of energy deposit, corresponds roughly to apulse 30 ADC counts above background with 100 ns FWHM on these plots. The horizontal timeaxes are relative to the detectors’ individual triggers (different from the overall ‘event’ trigger, seeAppendix A1). –7–anuscript submitted to
JGR: Atmospheres
Figure 3.
INTF and FA observations of TGF A. Panels show interferometer elevation ver-sus time (circled dots, sized and colored by power), fast electric field sferic waveform (greenwaveform) and TASD particle surface detections (vertical purple bars).
Top:
Observations frominitial breakdown through time of –38.3 kA initial cloud-to-ground stroke. Initial TGF detec-tion occurred in coincidence with the strongest (–36.7 kA) sferic pulse, 326 µ s after flash start(Supporting Table S1). Middle: µ s of observations around the time of the three gamma-rayshowers of the flash, showing their correlation with the two largest amplitude initial breakdownpulses (IBPs) and episodes of fast downward negative breakdown (FNB). TASD footprints for theshowers are shown in Figure 2. Bottom:
Detailed 40 µ s view of the upper and lower scintillatorresponses (blue and orange traces) relative to the IBP sferic and the downward FNB.–8–anuscript submitted to JGR: Atmospheres
Figure 2 shows “footprints” of the TA surface detections for each of the two trig-gered events, along with the corresponding set of scintillator observations at a centralSD station. The triggers occurred within ’ µ s of each other, in the southeastern cor-ner of the TASD. The observations are similar to those reported in our previous study (Abbasiet al., 2018), in that they consisted of gamma bursts typically 10 µ s or less in durationand were detected at 9–12 adjacent SDs, over areas ’ ’ −
38 kA) IBPsferic, comparable in magnitude to the sferic of the ensuing return stroke, which had anNLDN-detected peak current of −
37 kA. The second TGF was less strong (192 total VEM,or 393 MeV) and was associated with the next-strongest IBP sferic (middle panel). Bothgamma bursts were associated with episodes of accelerated downward negative break-down.The bottom panel of Figure 3 shows in detail how the initial gamma burst was re-lated to the VHF radiation and sferic waveform, during a 40 µ s window around the timeof the burst. From the INTF elevation angles and the LMA-indicated 17 km plan dis-tance to the source location, the VHF radiation sources descended ’
150 m in 10 µ s, cor-responding to an average propagation speed v ’ . × m/s. By coincidence, thisis the same as the extent and speed of the upward fast positive NBE breakdown at thebeginning of the flash (also ’
150 m in 10 µ s), and is indicative of the downward activ-ity being caused by analogous fast negative breakdown (FNB) (Tilles et al., 2019). Thegamma burst occurred partway through the fast downward breakdown, ’ µ s afterthe peak of the negative sferic, and continued for about 5 µ s before dying out shortlyafter the end of the FNB. Figure 4 shows observations of the strongest gamma-ray event for each of the TGF-producing flashes, along with time-shifted scintillator detections for each participatingTASD station. The vertical line for each flash serves as a reference time for comparingthe different SD waveforms with each other and with the INTF/FA. As described be-low, it corresponds to the median onset time at the different SD stations. Similarly, thehorizontal line indicates the elevation angle corresponding to the median source altitudeimmediately around that time. –9–anuscript submitted to
JGR: Atmospheres
Figure 4.
Detailed comparative observations. Time-shifted surface detector data for the pri-mary gamma-ray event during each of the four TGF-producing flashes, showing how the TASDdetections (lower axes) compare to each other, and their relation to the VHF radiation sourcesand fast electric field sferics (upper axis) of the developing discharges. Black vertical and horizon-tal lines in each panel show the median onset time of the gamma burst(s) during the downwardFNB, obtained from analysis of the collective onset times t b at the different TASD stations andthe observed INTF elevation angle vs. time (see Section 2.2). Light blue traces show the VHFtime series waveform observed by the INTF. Station numbers XXYY in the lower axes identifyeach TASD’s easterly (XX) and northerly (YY) location within the array in 1.2 km grid spacingunits. FNB propagation speeds are indicated by the dashed lines and associated values. Full-pageversions of these plots are given as Figs. S15–S18. in the Supporting Information–10–anuscript submitted to JGR: Atmospheres
The coordinate system for comparing the TASD observations with the INTF andFA data is shown in Figure A1a of the Appendix. It is a source-centric system in whichthe plan position on the ground beneath the TGF serves as the coordinate origin. Toshift the scintillator detection times, we need to know the slant ranges r and R from theTGF source to the SD and from the source to the INTF. The x, y plan location of thesource is obtained from the LMA observations within ± D and d to the INTF and to each TASD station. The TGF istherefore at point a = [0,0, z a ] in the coordinate system, where z a is the altitude of thesource above a reference plane of 1400 m MSL. A generic TASD station is at point b , typ-ically within ’ c , typically15–25 km plan distance from the TGFs. The net time shift ∆ t between the surface de-tector data at a given TASD station and the INTF is given by the difference in prop-agation delays. In particular, ∆ t = ( R/c ) − ( r/c ) = ( R − r ) /c . Because the plan dis-tances are known, the slant ranges and hence time shifts ∆ t are functions only of z a . Once z a is determined, the time shifts are calculated for each TASD individually and used tocompare the different TASD waveforms a) with each other, and b) with the FA sferic andthe VHF source activity and centroid observations, as seen in Figure 4. For each TASDstation, the onset time at the INTF is given by t c = t b +∆ t , where t b is the onset timeat the TASD in question. As mentioned above, the vertical line in Figure 4 correspondsto the median of the onset times at the different stations. At the same time it also servesas a reference point for identifying stations having onset times that differ from the me-dian value.Because the LMA typically mislocates non-impulsive, VHF-noisy sources, the TGF’saltitude is determined from the INTF elevation angles θ c . The difficulty with doing thisis that the angle changes with time during the IBP, namely θ c = θ c ( t c ), making it un-clear which time to pick. Even though the elevation change corresponds only to a ’ µ s duration of theVHF and FA sferic observations. The ambiguity is resolved by recognizing that two in-dependent measurements are necessary to determine the two unknowns, namely the sourcealtitude z a and time t a . In addition to the INTF elevation angle θ c , the second measure-ment comes from onset time t b at the particular TASD in question. Although this pro-vides enough information to obtain the solution, the different variables of the problem,namely [ θ c , t c , z a , t a ], wind up depending upon each other, requiring an iterative approachto obtain the solution.Figure S14 shows a block diagram of the iteration process. For each TASD the on-set time t b is used along with an initial value of z a to determine the corresponding on-set time t c at the INTF. The INTF data relating t c and θ c is then used to determine thecorresponding source altitude z a and time t a . If the resulting z a is different from the ini-tially assumed value, the new value is used as the starting altitude for the next step. Theiteration is stable and convergence is reached within a couple of steps. The process isrepeated for each of the participating TASDs to obtain a set of z a , t a , t c , and θ c values,from which the median is determined. Table S2 lists the full set of solutions for each TASDof the different TGFs. The median t c and θ c values are shown in bold and correspondto the vertical and horizontal lines in Figure 4. For TGFs A, C and D, the participat-ing TASDs all have similar onset times. The exception is TGF B, which has two or moreonset times, as discussed in the next section. An analogous but somewhat different methodof time-shifting and comparing the TASD and INTF/FA observations, developed inde-pendently during the course of the study, is described in Appendix A2 and shown in theSupporting Figures. The approach utilized measurements at two TASD stations havingthe strongest detections to determine the time shifts for the other TASDs and alignmentwith the INTF/FA observations, and provided an alternative way of investigating theobservations. –11–anuscript submitted to JGR: Atmospheres
The above analyses provide accurately-determined estimates of i) each TGF’s planlocation x a , y a , altitude z a , and time t a , ii) the onset times t c of the gamma events dur-ing the IBP, and iii) the INTF elevation angle θ c corresponding to t c and z a . The t c and θ c values are shown by the vertical and horizontal lines in each of the panels of Figure 4.We re-emphasize the fact that the t c values serve as reference times for comparing thedifferent TASD detections with each other. For TGFs A, C, and D, most or all of thestations detected the onset at the same time. The onset times are well-identified by theanalysis technique and are indicative of the TGFs in question all having a single onset.An important exception is TGF B, for which TASD 1421 had a noticeably earlier on-set time. Three other stations (1519, 1419, and 1320) appeared to have slightly delayedonsets. As discussed below, the different apparent onsets are notable because the foot-print of the stations involved were systematically displaced in a fully 360 degree circu-lar pattern around a central hole. The observations are also illustrative of the compar-isons being able to identify multiple onset times.For each of the four flashes, the gamma bursts were associated with well-definedepisodes of downward-propagating fast negative breakdown. The average propagationspeeds during the episodes ranged from ’ × m/s (slanted dashed lines ineach panel of Figure 4). This is compared to average speeds of ’ × m/s forthe breakdown immediately preceding the IBPs and TGFs (Figure 3 and Supporting Fig-ures S7–S9). The sferics associated with the TGFs constituted the strongest initial break-down pulses of the flashes. Whereas the onset time of the gamma burst of TGF A (Fig-ure 4a) occurred slightly after the main peak of the IBP sferic, the bursts during otherflashes occurred during or at various times prior to the peak. For TGF C, the onset wasat or shortly after the beginning of the IBP and FNB, while for TGF B, the primary on-set was closely correlated with the main IBP peak. For TGF D, the onset appeared tobe exclusively correlated with a strong, leading-edge sub-pulse during the IBP’s FNB.IBPs having such sub-pulses are called “classic” IBPs (Karunarathne et al., 2014; Mar-shall et al., 2013; Nag et al., 2009; D. Shi et al., 2019). The sub-pulse feature of the pre-liminary breakdown has long been recognized, beginning with Weidman and Krider (1979),but the cause both of IBPs and their sub-pulses has remained unknown. The present re-sults show that the IBPs are produced by fast negative breakdown, and that the sub-pulses are capable of initiating gamma bursts.For TGF A at 14:17:20 (Figures 4a and 5a), the scintillator detections in Figure 3are from TASD 2308, corresponding to the station having the most energetic footprint.However, the estimated plan location of the burst from the LMA observations, as wellas the NLDN location for the sferic associated with the burst, indicate the breakdownwas almost directly above TASD 2307, 1.2 km to the south and 17 km southwest of theINTF (Supp. Figs. S1 and S10e). The energy deposit in TASD 2307 was slightly weakerthan that in 2308 (145 vs. 230 VEM), indicating that the gamma burst was tilted slightlynorthward from vertical. A significant feature of the observations in Figure 4a is thatthe apparent onset time of the burst coincided with a step discontinuity in the VHF el-evation centroid values. We later show (Figure A1b) that the discontinuity was due toa brief interval of enhanced propagation speed, in which the FNB descended ’
50 m in1.5 µ s, corresponding to a speed v ’ × m/s, two times faster than the averagespeed of the IBP’s FNB. Observations of the second set of gamma bursts during the flashshows them to be similarly associated with brief episodes of enhanced fast breakdownspeeds ( ’ . × and 4 . × m/s; Supp. Fig. S10d,g). –12–anuscript submitted to JGR: Atmospheres
Figure 5.
INTF observations of the TGF-producing flashes. Azimuth-elevation plots of INTFobservations for the parent flashes of TGFs A–D, showing the initial downward developmentleading to the TGF occurrences (dark red sources and a,b labels, indicating the TGF altitudes).Continuation of VHF activity is shown up to the time of the initial stroke to ground for –CGflashes A,B,C, and for a comparable time during the low-altitude intracloud flash of TGF D.Dashed lines indicate the directions of the FNB associated with each TGF, and the inferredpossible beaming direction. Baseline circles indicate detected TGF strength (VEM counts) andazimuthal directions of participating TASDs. Dotted line pairs indicate maximum angular spread(labelled ‘Cnt Extent’) of the SD detections, as viewed in the transverse plane from the INTFsite. Vertical/horizontal aspect ratios are adjusted to show true angular extent. TGF B appearedto have multiple onset times at the different TASDs, and therefore narrower beaming than in-dicated by the overall angular extent. Baseline symbols show NLDN locations of CG and ICevents. Full page versions of each panel are given in Figures S19-S22 of the Supporting Informa-tion –13–anuscript submitted to
JGR: Atmospheres
TGFs B and C (Figures 4b,c and 5b,c) occurred in a later storm over the north-central part of the TASD, but at the same plan distances (16–17 km) from the INTF.Both were relatively weak in comparison with TGF A, with total surface detections of112 and 212 VEM, respectively (Supp. Table S1 and Figs. S2 and S3). The parent flashof TGF B was similar to that of TGF A in terms of its initiation altitude ( ’ . × m/s). The gamma bursts began 0.65 msafter flash start, again during the strongest initial breakdown pulse of the flash, whosepeak current was as strong as that of TGF A (–30 kA). However, instead of the SD wave-forms having a common onset time, as for TGF A, the onset times varied noticeably atdifferent sets of TASDs. In addition, the overall footprint of the TGF was annular-shapedaround a central hole (Supp. Fig. S2). The LMA and NLDN observations indicate theburst’s source was over the western side of the footprint, adjacent to the hole. The ini-tial burst was detected only at a single station, SD 1421 immediately northeast of thesource. The primary onset occurred 2–3 µ s later, and was detected at four adjacent sta-tions 2–3 km to the east on the opposite side of the hole (SDs 1521, 1520, and 1621, 1620).This was followed by the two southern stations having an additionally delayed onset (SDs1519 and 1419), and finally a fourth onset back at the western-most station, almost di-rectly below the source (SD 1720).Concerning the correlation with the INTF and FA data for TGF B, the early gamma-ray detection at TASD 1421 coincided with a prominent sub-pulse of the IBP, and rep-resents a separate onset time. The sub-pulse occurred during an apparently brief inter-lude of upward rather than downward development of the VHF radiation sources. Sub-sequently, the gamma-ray activity occurred during downward fast negative breakdownhaving a propagation speed of 2 . × m/s, with the primary onset time coincidingwith the main sferic peak. Less than a microsecond after the peak, the elevation cen-troids exhibited a 20–30 m step discontinuity similar to that seen during TGF A, whichappeared to initiate the bursts detected at the southern TASDs.The parent flash of TGF C occurred 2.5 minutes later in essentially the same lo-cation as TGF B, and produced two gamma bursts 117 µ s apart in time, similar to TGF A.In contrast with TGF B, both bursts were relatively simple and provide canonical ex-amples of the basic processes of TGF production. For each event the gamma radiationwas downward-directed and detected immediately below and north of the source (Supp.Figs. S3 and S12). The first event was weaker and produced a total of 35 VEM (72 MeV)at four adjacent TASDs below the source. Figure 4c focuses on the second event, whichwas stronger and produced a total of 212 VEM (434 MeV) at nine adjacent stations be-low the source. As seen in Figures 4c and S12d, the parent IBP was temporally isolatedfrom preceding and subsequent activity, and a sudden increase of the VHF radiation sig-naled the onset of downward negative breakdown and the IBP sferic. The breakdowndescended ’
120 m in 4.7 µ s at a steady rate 2 . × m/s, indicative of FNB. In thissimple case, the gamma radiation began immediately after the start of the FNB and con-tinued with varying but generally increasing intensity through the entire descent untilthe breakdown ceased. In the process, several unresolved sub-pulses occurred, similarto the sub-pulses of TGF A. Also seen in other IBPs but more clearly shown in this flash,onset of the FNB was immediately preceded by brief upward-developing VHF sources,indicative of characteristic FPB breakdown that appeared to trigger the downward FNB.TGF D (Figures 4d and 5d) occurred during a nocturnal storm on October 3 ina similar southward direction as TGF A, but further to the south at 24 km plan distanceover the southeastern corner of the TASD (Supp. Fig. S4 and S13). Again, the flash pro-duced two triggers, the first of which contained three weak gamma bursts that were par-tially outside the southern boundary. The second trigger and burst occurred 140 µ s later, ’ µ s after the flash start. Its footprint was shifted about 2 km northward from thatof the first burst, placing it entirely inside the TASD. The apparent source of the burstswas on the eastern part of the overlapping region between the two footprints (Supp. Fig. –14–anuscript submitted to JGR: Atmospheres
S13e). The first burst was therefore beamed southwestward from its source and the sec-ond burst was beamed northwestward. The westward component of the beaming is clearlyevident in the INTF observations of Figure 5, which showed an increasingly strong WNW-ward tilt of the azimuthal locations as the breakdown descended, with the tilt angle be-coming as large as 45 ◦ from vertical by the time of the gamma burst. A total of 440 VEM(962 MeV) was detected at 12 stations during the second burst, compared to a partialtotal of 100 VEM (205 MeV) at 9 stations during the first burst.Concerning the second trigger and main burst of TGF D, the IBP of the burst hada complex, relatively long-duration (15 µ s) sferic waveform that was accompanied by steadydownward development of the VHF radiation sources. Overall, the breakdown descended ’
240 m in 13.4 µ s at an average rate of 1 . × m/s. The gamma burst was initiatedpartway through the descent, coincident with a major sub-pulse and the onset of increasedVHF radiation. The sequence of events is similar to that of TGF C in that the radia-tion increase and corresponding sub-pulse was preceded by a brief interval of fast up-ward positive breakdown. The ensuing fast downward activity exhibited a small step dis-continuity in the VHF centroids that coincided with the onset of the gamma burst andsub-pulse. As in each of the other TGF flashes, the gamma radiation continued up un-til the approximate end of the FNB, shortly after the main negative peak of the IBP sferic. The results of this study demonstrate that TGFs are produced during strong ini-tial breakdown pulses (IBPs) in the beginning stages of negative-polarity breakdown. Thisis shown with a high degree of temporal and spatial resolution provided by a unique com-bination of a state-of-the-art cosmic-ray facility, coupled with high-quality VHF and LFsferic observations of the parent lightning discharges. In addition to showing how TGFsare related to IBPs, the observations reveal how the initial breakdown pulses themselvesare produced, which has remained unknown for over 50 years. In particular, IBPs areproduced by a recently-identified type of discharge process called fast negative break-down (FNB) (Tilles et al., 2019). FNB is the negative-polarity analog of fast positivebreakdown that has been identified as the cause of high-power narrow bipolar events (NBEs),and which is instrumental in initiating lightning (Rison et al., 2016). Both polarities offast breakdown propagate at speeds around 1/10 the speed of light, with FPB sometimesreaching (1 / c . FPB is understood to be produced by a system of propagating positivestreamers that, when occurring at the beginning of a flash, is initiated by corona fromice hydrometeors in a locally strong electric field region inside storms (Rison et al. (2016);Attanasio et al. (2019)).Although the nature of fast negative breakdown is uncertain (Tilles et al., 2019),its similarities with FPB strongly suggest that FNB is also streamer-based, except forbeing of negative polarity. Independent of polarity or direction, both positive and neg-ative fast streamer systems would significantly enhance the ambient electric field aheadof their advancing front (Attanasio et al., 2019), facilitating the development of high en-ergy electron avalanches necessary for gamma-ray production.Owing to its simplicity, TGF C provides a canonical example of the basic processesinvolved during an IBP. In particular, the IBP of TGF C was initiated by a brief (1–2 µ s)interval of fast upward positive breakdown, immediately followed by a sudden increasein the VHF radiation and the onset of oppositely-directed downward FNB (Figures 4cand S8). The positive breakdown began slightly beyond the lowest extent of the preced-ing negative breakdown and propagated weakly but rapidly back into preceding activ-ity, whereupon it initiated oppositely-directed and VHF-strong FNB back down and be-yond the path of the upward FPB, extending the negative breakdown to lower altitude –15–anuscript submitted to JGR: Atmospheres (see also Fig. S12d,g). Similar sequences of upward positive/downward negative break-down were associated with TGF-producing IBPs of the other flashes, including a pre-ceding, weaker gamma-ray event of TGF C (Fig. S12c,f).The TGF observations show that the onset of the electron avalanching and gamma-ray production occurred at various stages during the IBPs. For TGF A, the onset oc-curred after the sferic peak, but during still-continuing FNB. TGF C occurred at or shortlyafter the beginning of its IBP and FNB onset. For the more complex discharges of TGFs Band D, the onset was often associated with leading-edge sub-pulses that are a charac-teristic feature of classic IBPs (Weidman & Krider, 1979; Nag et al., 2009; Karunarathneet al., 2014). Like IBPs, the nature and cause of sub-pulses has continued to be a mys-tery (e.g., da Silva and Pasko (2015); Stolzenburg et al. (2016)). The results of the presentstudy show that the main driving force of the IBPs is fast negative breakdown, whichhas the sub-pulses as embedded components. Basically, the sub-pulses are indicative ofrepeated breakdown events within the developing IBP discharge. The observation thatTGFs are often associated with sub-pulses, and that this occurs during fast negative streamerbreakdown, provides a possible explanation for the sub-pulses’ occurrence. Namely, thatthey are produced by spark-like transient conducting events (TCEs) embedded withinthe negative streamer system. That the events are spark-like is indicated by the pointed,cusp-like nature of their sferics, evidence of a sudden current onset and rapid turnoff,and also by the sub-pulses repeating several times as the IBP progresses. It should benoted that the final peak of the overall IBP sferic is also cusp-like, indicating that it toois produced by a spark-like sub-pulse.Once initiated, the gamma radiation typically lasts ’ µ s for the flashes of thisstudy. GEANT4 simulations presented in Figure S24 of the Supporting Information showthat multipath Compton scattering does not artificially extend the duration, as 95% ofdetectable particles produced by 10 MeV (100 MeV) photons at 3 km AGL will arrivewithin 20 ns (60 ns). The total energy available for deposit after the first 100 ns is smallenough to be indistinguishable from background levels, thus the observed durations re-flect the intrinsic duration of the sources. An important implication of this result is thatrelativistic avalanching lasting 3–5 µ s would propagate a distance of ’ ’ × V/m) (Dwyer,2003).Before proceeding, we emphasize the fact that the TASD is detecting multi-MeVgamma radiation from the lightning discharges, and not lower energy x -radiation. Werepeat here the simple arguments for this, presented by Abbasi et al. (2018) and basedon the well-understood physics of Compton electron production and the well-calibratedTASD response to minimum-ionizing charged particles. In particular, TASD responsesfor the events of the present and earlier studies (e.g. Supplemental Figure S3) can clearlybe resolved into individual minimum-ionizing Compton electrons that result in the de-posit of approximately 2.4 MeV into either the upper or lower scintillator plane, or incorrelated deposits into both planes. A property of particles above the minimum-ionizationthreshold is that higher-energy particles would still deposit only 2.4 MeV per plane (Zylaet al., 2020). Thus, the TASD cannot determine the maximum energy of Compton elec-trons, but it can place a lower limit on the energy values. Compton electrons that de-posit 2.4 MeV into one plane are produced by a photon with no less than 2.6 MeV (Sup-plemental Figure S9 of Abbasi 2018). Electrons that deposit 2.4 MeV into both planes,and also traverse the 1 mm steel separating sheet, have a total energy loss of 6.2 MeVand must be produced by photons with a minimum energy of 6.4 MeV.The above inferred photon energies should be interpreted as minimal values, as theyassume that the Compton electrons are produced by head-on collisions in which the gammaray is backscattered and transfers the maximum amount of energy to the electron. The –16–anuscript submitted to JGR: Atmospheres likely contributions of grazing incidence collisions to our signal would imply the actualphoton energies are several times higher, depending on the grazing angle (Supplemen-tal Figure S10 of Abbasi et al. (2018)). Even for single-scintillator layer detections, theseare comparable to the average 7–8 MeV energy of relativistic runaway spectra detectedby satellites. In any case, there is no question that the TASDs are detecting multi-MeVgamma-rays.
Although obtained for downward negative breakdown at the beginning of –CG andlow-altitude IC flashes, the results apply equally well to upward negative breakdown atthe beginning of normal-polarity IC flashes at higher altitudes in storms. Figure 6 com-pares INTF and FA observations of the –CG flash of TGF C with those of an IC flashthat was the next lightning discharge in the storm (see Figs. S27–S29 for additional ob-servations of the flashes). The top two panels show 2 ms of data for the two flashes withtime scales of 500 µ s/division. The bottom panel shows an expanded view of the large-amplitude classic IBP near the end of the IC interval. Taken together, the plots illus-trate the differences and similarities of the initial breakdown processes of IC and –CGflashes. In particular, and as has long been known (e.g., Kitagawa and Brook, 1960; Wei-dman and Krider, 1979), the downward negative breakdown of –CG flashes intensifiesmore rapidly and continuously than the negative breakdown of upward IC flashes. Thedifference is clearly seen in the top two panels and is due to a combination of effects: first,the IC flashes needing to propagate through a relatively large vertical extent of quasi-neutral charge before reaching upper positive storm charge, compared with little or nospacing of the lower positive charge during –CG flashes (e.g., Fig. 1 of Krehbiel et al. (2008),and Fig. 3 of da Silva and Pasko (2015)), and secondly the IC discharges occurring atreduced pressure. The overall result is that IC flashes develop more intermittently andwith longer stepping lengths than –CG flashes (e.g., Edens, 2014).Despite the intensification differences, individual initial breakdown pulses of IC flashesexhibit the same features as those of –CG flashes. In both instances, classic IBP sfer-ics consist of an initial strong electric field change having embedded sub-pulses, followedby a characteristically large and relatively slow opposite-polarity field change. The sim-ilarity is illustrated by comparing an expanded plot (bottom panel of Figure 6) of thelarge-amplitude IBP at the end of the middle panel with that of TGF B seen in Figures 4band S16, which occurred in the same storm ’ ’ µ s for the IC IBP vs. ’ µ s for the IBP of TGF B. The fastnegative breakdown component of the IC IBPs is also similarly longer, being ’ µ s forthe IC vs. ’ µ s for TGF B. The factor of two overall duration difference agrees withthe study by Smith et al. (2018) of median durations of large IBP sferics in Florida storms.Another example of a similar classic IC IBP sferic is seen in Fig. 4 of the study of FloridaIBPs by Marshall et al. (2013), which had a duration of ’ µ s and was considered tobe a ‘candidate’ TGF flash. At this point it should be noted that in many instances thedurations of IC and CG IBPs are the same for both types of flashes. This is seen in thescatter diagram of Figure 5 of Smith et al. (2018), and is shown in detail by the com-prehensive observations of Tilles (2020). Figures 9.3 and 9.4 of the latter study, conductedin Florida with the same INTF and FA instrumentation as in the present Utah study,show that (except for polarity) the IC and –CG IBPs were essentially indistinguishableboth in terms of their sferics and durations. –17–anuscript submitted to JGR: Atmospheres
Figure 6.
Comparison of the –CG flash that produced TGF C with the IC flash that wasthe next flash in the storm, illustrating the differences and similarities between the two types offlashes. Top two panels show 2 ms of observations for the downward –CG and upward IC. Bot-tom panel shows an expanded view of the large IBP near the end of the IC interval which, exceptfor polarity and overall duration, is basically identical to the IBP that produced TGF B threeflashes earlier in the storm. The propagation speed of the upward FNB is also similar, being ’ . × m/s. –18–anuscript submitted to JGR: Atmospheres
Figure 7.
Expanded views of the complex IBP clusters of the IC flash of Figure 6, showingthe increased number and highly-impulsive nature of the sub-pulses. The FNB breakdown of theIBPs and the sub-pulses are each embedded in continuous upward negative streamer breakdownhaving a propagation speed of ’ × m/s, showing that negative streamer breakdown doesn’thave to travel at speeds of 10 m/s to produce the sub-pulse sparks. The durations of the twoclusters were ’
130 and 400 µ s, respectively, with the sferic of the first cluster resembling that ofthe TGF-producing IBP of Figs. 2 of Lyu et al. (2018); Pu et al. (2019), and the second clusterresembling the sferic of another complex TGF-producing sferic of Pu et al.–19–anuscript submitted to JGR: Atmospheres
Due to the TGF-producing storms having low flashing rates (typically 1–2 min be-tween flashes in the present study), the electrification is allowed to build up to large val-ues, causing both the –CG and IC flashes to be highly energetic when they finally oc-cur. For the IC flash of Figure 6, this is reflected not only in the amplitude and dura-tion of the classic IBP, but also by the preceding activity being produced by two com-plex sequences (clusters) of IBPs and sub-pulses, seen in the middle panel. Each of theclusters is linked together by continuous, upward-developing high power negative break-down, producing long-duration complex steps. The overall durations of the two clusterswere ’
130 and 400 µ s, respectively. Expanded views of the complex IBPs are seen inFigure 7, which show the sferics were dominated by increasing numbers of sub-pulses thatassisted in continuing the negative breakdown and extending the cluster durations. Inaddition to their increased numbers, the sub-pulses are dramatically more impulsive andstronger in amplitude than those of the –CG flashes. The IC sub-pulses had amplitudesof ’ ’ As summarized in the recent modeling study of TGFs by Mailyan et al. (2019), thereare two classes of models for TGF production: First, what is termed the relativistic run-away electron avalanche (RREA) or relativistic feedback (RFD) model, in which elec-tron avalanches develop in km-scale regions of strong electric fields in storms (Dwyer,2003). In this model, the avalanching is enhanced by relativistic feedback that increasesthe avalanche currents by several orders of magnitude (Dwyer, 2012). The second classis broadly termed the ‘leader’ model, in which the relativistic avalanches are initiatedin the highly concentrated electric field produced at the negative tip of a conducting leaderchannel. The electric field at the tip is extremely strong as a result of the leader hav-ing kilometer-scale extents and shorting out tens to a few hundred MV of potential dif-ference in the storm. Whereas the RREA process by itself requires cosmic ray-producedor other seed relativistic electrons to get started, the leader process begins with low en-ergy thermal electrons, and requires exceedingly large electric fields ( ’ × V/m— an order of magnitude larger than the breakdown strength of air) to be acceleratedinto the runaway electron regime, where their number and energy increases exponentiallywith time and distance (e.g., Dwyer (2004)). Electric fields of this strength are producedonly at the tips of conducting leader-type channels, and then only transiently during rapidchannel development. Thermal electrons are accelerated into the relativistic regime asa result of transient negative streamers within the strong E region (the so-called ‘neg-ative corona flash’), as described by Moss et al. (2006), Celestin and Pasko (2011), andCelestin et al. (2015). Once the leader/streamer-initiated avalanches are started they wouldbe able to initiate the relativistic feedback process.While relativistic feedback can explain the large currents and fluxes of highly en-ergetic satellite-detected events, it does not appear to be playing a role in initiating thesmaller-scale observations of the present study. Instead, the inference that IBP sub-pulsesare caused by spark-like transient discharges embedded within the fast negative streamersystem points to the leader/streamer model as playing an important and possibly dom-inant role in generating runaway avalanches and TGFs. Once initiated, the runaway elec- –20–anuscript submitted to
JGR: Atmospheres trons would additionally increase in energy while propagating through the enhanced fieldregion ahead of and beyond the relatively broad streamer front (Attanasio et al., 2019).An important question is whether the conducting channels of the sub-pulses (whichwe refer to as transient conducting events, or TCEs) are isolated within the negative streamersystem and from each other, or if they are connected back into, or originate from, theconducting channel of the incoming negative leader. If so connected, the potential dropbeyond the negative tip of the sub-pulse channel would be comparable to the amountshorted out by the km-long or longer leader, envisioned to be as large as 60 to 200 MVor more (e.g., Celestin et al. (2015); Mailyan et al. (2019)). Such a leader is termed a‘high potential’ leader, which by itself can produce the large ( ’ –10 ) gamma pho-ton fluxes inferred by satellite observations (Celestin et al., 2015).To address the question of the sub-pulse connectivity, we note that the sub-pulsescontinue to occur until one suddenly causes the IBP sferic to begin transitioning to anopposite-polarity field change during the final part of the IBP. Although the flash cur-rent does not change direction, the electric field waveform becomes dominated by theelectrostatic and induction components, which are inverted in polarity from the radia-tion component due to the flash being beyond the reversal distance d for vertical dipo-lar discharges, where d = √ h and h is the discharge height above ground level (e.g.,MacGorman et al. (1998)). At the same time, the fast negative breakdown continues topropagate for several microseconds before finally dying out. From the large amplitudeand relatively long duration of the opposite-polarity field change, one can infer that thecurrent is not constrained to the IBP itself but develops retrogressively back through thenegative breakdown leading to the IBP, converting a potentially weak streamer-leaderchannel to a hot conducting leader and completing the step. That the current duringa negative leader step develops in a retrograde manner back along the incoming break-down channel has been shown by in-situ balloon-borne observations of negative leaderstepping during an IC flash by Winn et al. (2011), and by high speed video observationsaround the time of IBPs of –CG flashes by Stolzenburg et al. (2013), as discussed later.Because sub-pulses previous to the final sub-pulse do not initiate the opposite polarityfield change, one can infer they are not connected to the incoming leader breakdown, butinstead are isolated from the leader and from each other. The question then becomes whetherthe sub-pulse sparks short out enough potential difference to account for the observedTGFs.In terms of the space stem/space leader model of negative leader stepping (e.g., Petersenet al. (2008); Biagi et al. (2010)), the sub-pulse sparks would correspond to conductingspace leaders that occur in the negative streamer region ahead of the developing leader.Continuing the space leader interpretation, the final sub-pulse develops back into the in-coming leader, at which point the leader’s potential rapidly advances to the opposite endof the space leader, producing the negative corona flash that launches the relativistic elec-trons. This scenario could explain TGF A, which was initiated a few microseconds af-ter the final, sharply-pointed negative peak of the sferic (Figs. 4a and S15). TGF A alsoproduced the most surface-detected energy of the different TGFs (561 VEM total, or 1150MeV; Table S1). Because the TGF occurred just above the TASD boundary (Figs. 2 andS1), the detected energy could have been up to 50% larger had it been entirely captured.Similarly, the scenario could also explain the main onset of TGF B, which occurred atthe same time as the final sub-pulse peak (solid vertical line in Figs. 4b and S16).For TGFs C and D, however, and for the early initial detection of TGF B, the TGFonsets were associated with sub-pulses that did not initiate a retrograde current (Figs. 4,S17, S18, and the left-most vertical dotted line in Fig. S16). These and the other earlysub-pulses of the IBPs would be characterized as attempted space leaders, and may havesomehow paved the way for the final sub-pulse, but otherwise appeared to be indepen-dent of each other and not connected back to an incoming leader. The gamma eventsof TGFs C and D had total surface detections of 212 and 440 VEM (434 and 902 MeV), –21–anuscript submitted to JGR: Atmospheres respectively, with TGF D being the second strongest TGF after TGF A. At the sametime, the total activity of TGF B, which was most closely associated with the IBP’s fi-nal sub-pulse and presumably the best candidate for being connected to the incomingleader, had the weakest total surface detection of all, 112 VEM (229 MeV).Storm-to-storm variability, as well as that from flash to flash in the same storm,coupled with the small sample size makes it difficult to compare the different observa-tions. However, the fact that three TGF events (C, D, and the initial lone detection ofTGF B) were initiated by sub-pulses that did not connect back into the incoming break-down of the IBP, and the subsequent activity of TGF B producing a weak TGF despiteits sub-pulse eventually connecting back into the incoming breakdown, indicates that theoccurrence and strength of the gamma bursts are determined more by the amplitude andimpulsiveness of the initiating sub-pulse rather than by the incoming breakdown con-sisting of a hot conducting leader.From the above results, as well as the IBPs being produced by fast negative streamerbreakdown, the sub-pulses are analogous to the space leader in negative leader steppingin that they occur within negative streamers ahead of the leader. Instead of being pro-duced by a relatively slow-developing thermal space stem, the sub-pulses are impulsivesparks caused by sudden instabilities in extended-length streamer channels associatedwith fast propagation speed of streamers. And instead of the impulsivity of the step be-ing produced by the space leader suddenly contacting a conducting leader channel andrapidly propagating the leader potential forward to the head of the space leader, the im-pulsiveness and negative corona burst is produced by the spark itself. The succession ofsub-pulse sparks eventually causes one to develop back into a somewhat diffuse leader,giving rise to the backward-developing current that further establishes and converts theincoming breakdown into a well-defined hot conducting channel. This scenario agreeswith high-speed video observations by Stolzenburg et al. (2013, 2014), indicating thatthe ‘unusual’ steps of IBPs occur ahead of a weakly-conducting nascent leader rather thana continuously hot, conducting channel (see later discussion).If the space stem/space leader process is what initially advances the conductingleader channel, a legitimate question concerns how such a hot leader is produced in prop-agating from the end of the preceding IBP (or from the flash start) to the beginning ofthe IBP in question, in the absence of discernible space stem/space leader activity. Atsome point the leader becomes self-propagating (e.g., da Silva et al. (2019)), but appar-ently this does not occur in the early stages of the breakdown, as evidenced by the in-creasing need for and strength of IBPs in the initial few milliseconds of negative break-down. Up until then, the advancing negative breakdown between IBPs appears to be asystem of relatively weakly conducting negative streamers, which can self-propagate morereadily.From the INTF observations, the average speed of the downward negative break-down at the beginning of the TGF-producing flashes is ’ × m/s (e.g., Fig-ure 3a and Supporting Figures S7–S13), an order of magnitude or so faster than otherestimates of developing leader speeds (e.g., Behnke et al. (2005)). Similarly fast progres-sion speeds were reported during the upward development of TGF-producing IC dischargesby Cummer et al. (2015), who used ionospheric reflections to determine the altitude andhence the upward progression speed of successive radio pulses of TGF-producing IC flashes.For three different flashes, the speeds were noted to be remarkably similar and fast, rang-ing from 0.8–1.0 × m/s. As in the present study, the TGFs were produced partwayalong the vertical development (in their case upward), when the leader was ’ –22–anuscript submitted to JGR: Atmospheres
Taken together, the results suggest a scenario in which a ‘step’ consists of a) intermediate-speed negative streamer breakdown being launched at the end of the previous step’s IBP,which progresses in a forward direction until b) initiating accelerated-speed FNB andan IBP having embedded sub-pulses, one of which c) initiates a strong current that de-velops retrogressively backward through the IBP and its preceding negative breakdown,thermalizing and extending the negative leader. The IBP then reverts back to interme-diate or slower-speed negative streamer breakdown, beginning the next step. Whethera TGF is produced during the IBP is largely decoupled from the preceding negative break-down, explaining the independence of TGF production on the extent of the negative break-down up to that point. Where the preceding extent plays a role is in enhancing the elec-tric field ahead of its developing front, to the point that the FNB is initiated. The fieldenhancement is due to the cumulative dipolar charge transfer of the negative breakdownduring each step (e.g., Krehbiel (2018); Attanasio et al. (2019); Cummer (2020)), caus-ing successive IBPs to become stronger with time. The TGFs of this study were producedby the strongest IBP of the flash, but in 3 of the 4 flashes one or two additional burstsoccurred that were associated with separate episodes of FNB and sub-pulse activity (seeFigs. S10d,g, S12c,f and S13c,f). The additional gamma events occurred during less strongIBPs within ’ µ s either before or after the main gamma events, and representsparsified examples of the TGF activity that would be expected during the kind of com-plex IC IBP events seen in Figures 6 and 7.The above scenario for the stepping provides an explanation for the optical obser-vations of Stolzenburg et al. (2013), in which partially-obscured luminosity in the first1–2 ms of a –CG flash advanced downward with a series of surges associated with brightoptical emissions at the times of successive IBPs. The observations were obtained fromhigh speed video recordings having 20 µ s time resolution. Each bright surge lasted about80–100 µ s and was preceded by dim, linearly downward extension of the channel, withthe brightest frame “immediately followed by backward lighting of the entire tail” thatpreceded the bright surge. The sequence then started over again with renewed dim down-ward extension of the channel to a lower elevation angle, with the process repeating forup to five surges. In terms of the above scenario, a) the linear downward channel exten-sions would correspond to the intermediate-speed, inter-IBP negative streamer activity,b) the succeeding bright optical emissions would have been produced by the spark-likesub-pulses of the IBP, and c) the immediately following upward propagating light wouldbe produced by the retrograde current traveling back up along the path of the pre-IBPactivity, converting it into a hot conducting leader. As noted earlier, Winn et al. (2011)observed similar backward propagating current events following individual steps of analready-developed negative leader toward the end an IC flash, using close balloon-borneelectric field change observations of the flash. The correlation of bright optical pulses with–CG IBPs was extended by Stolzenburg et al. (2016) to be produced by IC-type IBPsat the beginning of hybrid –CG flashes. Similar to Marshall et al. (2013), the IBPs wereconsidered to be candidate producers of TGFs, on the basis of the IBPs being complexand having strong sub-pulses.The mechanism for producing the spark-like sub-pulses and TCEs within the fastnegative breakdown would be essentially the same as that which causes the FPB and FNBto be the producer of high-power VHF radiation, described as being the strongest nat-ural source of VHF radiation on Earth (LeVine, 1980). Due to their fast propagation speed,both polarities of streamers would have extended partially-conducting tails that wouldbecome unstable in the strong ambient fields (F. Shi et al., 2016; Malagon-Romero &Luque, 2019). The resulting rapid current cutoff, coupled with meters-long extents andlarge numbers, make both polarities of streamer systems potent radiators at VHF (Risonet al., 2016). The negative polarity streamers of FNB would have more robust and ex-tensive tails than positive streamers, that could occasionally extend over longer distances,with the resulting instabilities and currents producing hot, spark-like conducting chan-nels of the sub-pulse TCEs. In addition to explaining the optical emissions associated –23–anuscript submitted to JGR: Atmospheres with IBPs, the sudden occurrence of a dynamically impulsive conducting channel wouldprovide the means for initiating relativistic electron avalanches (Moss et al., 2006; Ce-lestin & Pasko, 2012; Celestin et al., 2015).It is interesting to note that, in addition to being produced by sub-pulses, it mayalso be possible for relativistic electron avalanches to be initiated by individual negativestreamers themselves. This is suggested by the modeling study of Moss et al. (2006), whoshowed that the extremely strong electric fields sufficient to accelerate electrons into therunaway regime will occur briefly immediately prior to branching of the streamers. Elec-trons produced in association with branching can reach kinetic energies as large as 2–8 keV or larger, well into the runaway electron regime. Although determined to occurin the corona flash and streamer zone at the tip of a conducting leader, the process mightalso occur at the tips of streamers having relatively long conducting tails. The branch-ing process was noted to strongly favor negative streamers over positive, due to positivestreamers requiring photoionization to sustain their propagation. If it occurs, the branch-ing mechanism would be a powerful adjunct to TCEs, since large numbers of individ-ual streamers exist within a propagating system that are spread over a much larger cross-sectional area than an individual conducting leader or TCE channel, and are continu-ally branching.Other issues of note concerning the observations are a) that the TGFs are broadlyrather than narrowly beamed, favoring a tip-based conducting channel model (Mailyanet al., 2019), and b) are commonly tilted at substantial angles from vertical. From theTASD footprints and source altitudes, the half angular width of the beaming is on theorder of 35 ◦ or so ( ’ ◦ or more, depending on the 3-dimensional development of the dis-charge. Finally, successive sub-pulses can be oriented in different directions, as indicatedby successive onsets occurring in different directions for TGF B (Figs. S16 and S20).We note that the simulations of our previous study (Abbasi et al., 2018) impliedTGF fluences on the order of 10 –10 relativistically-generated gamma photons, sev-eral orders of magnitude less than satellite-inferred fluences of ’ –10 photons. From Celestinet al. (2015) (Table 1), total fluences of 10 –10 photons correspond to potential dropsof ’
10 to 50 MV or so at the conducting channel tips, while fluences of ’ –10 pho-tons correspond to larger potential drops of 160–300 MV. That the observed fluences arerelatively weak would be consistent with the inference that the TGFs are produced byisolated conducting sparks that short out lesser amounts of potential difference. How-ever, if km-long conducting leaders are not involved, the question is whether sufficientpotential difference is available for producing the relativistic electrons and the observedgamma radiation. For example, from Celestin et al. (2015) (Fig. 3), 5–10 MV potentialdrops would not produce relativistic electrons greater than ’ ’ × ( ’ × ) photons,two orders of magnitude greater than the inferred fluences of these TGFs. Thus the ob-servations are inconsistent with the leader-streamer modeling, in that the fluences cor-responding even to the minimum likely detected photon energy produced by 60 MV po-tential drop would be at the upper end of the implied fluence values of Abbasi et al. (2018).The question of available potential energy can be addressed by considering the elec-tric field required for streamer propagation, called the stability field E st . From da Silvaand Pasko (2013), at one atmosphere of pressure E st ’ × V/m for positive stream-ers, but ’ . × V/m for negative streamers in virgin air. The fields scale accord-ing to pressure, so at 5 km altitude (0.5 atm) E − st ’ × V/m. Thus FNB propa-gating over the 100–240 m long extents of the TGF IBPs (Table S3) would experience –24–anuscript submitted to
JGR: Atmospheres total potential differences of ’
60 to 150 MV, with 60 MV being consistent with observedphoton energies up to ’ × V/m, which is not accounted for in the Celestin et al. (2015)calculations. Also not accounted for are dynamical effects in initiating the relativisticelectrons that are associated with the sparking being impulsive, which are significant forpulsed discharges (Section 5.4.3 of Nijdam et al. (2020)). Finally, using the stability fieldvalues doesn’t account for the field intensification ahead of the advancing streamer front,which can be as much as 50% above the ambient E st value (e.g., Attanasio et al. (2019);da Silva et al. (2019)). For IC flashes at higher altitudes, E st would be reduced by aboutanother factor of two, but this would be offset by the IC events typically being longerby a factor of two or more, leaving the total potential differences about the same. Fi-nally, we note that vertical profiles of the electric potential in electrified storms similarto those being studied show the total potential differences available for IC and –CG flashesare both on the order of 200 MV (e.g., Fig. 1 of Krehbiel et al. (2008); Fig. 3 of da Silvaand Pasko (2015)).In short, while the details remain to be understood, taken together, sufficient po-tential difference is available to produce gamma radiation into the 10–20 MeV range orpotentially higher, consistent with the observations and the physics of the Surface De-tector responses. The main issue is the fluence values. A possible explanation for the flu-ence inconsistency that allows both the observational data and the modeling to be cor-rect would be that the gamma photons are produced by ’
10 to 50 MV of potential drop,which from Fig. 3 and Table 1 of Celestin et al. (2015) would produce relativistic elec-tron energies in the range of ’ –10 photons. Once initiated, the electron energies would be further accelerated up to ’ × V/m. Because the extent of the field aheadof the streamer system would be less than an e-folding avalanche length, the fluences wouldnot change significantly while the electron energies increase.To the extent that satellite-detected TGFs from IC flashes have substantially largerfluences, the implication is either a) that the satellite detected events emanate from thetips of fully-formed, kilometer-length or longer conducting leaders, in which case fluencesof 10 –10 photons are achieved directly from the negative corona flash produced bypotential drops as large as several hundred MV, or b) that the fluences of lesser poten-tial drops are enhanced by the relativistic feedback process. The above-mentioned ob-servations by Cummer et al. (2015) raise the important question about the leader hy-pothesis of why TGFs are not produced later in the development of upward, kilometeror multi-km conducting leaders. Instead, and as additionally discussed below, the ob-servational data supports the idea that the much greater satellite-detected fluences aredue to the relativistic feedback mechanism, which was initially developed to explain thisvery issue (Dwyer, 2012).Another substantial difference between the present observations and those obtainedby satellites concerns the durations of the TGFs, being 5–10 µ s for the downward –CGTGFs, versus ’ µ s for the upward, IC-generated TGFs (e.g., Mailyan et al. (2016,2018); Østgaard et al. (2019)). The difference can be at least partially explained by ob-servations that IC flashes can often have long-duration, complex sferics, consisting of mul-tiple sub-pulses and IBPs, each of which would be capable of producing TGFs. Exam-ples of such sferics are seen in Figures 6 and 7. Of particular note are the observationsof three TGF events by Lyu et al. (2018), in which complex dB/dt events produced Fermi-detected TGFs having continuous durations of ’
50, 100, and 120 µ s. In the latter twocases, gamma detections occurred intermittently for an additional 60 and 100 µ s bothbefore and/or after the main activity, extending their overall durations to ’
160 and 220 µ s,respectively. For each of the three events, the TGFs were produced during the occur- –25–anuscript submitted to JGR: Atmospheres rence of a slow, smooth component of the sferic, indicative of being caused by electronavalanching that produced the TGFs. Complex, lengthy sferics were also produced bythe other two events of the same Lyu et al. study.Of particular interest, and the best-studied example, was the first event of 4 Septem-ber 2015 (Fig. 2 of Lyu et al. (2018)), which occurred over west-central Florida. Its sfericclosely resembled that of the first complex IBP of the Utah IC, seen in the top panel ofFigure 7. In both cases, the sferic lasted for ’ µ s and consisted of several highly im-pulsive sub-pulses before and after a central event. For the Utah IC the central eventwas itself a large-amplitude IBP, while for the Florida IC it was the large-amplitude slowfield change of the electron avalanche. The comparison, along with the other Lyu et al.examples illustrates the fact that a) long-duration TGFs can be produced by IC flasheshaving complex sferics, and b) that the only difference between the Utah and FloridaICs is that the latter initiated strong runaway avalanching, while the former did not, butbased on the sferic similarities, could well have done so. The second complex IBP of theUtah IC, seen in the bottom panel of Figure 7, would have been even more capable ofgenerating a long-duration TGF based on its greater duration and VHF signal strength.Pu et al. (2019) extended Lyu et al.’s study to include five additional examples ofcontinuously and intermittently long-duration TGFs being produced by other IC flasheshaving complex IBP sferics. Finally, we call attention to the study by Tilles et al. (2020)of a high peak current (247 kA) energetic in-cloud pulse (EIP) that was observed in Floridawith the same physical INTF and FA instrumentation of the present study. The EIP wasproduced by a complex sequence of repeated IBP-type fast breakdown activity, but itssferic was completely dominated by a sequence of three successive slow, smooth relativis-tic avalanches indicative of being produced by relativistic feedback. No gamma-detectingsatellite happened to be in view of the EIP, but the flash undoubtedly produced an up-ward TGF (Lyu et al., 2016; Cummer et al., 2017) and is an example of how IC flashesare capable of producing extremely strong avalanching as a result of complex IBP-typeactivity. The results can be summarized as follows:1. Downward TGFs occur during strong, “classic” initial breakdown pulses (IBPs)of downward negative CG and IC flashes. In turn, the IBPs are produced by streamer-based fast negative breakdown (FNB).2. The TGFs consist of short, ’ µ s duration bursts of gamma rays initiated bysub-pulses during the IBPs, and apparently also by brief episodes of enhanced speedFNB.3. The correspondence of TGFs with sub-pulses is indicative of the sub-pulses be-ing produced by spark-like transient conducting events (TCEs), consistent withtheir sferics being impulsive or cusp-like and explaining the bright optical activ-ity observed during IBPs of –CG and IC flashes.4. In turn, the TCEs are considered to result from instabilities in occasionally longstreamer tails or partially conducting channels embedded within the FNB of theIBP, and to be isolated from each other and from the incoming breakdown pre-ceding the IBP.5. Based solely on the well-understood physics of surface detector responses and Comp-ton electron production, individual electrons detected by the TASD surface sta-tions correspond to photon energies no less than 2.6 MeV if detected in a singlescintillator layer and 6.2 MeV if detected in both layers.6. From the electric field required to propagate negative streamers in virgin air at–CG altitudes, the electric potential difference experienced by the FNB over the100-m to 240 m extents of TGF-producing IBPs is ’
60 to 150 MV. –26–anuscript submitted to
JGR: Atmospheres
7. Instead of the breakdown leading up to an IBP being a long conducting leader,it appears to be due to weakly-conducting negative streamer breakdown that getsaccelerated to produce the IBP.8. The observational data indicate that the streamer to leader transition of succes-sive steps is caused by current generated during the characteristic opposite-polarityfield change in the final stage of the step’s IBP.9. The initial upward negative breakdown of IC flashes is shown to be produced inthe same basic manner as the initial downward breakdown of –CG discharges, butgenerally lasting longer and having longer step sizes.10. The long durations of satellite-detected TGFs can be explained by IC flashes pro-ducing complex clusters of sub-pulses and IBPs, which enable the developmentof continuous and intermittent electron avalanching. Sparse versions of this areseen during successive IBPs of –CG flashes.While the present study has been underway, the TASD has been in the process ofexpanding by a factor of four in its coverage area, and the TGF and lightning observa-tions are continuing. The LMA network is being similarly expanded, and an additionalVHF interferometer instrument is to be added in the current year. Detailed analyses ofadditional observations are the subject of continued study.
Appendix A Methods
A1 InstrumentsTelescope Array Surface Detector.
The TASD consists of 507 scintillator de-tectors arranged on a 1.2 km square grid. The array is situated on a relatively high, 1400 maltitude desert plain in west-central Utah, and covers an area of ’
700 km . Each detec-tor has two scintillator planes, each 3 m × . ’
150 FADC counts) within 8 µ s. When an event trigger occurs, the sig-nals from all individually-triggered SDs within ± µ s are recorded (Abu-Zayyad et al.,2013). An individual SD trigger occurs upon observing a signal of amplitude greater than0.3 MIP ( ’
15 FADC counts) within 8 µ s.The TASD is an inefficient detector of gamma radiation, relying on the productionof high-energy electrons through the Compton scattering mechanism in either the thinscintillator, steel housing, or air above the detector units. Detailed simulations of thisprocess have been described in the authors’ previous study (Abbasi et al., 2018). Inci-dent gamma-ray photons with energy above 10 MeV will on average deposit about 20%(30%) of the energy of a MIP in the upper (lower) scintillator. The majority of photonswill not interact in the detector at all; those that do will primarily create Compton re-coil electrons with kinetic energies at or below the photon energy level. The Comptonelectrons can then deposit energy up to a MIP (2.4 MeV) in each plane of the scintil-lator, though the amount deposited in each plane will depend on where the Comptonscatter occurs. Lightning Mapping Array.
As shown in Figure 1, the LMA consisted of ninestations located within and around the TASD, and determines accurate 3-D observationsof peak VHF radiation events above threshold in 80 µ s time intervals. (Rison et al., 1999;Thomas et al., 2004) In addition to showing the large scale structure and developmentof flashes and the lightning flashing rate, its observations were used to determine the plandistance to the TGF events and also to finely calibrate the INTF azimuth and elevation –27–anuscript submitted to JGR: Atmospheres n1 ba n2 Figure A1.
Methods information. ( a ) Source-centric coordinate system for temporal corre-lations. The TGF source is at ( x a , y a , z a ), with the plan x , y location serving as the coordinateorigin. The TASD station is at location b relative to the origin and the reference altitude, andthe INTF/FA is at the more distant location c . ( b ) Iteration at 0.5 µ s time steps used in thealternative approach for determining the source altitude (TGF A in this case), showing theoccurrence of enhanced-speed downward FNB immediately before the TGF onset (red ‘x’). values. The angular calibration was done separately on a flash-by-flash basis for each TGFevent. VHF lightning interferometer (INTF) and fast electric field change an-tenna (FA).
The INTF records broadband (20–80 MHz) waveforms at 180 MHz fromthree flat-plate receiving antennas, and determines the two-dimensional azimuth and el-evation arrival directions of the VHF radiation with sub-microsecond resolution (Stocket al., 2014). This is done on a post-processed basis, and determines the radiation cen-troid in overlapping 0.7 or 1.4 µ s windows. Triangular baselines of 106–121 m were usedto maximize the angular resolution over the TASD. The elevation angles were used todetermine the source altitude of the TGFs, based on the LMA-determined plan distanceto the source, and the amplitude of the received signals was used to determine the VHFpower of the centroids. The fast electric field change antenna (FA) provided high res-olution (180 MHz) measurements of the low frequency (LF/ELF) discharge sferics thatare key to interpreting the INTF and LMA observations. –28–anuscript submitted to JGR: Atmospheres
A2 Analysis procedures
Figure A1a shows the coordinate system used for analyzing the INTF and TASDobservations. For simplicity, this is done in a Cartesian coordinate system centered atthe x a , y a plan location of the TGF’s source. The plan location is determined from themean values of the latitude and longitude of LMA sources within ± x a and y a , two additional measurements areneeded to determine the TGF’s onset altitude z a and time t a . The source altitude canbe estimated from the LMA observations, but has insufficient accuracy and temporal res-olution to resolve the fast downward breakdown that occurs during the parent IBP (typ-ically 100–150 m in 5–10 µ s). Instead, the altitude is more accurately determined fromthe INTF elevation angle θ c vs. time, which is obtained with sub-microsecond resolution.In particular, z a = D tan θ ( t c ) = z a ( t c ), where D = p x c + y c is the plan distancebetween the INTF and TGF. For an event at altitude z a and time t a , the arrival timesat TASD i and the INTF are given by t b = t a + r b /c (A1) t c = t a + R/c , (A2)where r b = [ x i + y i + ( z a − z i ) ] and R = [ x c + y c + z a ] are the slant ranges fromthe TGF source. Because the plan locations are considered to be known, r b = r b ( z a )and R = R ( z a ), so the time-of-arrival equations represent two equations and two un-knowns, t a and z a . The unknowns are determined from two measurements, in particu-lar the arrival time t b at a given TASD station, and the INTF elevation measurements, θ c ( t c ). Since θ c varies with time during the IBPs, it is not known in advance which timevalue t c to use for determining z a . This results from z a depending on itself in a mannerthat is not amenable to analytical inversion. But the equations are readily solved by it-erating over the range of values for z a , or equivalently over the possible θ c or t c values.Two semi-independent approaches were used to determine the solutions. Both usedan alternative form of (A2) obtained by eliminating t a to obtain t c = t b + ( R − r b ) c = t b + ∆ t b , (A3)where ∆ t b = ( R/c ) − ( r b /c ) corresponds to the time shift for comparing a given TASD’sobservations with the INTF/FA observations. For an assumed source altitude z a , the timeshift between the onset time t b at a given TASD station and its arrival time t c at theINTF is readily calculated from the difference of the slant ranges R and r b of the sourcerelative to the INTF and the TASD in question. In turn, the t c value can be used to de-termine θ c ( t c ) and hence z a . Comparing the assumed and inferred z a values forms thebasis for a closed loop iteration procedure, in which the assumed z a is simply replacedby the new z a value (Supp. Fig. S14). Consistency is reached in just a few steps. At thesame time, the corresponding INTF elevation angle θ c and arrival time t c at the INTFis also determined.The above is the method used by the first approach, as described in Section 2.2.For each of the primary TGFs shown in Figure 4, the source altitudes inferred from the –29–anuscript submitted to JGR: Atmospheres onset times at the different TASDs were in good agreement, having uncertainties of 30 m,16 m, 10 m, and 40 m for TGFs A, B, C and D, respectively (see Supporting Table S2).To guard against outliers, median values were used for determining the final z a and t a values at onset, as well as θ c and t c . The final t c values provide a reference time for eval-uating the onset times of each gamma-ray event. As can be seen from the TASD plotsin Figure 4, in most cases the waveforms begin within a microsecond or so of the indi-cated t c onset time. Detections that begin in advance of or after the indicated onset, asfor TGF B, are indicative of different onset times.Instead of using a closed-loop iteration process, as above, the second approach workedbackward from the INTF observations of the elevation angle θ c vs. t c to determine z a and ∆ t in reverse. This was used to predict the arrival times at two of the TASD sta-tions that detected the TGF most strongly, and involved stepping through the t c timesand corresponding θ c values in 0.5 µ s increments and determining the time when the dif-ference between the predicted and observed t b values passed through zero. The commonreference time t b was defined to be when the TASD signal first ascended to half of itseventual peak amplitude on the 2 stations with the strongest signals (short vertical dot-ted lines in the TASD waveforms of Supp. Figs. S10-S13c,d), which were averaged to ob-tain the final estimate of the time alignment.Figure A1b shows the results of the stepping procedure for TASD 2307 of TGF A.The plot shows the difference between the observed and trial t b times of the main gamma-ray event, with the interpolated step value where ∆ t b goes through zero determining thevalue of t c (red ‘x’ in the figure). For this (and the iterative) procedure to work, the INTFdata was processed with higher time resolution and increased overlap to make θ c ( t c ) morecontinuous. This is a standard procedure for analyzing INTF observations (Stock et al.,2014), and allows more detail to be seen in θ c vs. time. For these analyses, the higherresolution data was downsampled to 0.5 µ s intervals by using the median of the higherfrequency processing over a ± µ s interval around each 0.5 µ s point (unfilled gray cir-cles in panels c and d of Supp. Figs. S10-S13).What is informative and notable about the example of Figure A1b is that the on-set time of the strong gamma burst of TGF A coincided with the end of a brief inter-lude of rapid descent in the source altitude, denoted by the vertical dashed line in thefigure. The speed of the descent is determined from the spacing between the dots, whichoccur at 0.5 µ s intervals. In 1.5 µ s (three step intervals), the source descended about 50 m,corresponding to a downward speed of 3 . × m/s. This enhanced-speed interludewas unresolved by the normal processing, and instead caused the step discontinuity seenin Figure 4a during the fast negative breakdown. The stepping method of determiningthe onset time agreed well with the result of the iterative approach, which showed thegamma-ray onset to be at the end of the discontinuity (bold vertical line in Figure 4a).The agreement is not surprising, given that the same basic data was used in the two anal-ysis approaches. But the correspondence with different approaches indicates good pre-cision in the procedures, and reinforces the observation that the gamma bursts occur inassociation with intervals of enhanced speed breakdown. A3 Measurement uncertainties
Whereas the INTF and FA data are well-synchronized timewise by being simul-taneously digitized at a high rate, the main question is how accurately the TASD wave-forms from the different TASDs are synchronized with the INTF/FA data. As discussedabove, this can be qualitatively determined by examining the waveforms from the dif-ferent SDs relative to the inferred onset time (vertical line) for each of the TGF eventsin Figure 4. In most cases, the observed onsets are within a microsecond or less of theinferred time, with important exceptions in TGFs B and C. –30–anuscript submitted to
JGR: Atmospheres
A quantitative result can only be obtained from propagating the measurements’standard errors through calculations in the previous section, using the general form of δf = r ( ∂f∂x δx ) + ... + ( ∂f∂x n δx n ) (A4)where f = f ( x , ..., x n ). Detector locations are known to centimeter accuracy and havenegligible contributions. Similarly, gamma-ray detection trigger times are known on theorder of sampling rate (10s of ns). Both are taken into account, but have very little ef-fect on final uncertainties. Primary error sources, then, come from the two instances oftaking averages described the previous section; TGF source plan locations are taken asthe mean GPS location of LMA sources within 1 ms of particle detections, and its un-certainty is the standard error. TGF source elevations are done the same way — a meanis taken of all INTF sources within 4 µ s of the TGFs inferred arrival at the interferom-eter (from Equation A3), and its uncertainty is the standard error.All subsequent calculations can then be shadowed by their error counterparts us-ing Equation A4 and are presented in Tables S2 and S3. Typically, altitude measurementsare much less precise for this type of study, but here altitude determination comes fromthe higher-sampled INTF data whereas plan location data is supplied by only a few LMApoints. As a result, altitude uncertainties are 30, 20, 10, and 40 meters for TGFs A, B,C, and D respectively, compared to horizontal location errors of 150, 80, 40, and 300 me-ters. Timing uncertainties follow the same trend, with 0.7, 0.4, 0.2, and 1.4 µ s for eachrespective TGF. Standard errors for all other calculations are shown in Tables S2 andS3. Notice that elevation errors are nearly equal (Table S2), but poor grouping of LMAdata at the time of TGF D means a larger error in the plan location. As the error is prop-agated through each calculation, quantities for TGF D continue to be the least reliableamong the four, showing that the low LMA sampling rate and possible mislocations dur-ing fast breakdown are the main contributors to all further uncertainty. Acknowledgments
The lightning instrumentation, operation and analyses of this study have been supportedby NSF grants AGS-1205727, AGS-1613260, AGS-1720600 and AGS-1844306. The Tele-scope Array experiment is supported by the Japan Society for the Promotion of Sciencethrough Grants-in-Aids for Scientific Research on Specially Promoted Research (15H05693)and for Scientific Research (S) (15H05741), and the Inter-University Research Programof the Institute for Cosmic Ray Research; by the U.S. National Science Foundation awardsPHY-0307098, PHY-0601915, PHY-0649681, PHY-0703893, PHY-0758342, PHY-0848320,PHY-1069280, PHY-1069286,PHY-1404495, PHY-1404502 and PHY-1607727; by the Na-tional Research Foundation of Korea (2015R1A2A1A01006870, 2015R1A2A1A15055344,2016R1A5A1013277, 2007-0093860, 2016R1A2B4014967, 2017K1A4A3015188); by theRussian Academy of Sciences, RFBR grant 16-02-00962a (INR), IISN project No. 4.4502.13,and Belgian Science Policy under IUAP VII/37 (ULB). The foundations of Dr. EzekielR. and Edna Wattis Dumke, Willard L. Eccles, and George S. and Dolores Dor´e Ecclesall helped with generous donations. The State of Utah supported the project throughits Economic Development Board, and the University of Utah through the Office of theVice President for Research. The experimental site became available through the coop-eration of the Utah School and Institutional Trust Lands Administration (SITLA), U.S.Bureau of Land Management (BLM), and the U.S. Air Force. We appreciate the assis-tance of the State of Utah and Fillmore offices of the BLM in crafting the Plan of De-velopment for the site. We also wish to thank the people and the officials of Millard County,Utah for their steadfast and warm support. We gratefully acknowledge the contributionsfrom the technical staffs of our home institutions. An allocation of computer time fromthe Center for High Performance Computing at the University of Utah is gratefully ac-knowledged. We thank Ryan Said and W. A. Brooks of Vaisala Inc. for providing high- –31–anuscript submitted to
JGR: Atmospheres quality NLDN data lightning discharges over and around the TASD under their academicresearch use policy as well as several anonymous reviewers for their requests and com-ments, the responses to which significantly improved the paper. Data that support theconclusions presented in the manuscript are provided in the figures of the paper. Ad-ditional information can be found in the supporting material and is available on the OpenScience Framework (DOI: 10.17605/OSF.IO/Z3XDA).
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OURNAL OF GEOPHYSICAL RESEARCH
Supporting Information for “Observations of theOrigin of Downward Terrestrial Gamma-Ray Flashes”
J.W. Belz , P.R. Krehbiel , J. Remington , M.A. Stanley , R.U. Abbasi , R. LeVon , W. Rison ,D. Rodeheffer and the Telescope Array Scientific Collaboration T. Abu-Zayyad , M. Allen , E. Barcikowski , D.R. Bergman , S.A. Blake , M. Byrne , R. Cady ,B.G. Cheon , M. Chikawa , A. di Matteo ∗ , T. Fujii , K. Fujita , R. Fujiwara , M. Fukushima , ,G. Furlich , W. Hanlon , M. Hayashi , Y. Hayashi , N. Hayashida , K. Hibino , K. Honda ,D. Ikeda , T. Inadomi , N. Inoue , T. Ishii , H. Ito , D. Ivanov , H. Iwakura , H.M. Jeong ,S. Jeong , C.C.H. Jui , K. Kadota , F. Kakimoto , O. Kalashev , K.Kasahara , S. Kasami ,H. Kawai , S. Kawakami , K. Kawata , E. Kido , H.B. Kim , J.H. Kim , J.H. Kim ,V. Kuzmin † , M. Kuznetsov , , Y.J. Kwon , K.H. Lee , B. Lubsandorzhiev , J.P. Lundquist ,K. Machida , H. Matsumiya , J.N. Matthews , T. Matuyama , R. Mayta , M. Minamino ,K. Mukai , I. Myers , S. Nagataki , K. Nakai , R. Nakamura , T. Nakamura , Y. Nakamura ,T. Nonaka , H. Oda , S. Ogio , , M.Ohnishi , H. Ohoka , Y. Oku , T. Okuda , Y. Omura ,M. Ono , A. Oshima , S. Ozawa , I.H. Park ,M. Potts , M.S. Pshirkov , , D.C. Rodriguez ,G. Rubtsov , D. Ryu , H. Sagawa , R. Sahara , K. Saito , Y. Saito , N. Sakaki , T. Sako ,N. Sakurai , K. Sano , T. Seki , K. Sekino , F. Shibata , T. Shibata , H. Shimodaira ,B.K. Shin , H.S. Shin , J.D. Smith , P. Sokolsky , N. Sone , B.T. Stokes , T.A. Stroman ,Y. Takagi , Y. Takahashi , M. Takeda , R. Takeishi , A. Taketa , M. Takita , Y. Tameda ,K. Tanaka , M. Tanaka , Y. Tanoue , S.B. Thomas , G.B. Thomson , P. Tinyakov , , I. Tkachev ,H. Tokuno , T. Tomida , S. Troitsky , Y. Tsunesada , , Y. Uchihori , S. Udo , T. Uehama , October 14, 2020, 12:07am a r X i v : . [ phy s i c s . a o - ph ] O c t - 2 : F. Urban , T. Wong , M. Yamamoto , H. Yamaoka , K. Yamazaki , K. Yashiro , M. Yosei ,H. Yoshii , Y. Zhezher , , Z. Zundel Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, USA Langmuir Laboratory for Atmospheric Research, New Mexico Institute of Mining and Technology, Socorro, NM, USA Department of Physics, Loyola University Chicago, Chicago, Illinois, USA The Graduate School of Science and Engineering, Saitama University, Saitama, Saitama, Japan Graduate School of Science and Engineering, Tokyo Institute of Technology, Meguro, Tokyo, Japan Department of Physics and The Research Institute of Natural Science, Hanyang University, Seongdong-gu, Seoul, Korea Department of Physics, Tokyo University of Science, Noda, Chiba, Japan Department of Physics, Kindai University, Higashi Osaka, Osaka, Japan Service de Physique Th´eorique, Universit´e Libre de Bruxelles, Brussels, Belgium The Hakubi Center for Advanced Research, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto, Japan Graduate School of Science, Osaka City University, Osaka, Osaka, Japan Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba, Japan Information Engineering Graduate School of Science and Technology, Shinshu University, Nagano, Nagano, Japan Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, Japan Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, Kofu, Yamanashi, Japan Earthquake Research Institute, University of Tokyo, Bunkyo-ku, Tokyo, Japan Academic Assembly School of Science and Technology Institute of Engineering, Shinshu University, Nagano, Nagano, Japan Astrophysical Big Bang Laboratory, RIKEN, Wako, Saitama, Japan Department of Physics, Sungkyunkwan University, Jang-an-gu, Suwon, Korea Department of Physics, Tokyo City University, Setagaya-ku, Tokyo, Japan
October 14, 2020, 12:07am
X - 3 Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo, Japan Department of Engineering Science, Faculty of Engineering, Osaka Electro-Communication University, Neyagawa-shi, Osaka,Japan Department of Physics, Chiba University, Chiba, Chiba, Japan Department of Physics, Yonsei University, Seodaemun-gu, Seoul, Korea Faculty of Science, Kochi University, Kochi, Kochi, Japan Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka City University, Osaka, Osaka, Japan Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga, Japan Sternberg Astronomical Institute, Moscow M.V. Lomonosov State University, Moscow, Russia Department of Physics, Ulsan National Institute of Science and Technology, UNIST-gil, Ulsan, Korea Graduate School of Information Sciences, Hiroshima City University, Hiroshima, Hiroshima, Japan Institute of Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki, Japan National Institute of Radiological Science, Chiba, Chiba, Japan CEICO, Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic Department of Physics and Institute for the Early Universe, Ewha Womans University, Seodaaemun-gu, Seoul, Korea Department of Physics, Ehime University, Matsuyama, Ehime, Japan † deceased ∗ Currently at INFN, sezione di Torino, Turin, Italy, T. Fujii
October 14, 2020, 12:07am - 4 : Contents of this file
1. Figures S1 to S312. Tables S1 to S3
Introduction
The tables and figures in this supporting document provide further detail on the Ter-restrial Gamma-Ray Flash (TGF) observations by the Telescope Array Surface Detector(TASD), Lightning Mapping Array (LMA), fast electric field change antenna (FA), andVHF interferometer (INTF).
October 14, 2020, 12:07am
X - 5
Distance East, [1200m]17 18 19 20 21 22 23 24 25 26 27 28 D i s t an c e N o r t h , [ m ] s] m Time, [4
LMA hit hit C NLDN s] m Time [0 2 4 6 8 10 12 14 16 A DC c oun t XXYY=2308
Upper Scintillator Lower Scintillator
Integrated VEM=230
XXYY=2308
Distance East, [1200m]17 18 19 20 21 22 23 24 25 26 27 28 D i s t an c e N o r t h , [ m ] s] m Time, [4
LMA hit hit C NLDN s] m Time [0 2 4 6 8 10 12 14 16 18 A DC c oun t XXYY=2307
Upper Scintillator Lower Scintillator
Integrated VEM=96
XXYY=2307
Figure S1. TASD observations for TGF A.
Footprints for the two triggers of TGF A andthe waveforms at the TASD recording the strongest energy deposit. Numbers in the footprintcircles indicate the VEM energy deposit, and color indicates the relative onset times (4 µ s in-tervals). The yellow star indicates the median plan location of the LMA sources within ± October 14, 2020, 12:07am - 6 : Distance East, [1200m]8 9 10 11 12 13 14 15 16 17 18 19 D i s t an c e N o r t h , [ m ] s] m Time, [4
LMA hit hit C NLDN s] m Time [0 5 10 15 20 A DC c oun t XXYY=1521
Upper Scintillator Lower Scintillator
Integrated VEM=28
XXYY=1521
Figure S2. TASD observations for TGF B.
Same as Figure S1, except for the single triggerof TGF B. The TGF was detected at four different TASDs or sets of TASDs at different onsettimes, beginning with TASD 1421 immediately NE of the LMA- and NLDN-indicated sourcelocation, and continuing in a rapid succession around a central annular hole to the eastern,southern, and finally western station, finishing up almost directly around the TGF’s source.TASD 1420 associated with the annular hole did not record a trigger, indicating the gammabursts were relatively well-beamed (the station was fully operational throughout the storm andwas active for a cosmic ray event later in the day).
October 14, 2020, 12:07am
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Distance East, [1200m]9 10 11 12 13 14 15 16 17 18 19 20 D i s t an c e N o r t h , [ m ] s] m Time, [4 LMA hit hit C NLDN s] m Time [0 0.5 1 1.5 2 2.5 A DC c oun t XXYY=1521
Upper Scintillator Lower Scintillator
Integrated VEM=10
XXYY=1521
Distance East, [1200m]8 9 10 11 12 13 14 15 16 17 18 19 D i s t an c e N o r t h , [ m ] s] m Time, [4
LMA hit hit C NLDN s] m Time [0 1 2 3 4 5 A DC c oun t XXYY=1422
Upper Scintillator Lower Scintillator
Integrated VEM=61
XXYY=1422
Figure S3. TASD observations for TGF C.
Same as Figure S1, except for two gammabursts/triggers of TGF C. Both events were canonical examples of the basic processes involvedin TGF production (see text at end of Section 3.3). The zoomed-in views of the TASD signals inthe right-hand panels illustrate the fact that the SDs are sensing individual Compton electrons,with first event of the top right panel corresponding to an electron that penetrated both theupper and lower layers, and therefore was produced by a gamma photon having a minimumenergy of 6.4 MeV for rebounding collisions and a most likely energy up to three times thatfor grazing collisions (text at end of Section 3.1). The bottom right panel further illustratesthe individual nature of detections and their quantization both in time and amplitude.The non-diagonal red lines of these footprints and the footprint of TGF B denote internal boundaries ofdifferent sub-sectors of the TASD.
October 14, 2020, 12:07am - 8 : Distance East, [1200m]10 11 12 13 14 15 16 17 18 19 20 21 D i s t an c e N o r t h , [ m ] s] m Time, [4 LMA hit s] m Time [0 5 10 15 20 25 30 A DC c oun t XXYY=1502
Upper Scintillator Lower Scintillator
Integrated VEM=22
XXYY=1502
Distance East, [1200m]10 11 12 13 14 15 16 17 18 19 20 21 D i s t an c e N o r t h , [ m ] s] m Time, [4
84 791105 413561231611 2
LMA hit s] m Time [0 1 2 3 4 5 6 7 8 A DC c oun t XXYY=1604
Upper Scintillator Lower Scintillator
Integrated VEM=123
XXYY=1604
Figure S4. TASD observations for TGF D.
Same as Figure S1, except for two trigger eventsof TGF D. This event occurred two months later in the season (Oct. 3) in a nighttime storm overthe southern-most eastern corner of the TASD, and was less-well located by the LMA. It was alow-altitude IC flash whose downward development was strongly tilted from vertical (Figure S22and Figure 5d of the main text). Rather than going to ground, the discharge terminated in astrong lower positive charge region of the storm, which was displaced to the northwest of theflash initiation point. The tilted development was also reflected in the TGF footprints, withthe initial burst being southwest of the estimated source of the gamma bursts (and partiallyoutside the TASD boundary). The second burst was tilted to the northwest, concomitant withthe north-westward tilt of the flash’s development in the INTF and LMA observations. Theparent IBP of the main, second burst was the most extensive of the four TGFs, lasting ’ µ sand propagating over a distance of 240 m (Table S3). October 14, 2020, 12:07am
X - 9 a b c Figure S5. Composite TASD waveforms.
Stitched-together waveforms for each of theTGFs that produced multiple triggers (TGFs A,C,D), showing their relative amplitudes andtemporal separations. Triggers 1 and 2 are colored in black and red, respectively. The waveformsshow the activity to be temporally resolved into discrete few-microsecond long bursts over a timeperiod of ’ µ s. Three bursts occurred for TGF A, two for TGF C, three for TGF D,and one for TGF B (not shown). The multiple sporadic nature of the bursting is similar to thatseen in the previous study by Abbasi et al., 2018. October 14, 2020, 12:07am - 10 : Figure S6. Initiating NBE of TGF A flash.
Classic example of a narrow bipolar eventproduced by fast positive breakdown that initiated the flash of TGF A. The FPB propagatedupward over a distance of 150 m in 11 µ s, corresponding to a speed of 1 . × m/s. Whilethe peak source powers of the VHF radiation of the NBE and IBP were indistinguishable (+27.6dBW vs. +27.7 dBW, respectively), the sferic amplitude was 24 times stronger for the IBP thanfor the NBE (58 V/m vs. 2.4 V/m), being barely noticeable in Figure 3a of the main text. As aresult of this difference, the NLDN detected the IBP sferic as having a peak current of –36.7 kA,but did not detect the initiating NBE sferic, whose peak current would have been only ’ October 14, 2020, 12:07am
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Figure S7. Observational data for TGF B.
Observations of TGF B on 2018/08/02 at15:23:25 UT. Panels show interferometer elevation versus time (circular dots), fast electric fieldsferic waveform (green curve) and TASD gamma detections (purple waveform). Top: Observa-tions from initial breakdown through time of –26.5 kA initial cloud-to-ground stroke. Gamma raydetections occur in coincidence with strong (–30.1 kA) sferic pulse), 341 µ s after flash start (Ta-ble S1). Middle: 250 µ s of observations around the time of the gamma burst, showing the TGF’scorrelation with the largest amplitude initial breakdown pulse (IBP) and episode of downwardfast negative breakdown (FNB). Bottom: Expanded 50 µ s view of the scintillator waveforms atTASD 1421, which detected the initial onset of the TGF, showing how the strong gamma peakwas associated with the second leading-edge, strong sub-pulse of the IBP. October 14, 2020, 12:07am - 12 : Figure S8. Observational data for TGF C.
Same as Figure S7, except for TGF C on2018/08/02 at 15:25:51 UT. In this case, two gamma bursts were produced 825 and 942 µ s afterflash start. While the main, second burst was associated with a –21.7 kA sferic, again comparableto the initial return stroke (–26.8 kA), the first burst was associated with a weaker sferic, butwith a similarly embedded episode of enhanced-speed negative breakdown (Figure S12f). Thecorrelation with FNB is seen in more detail in the bottom panel, which illustrates the FNB beinginitiated by upward positive VHF development at the beginning of the IBP—a characteristicfeature of FNB —and the gamma detection steadily increasing during the FNB. October 14, 2020, 12:07am
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Figure S9. Observational data for TGF D.
Same as Figure S7, except for TGF D on2018/10/03 at 04:03:48 UT. As in TGF C, two weak gamma bursts occurred in connection withrelatively weak IBP sferics (in this case, prior to the main burst, around 688,540 µ s in middlepanel), but not in stronger sferics both before and after the strongest sferic. The distinguishingcharacteristic appears to have been that the other IBPs did not have embedded episodes ofenhanced-speed FNB. Again, the main gamma burst was associated with a strong sub-pulse onthe leading edge of its IBP sferic (bottom panel). October 14, 2020, 12:07am - 14 : Figure S10. (Caption next page.)
October 14, 2020, 12:07am
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Figure S10. (Previous page.)
Additional data for TGF A.
More complete summary resultsfor TGF A, including observations for the two triggers and three gamma bursts of the TGF. (a,b)
Overview plots similar to the top and middle panels of Figures S7–S9, except showing the times ofNLDN detections (red dotted vertical lines) and (for panel b) times of LMA-located VHF sources(colored diamonds, when within the displayed range of elevation values), and the VHF time serieswaveform (cyan trace). (c,d)
Correlation results from the alternative analysis process presentedin the Methods section, illustrating time alignments obtained from the first point which exceedshalf-maximum at the two TASD stations with the strongest signals (short vertical dotted lines inthe TASD waveform panels), with the average of the two results shown in the top panel (dashedvertical line in the upper panel and in Figure A1b of the main paper). (e) Plan view of LMAsources within ± ± . (f,g) Detailed observations and correlations forthe two TASD triggers, showing waveforms from top and bottom scintillators at the most activeTASD station. (Note perfect correlation of time-shifted –36.7 kA NLDN event with sferic peakof initial trigger, and consistent correlation with downward FNB episodes even for weak IBPs ofsecond trigger.)
October 14, 2020, 12:07am - 16 : Figure S11. (Caption next page.)
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Figure S11. (Previous page.)
Additional data for TGF B.
Same as Figure S10, except forthe single trigger and burst of TGF B. Unfilled gray circles in panel c) indicate the 0.5 µ s higher-time resolution observations of the INTF elevation angle observations used in both the iterativeand alternative analysis procedures (see Methods Section A2). The TASD signals are sorted topto bottom according to increasing range from the source. Note the correlation in panel f) of theclose 1421 TASD waveforms with the sferic sub-pulses and sequence of upward and downwardFPB and FNB for the singular 1421-detected burst. The non-aligned TASD waveforms in panelc) reinforce multi-onset grouping seen in Figure 4d of the main text and the full-page versionin Figure S16. Also note the large number of NLDN-located events in the first ms of the flashin panel a), and their excellent correlation with IBP sferics in panel b). The relatively largeeast-west variability of the NLDN events in panel e) is not reflected in the LMA observationsand is presumably due to uncertainty in the NLDN location (caused by the particular NLDNstations used to locate the event). Otherwise, the LMA and NLDN sources are closely clusteredaround the LMA-indicated median source location. October 14, 2020, 12:07am - 18 : Figure S12. (Caption next page.)
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Figure S12. (Previous page.)
Additional data for TGF C.
Same as Figure S10, exceptfor the two triggers and bursts of TGF C. Again, the NLDN located a number of IBP eventsin the initial ms of the flash (panels a and b). One NLDN event was noticeably mislocated inan otherwise closely grouped set of LMA and NLDN events in the median plan location plot ofpanel (e). The main burst occurred during the second trigger and is notable for its simplicityof interpretation (see text). The alignment time is slightly delayed relative to the onset of theTASD 1422 signal by the use of a half-max threshold in the stepping analysis (multi-waveformpart of panel d). The results are consistent with the iterative approach utilizing median resultof all TASD stations(Figure 4c and associated main text) Accounting for the slight delay alsobetter aligns the initial burst of the first trigger with its relatively weak sferic and associatedVHF radiation (panel f).
October 14, 2020, 12:07am - 20 : Figure S13.
Caption next page.
October 14, 2020, 12:07am
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Figure S13. (Previous Page.)
Additional data for TGF D.
Same as Figure S10, exceptfor the two triggers and three bursts of TGF D. As discussed in connection with Figure S4, theflash did not go to ground and was not detected by the NLDN. Otherwise its initial breakdownwas no different than that of a –CG discharge. Despite the increased uncertainty of the medianplan location (panel e) and slightly greater plan distance from the INTF (24 km), both analysismethods gave essentially the same onset time for the main burst, which occurred during trigger2 (panel d). In particular, the burst occurred in association with FNB associated with one orboth sub-pulses of the IBP leading up to the main peak (panels d and g). The second of thetwo weaker bursts associated with the initial trigger was also associated with a slightly noisybut clear episode of downward FNB episode (and a weaker sferic) (panel f). The first burstwas associated with even weaker and noisier activity, but was still capable of producing gammaradiation. In contrast, intermediate to strong IBPs between and after the two triggers did notproduce detectable gamma bursts.
October 14, 2020, 12:07am - 22 : Figure S14. Source Reconstruction Flowchart . Iterative procedure for determining z a and t a , the altitude and time of the TGF source. Note that this is performed individually foreach participating TASD station. See full description in Section 2.2 and in Methods Section A2. October 14, 2020, 12:07am
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Figure S15. TASD correlations for TGF A . Enlarged view of panel a) of Figure 4 showingdata from all participating detectors, time-shifted relative to the INTF. The black vertical lineshows the median onset time of the TGF relative to the INTF and fast antenna data, and theblack horizontal line shows the corresponding elevation angle. The light blue trace shows theVHF time series waveform observed by the INTF, and dots represent VHF radiation sourceswith color and size representing relative power. Purple traces in the lower panels are particledetector responses, with station numbers XXYY identifying their easterly (XX) and northerly(YY) locations within the array in 1.2 km grid spacing units. The detection times are in goodagreement with one another as well as the median, indicating the onset time of the TGF duringthe sferic and the VHF radiation development.
October 14, 2020, 12:07am - 24 : Figure S16. TASD correlations for TGF B . Same as Figure S15, except for panel b) ofFigure 4. In contrast to the other TGFs, the TASD onset times are not all consistent with themedian; TASD 1421 had a noticeably early onset time associated with the second strong sub-pulse, while the median onset was associated the peak of the IBP and with a step-discontinuityin the VHF radiation development. Slightly delayed TASD signals suggest additional onsets asdiscussed in Section 2.3.
October 14, 2020, 12:07am
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Figure S17. TASD correlations for TGF C . Same as Figure S15, except for panel c)of Figure 4. This event is an example of a simple, canonical IBP. Fast positive breakdownbriefly propagates upward before turning into downward fast negative breakdown during theIBP. The TASD onsets are mostly in good agreement and are associated with a sub-pulse and astep-discontinuity in the VHF radiation development.
October 14, 2020, 12:07am - 26 : Figure S18. TASD correlations for TGF D . Same as Figure S15, except for panel d) ofFigure 4. The sferic of this TGF is similar to that of TGF B, with a slower build-up and multipleembedded sub-pulses. The TASD onsets are closely correlated with one another and with astrong, impulsive sub-pulse before the main peak. The fast negative breakdown had a relativelylong duration and extent (given in Table S3) with a step-discontinuity occurring immediatelybefore the median TASD onset.
October 14, 2020, 12:07am
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Figure S19. Azimuth-elevation plots for TGF A . Enlarged view of panel a) of Figure 5showing the initial downward development leading up to and following the TGF occurrences.Red highlighted sources and a , b labels indicate the TGFs’ calculated source locations. Dashedred and blue lines indicate the axes of the FNB associated with each TGF, while the finely dottedlines show the angular extent of the TASD surface detections. (The plot has a 1:1 aspect ratio sothat the angular directions are faithfully replicated.) Baseline circles indicate size-scaled relativeenergy deposit in each Surface Detector; other baseline symbols indicate NLDN locations of CGand IC events, all as viewed from the INTF site. October 14, 2020, 12:07am - 28 : Figure S20. Azimuth-elevation plots for TGF B . Same as Fig. S19, except for TGF B ofFigure 5b. This TGF had at least two onset times (and possibly one or two more) at different SDsand sets of SDs, and therefore narrower beaming than indicated by the overall angular extent(see Figure S16). This suggests successively different orientations of the sub-pulses and FNBactivity, which would be consistent with INTF observations starting to broaden angular-wise atthe IPBs location.
October 14, 2020, 12:07am
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Figure S21. Azimuth-elevation plots for TGF C . Same as Fig. S19, except for therelatively simple and conical TGF C of Figure 5c. The simplicity is seen in the vertically-downward development of the INTF sources. Of interest in this and the other TGFs, the mainTGF of each flash (event a of TGF A, the only event of TGF B, and event b of the presentTGF) are all produced by the strongest IBP of the flashes, which occur as the INTF sourcesstart to broaden out, indicative of the onset of branching. After that, the IBPs begin to weaken,suggesting the IBPs are strongest up until branching starts. The weakened IBPs can also producegamma bursts, however, as seen in TGF A, where the second, weaker gamma event ( b ) occurred ’ µ s after the main ( a ) trigger and further into the branching (Fig. S19). October 14, 2020, 12:07am - 30 : Figure S22. Azimuth-elevation plots for TGF D . Same as Fig. S19, except for TGF Dduring the strongly-tilted, low-altitude IC flash of Figure 5d. Again, the strongest IBP and TGFoccurred at the lowest exent of the downward negative breakdown before it started branching.The flash occurred in a late-season nocturnal storm that had a more complex electrical structure,as indicated by the disjointed nature of the downward negative breakdown before entering thestorm’s offset lower positive charge region. The IBP that generated the TGF had the longestduration ( ’ µ s) and extent (240 m vertical component—but longer due to being oriented ’ ◦ from vertical). October 14, 2020, 12:07am
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Figure S23. Zoomed azimuth-elevation plots . 6x6 degree view of TGFs A–D. Thelocation of the VHF sources for each TGF trigger are indicated by the ellipses. All VHF sourcesare rainbow color-coded from blue to red according to increasing power, rather than accordingto time as in Figures S19–S22.
October 14, 2020, 12:07am - 32 : Figure S24. Comparison of –CG and IC flashes.
INTF observations of the initial fewmilliseconds of the –CG flash that initiated TGF B (top panels) and an IC flash that occurred69 s later in the same storm (bottom panels). For each flash the temporal development is color-coded from blue to red, with the time scale being approximately the same for both flashes. Theupward stepping is well-delineated in the elevation vs. azimuth and elevation vs. time plots forthe IC flash, and more continuous for the –CG flash. The stepping lengths were ’ ’
180 m for the –CG flash (900 m in 5steps). Upper right panels show overviews of the entire flashes.
October 14, 2020, 12:07am
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Figure S25. Two millisecond zoom plots . Same as the lower right panels of Fig. S24, butshowing the first ’ ’ × m/s, with the second, complex IBP andsub-pulse sequence lasting ’ µ s. October 14, 2020, 12:07am - 34 : Figure S26. 240 microsecond zoom plots.
Comparison of the largest IBPs of the –CG andIC flashes in Fig. S25. In both cases the IBP was produced by fast negative breakdown, havingspeeds of 1–2 m/s. The sub-pulses of the IC IBP were noticeably stronger and more impulsivethan those of the –CG flash, which initiated TGF B. Note the onset of strong VHF radiation atthe beginning of the FNB, and sub-pulses occurring both before and during the opposite-polarityfield change of the IBP. The overall duration of the IC IBP sferic was somewhat longer than thatof the –CG flash, being ’
60 and 40 µ s, respectively. October 14, 2020, 12:07am
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Figure S27. Primary IC/CG flash comparison.
Same as Fig. S24, except providingoverviews of the –CG flash that initiated TGF C (top panels) and the following IC flash in thestorm (bottom panels), corresponding to the examples of Figures 6 and 7 of the main text. Ofparticular note in both this IC and that of Figure S24 is that the strongest IBP occurred asthe upward negative breakdown started to branch out, at which point the strong IBPs abruptlystarted dying out (lower right panel of the IC). The same observation has been noted in connectionwith the IBPs of the main TGFS, as noted for Figures S19–S22.
October 14, 2020, 12:07am - 36 : Figure S28. Two millisecond IC/CG comparisons.
Same as Fig. S25 and enlargedversions of the top two panels of Figure 6 of the main text, illustrating the complex sequencesof the initial breakdown during the post-TGF C IC flash and the role of high-power negativestreamer breakdown and sub-pulses in the upward negative breakdown of the IC (see Section 3.2of the main text). As in the IC/CG comparison of Figure S24, the stepping lengths of the ICwere longer than those of TGF C, being ’ ’
140 and 180 m for the two largest steps of TGF C’s –CG.
October 14, 2020, 12:07am
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Figure S29. 240 microsecond plots.
Comparison of the fourth IBP of the IC flash of Fig.S28 (bottom panel) with the IBP of TGF C (right-hand side of top panel), showing how the ICIBP is substantially stronger in amplitude, duration and in the strength and impulsiveness ofthe sub-pulses, but is otherwise produced by the same basic process of FNB having embeddedsub-pulses. Like TGF C’s IBP, the IC’s FNB is similarly fast (1.5 × m/s) and is initiatedwith brief fast positive breakdown (in this case downward). Note that the earlier gamma eventof TGF C (Figs. S8 and S12c,f) was produced by the relatively weak sferic and FNB event atabout –1310 µ s in the top panel, indicating how even weak FNB can produce gamma-producingavalanching. October 14, 2020, 12:07am - 38 : Figure S30. Complex IBP/sub-pulse events.
Expanded views of the two complexIBP/sub-pulse sequences of the post-TGF C intracloud flash of Fig. S28 and Figure 7 of themain text. The FNB breakdown of the IBPs and the sub-pulses are each embedded in continuousupward negative streamer breakdown having a propagation speed of ’ × m/s, showingthat negative streamer breakdown doesn’t have to travel at speeds of 10 m/s to produce the sub-pulse sparks. The overall durations of the sferics are ’
130 and 400 µ s, respectively, with the firstcomplex event being very similar to that of a Florida IC flash that produced a satellite-detectedTGF of 50 µ s duration (Sections 3.2 and 3.3 of main text). October 14, 2020, 12:07am
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Figure S31. GEANT4 simulation of the effects of Compton scattering , pair pro-duction, and bremsstrahlung on the time-of-arrival of gamma ray showers. The lower panelswith 10 and 100 MeV photons were generated 3 km above ground level; 1 MeV photons (upperpanel) will not produce detectable energy deposit from 3 km, and so were generated at 1 km. Ineach simulation, 10 monoenergetic photons were generated in air at the center of a spherical (inorder to remove geometric effects) “detector” of radius 3 km (1 km for 1 MeV case). Particleswere scored at the detector if their energies exceeded 0.1 MeV, corresponding to the minimumdetectable energy deposit above background (Abbasi et al., 2018). 95% of particles arrive within20 ns (60 ns) for 10 MeV (100 MeV) primary photons, and within 40 ns for 1 MeV. We concludethat temporal structure in the TASD waveforms on longer time scales is indicative of the intrinsicduration of the TGF source. October 14, 2020, 12:07am - 40 : LMA NLDN TASD energy sum Number ofDate Time µ sec dBW I pk VEM/MeV TASDs2018/08/02 14:17:20 616655 20.3848 -10.0 kA C851 21.5981 -36.7 kA C987 27.7994 561/1150 9617094 27.2104 192/393 8191 20.3288 -12.0 kA C294 27.6444 21.82018/08/02 15:23:25 042253 25.4255 -10.9 kA C259 +12.0 kA C279 -3.1 kA C329 -26.9 kA C332 27.2341 -30.1 kA C341 112/229 12416 18.1459 -7.6 kA C2018/08/02 15:25:51 913524 4.9615 -6.4 kA C633 15.3816 20.1825 35/72 5832 -5.0 kA C937 -21.7 kA C938 26.7942 212/434 8914016 14.4076 -5.9 kA C2018/10/03 04:03:48 687336 22.2696 23.2688177 26.1200 22.0346 24.6436 100/205 9508 31.8584 440/902 12599 30.5
Table S1. Quantitative event values.
Quantitative values of the LMA, NLDN, and TASDobservations for the flashes of TGFs A,B,C,D, during the initial 1–2 ms of the flashes. Shownare the times of the LMA, NLDN, and TASD events [ µ s], the VHF source powers of the LMAsources [dBW], the peak currents I pk of the NLDN detected events [kA], the sum total energydeposited in all adjacent surface detectors triggered by the gamma bursts, in [VEM] and [MeV],and the number of TASDs contributing to the total. TASD times reported here are the timeof detection at ground level, delayed by propagation from the source. LMA and NLDN timescorrespond to the time of the source itself. October 14, 2020, 12:07am
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Event SD θ c (deg) z a (km) t c ( µ s) ∆ t b ( µ s) U/L ratio TGF A 2208 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table S2. Calculated source values.
Converged iteration values and associated uncertain-ties for each TGF, calculated independently for each surface detector. SD is the surface detector’sidentifying number XXYY identifying their easterly (XX) and northerly (YY) locations withinthe array in 1.2 km grid spacing units. θ c is the elevation angle corresponding to z a , which is thesource altitude (above a reference plane of 1.4 km). t c is the determined microsecond of TGFsignal arrival at the INTF and ∆ t is the relative timing difference between INTF and SD signals,and U/L Ratio is the ratio of energy deposit between upper and lower levels of scintillator. Valuesin bold are the medians for that column and indicate the burst’s median onset time/elevation. October 14, 2020, 12:07am - 42 : Event D (km) z a (km) t a ( µ s) ∆ θ FNB (deg) ∆ z FNB (m) ∆ t FNB ( µ s) v FNB (m/s)
TGF A 16.96 ± ± ± × TGF B 16.64 ± ± ± × TGF C 15.98 ± ± ± × TGF D 23.9 ± ± ± × Table S3. Observed fast breakdown characteristics.
Extent and duration of fastbreakdown occurring during the brightest event for each of the four TGFs, specified by the firstcolumn. Second column gives D, the plan distance between each TGF and the INTF. The thirdcolumn z a is the median altitude result of the iteration process (Table S2). The fourth column, t a ,is the reconstructed source time. ∆ θ F NB is the angular extent of downward breakdown which,combined with D, gives the propagation distance, ∆z
F NB . The fifth column, ∆t
F NB , is thebreakdown’s duration in time, which allows for an estimation of the fast breakdown speed shownin the final column v
F NB . Note that the final four columns do not include uncertainties, astheir values are estimated by simply assuming a linear descent of FNB based on data shown inFigure 4 (and Figures S15-S18).. Note that the final four columns do not include uncertainties, astheir values are estimated by simply assuming a linear descent of FNB based on data shown inFigure 4 (and Figures S15-S18).