The production mechanism for terrestrial gamma ray flashes (TGFs) is not entirely understood, and details of the corresponding lightning activity and thunderstorm charge structure have yet to be fully characterized. Here we examine sub-microsecond VHF (14–88 MHz) radio interferometer observations of a 247-kA peak-current EIP, or energetic in-cloud pulse, a reliable radio signature of a subset of TGFs. The EIP consisted of three high-amplitude sferic pulses lasting ≃60 μs in total, which peaked during the second (main) pulse. The EIP occurred during a normal-polarity intracloud lightning flash that was highly unusual, in that the initial upward negative leader was particularly fast propagating and discharged a highly concentrated region of upper-positive storm charge. The flash was initiated by a high-power (46 kW) narrow bipolar event (NBE), and the EIP occurred about 3 ms later after ≃3 km upward flash development. The EIP was preceded ≃200 μs by a fast 6 × 10⁶ m/s upward negative breakdown and immediately preceded and accompanied by repeated sequences of fast (10⁷–10⁸ m/s) downward then upward streamer events each lasting 10 to 20 μs, which repeatedly discharged a large volume of positive charge. Although the repeated streamer sequences appeared to be a characteristic feature of the EIP and were presumably involved in initiating it, the EIP sferic evolved independently of VHF-producing activity, supporting the idea that the sferic was produced by relativistic discharge currents. Moreover, the relativistic currents during the main sferic pulse initiated a strong NBE-like event comparable in VHF power (115 kW) to the highest-power NBEs.

Key Points

Simultaneous broadband radio and interferometer observations show the detailed discharge processes involved in producing an EIP
The VHF radiation during the EIP is produced by fast streamer events and is uncorrelated with the large-amplitude sferic of the EIP
The relativistic discharges of the EIP are preceded and initiated by the fast streamer events in a compact region of strong positive charge

1 Introduction

Since their discovery by the Burst and Transient Source Experiment aboard the Compton Gamma Ray Observatory (Fishman et al., 1994), terrestrial gamma-ray flashes (TGFs) have been observed by numerous space-borne instruments, including the Reuven Ramaty High Energy Solar Spectroscopic Imager (Smith et al., 2005), Astro-rivelatore Gamma a Immagini Leggero (AGILE) (Marisaldi et al., 2010), Fermi (Briggs et al., 2010) and, most recently, the Atmosphere-Space Interactions Monitor (ASIM) (Neubert et al., 2020; Østgaard et al., 2019). TGFs are brief bursts of energetic (up to tens of MeV) photons originating inside thunderstorms, lasting tens to hundreds of microseconds, and are generated as the result of bremsstrahlung by relativistic runaway electrons (Lehtinen et al., 1996). Initial low-frequency (LF) electric field change measurements (160 Hz to 500 kHz) showed that TGFs are generated during intracloud (IC) lightning (Stanley et al., 2006). In particular, analysis of LF electric (Shao et al., 2010) and magnetic (Cummer et al., 2015; Lu et al., 2011) field waveforms (called “sferics”), as well as very high frequency (VHF) lightning mapping observations (60–66 MHz) (Lu et al., 2010; Lyu et al., 2018; Mailyan et al., 2018), show that TGFs occur during the upward development of normal-polarity (Williams, 1989) IC lightning. Furthermore, the measurements indicate that TGFs are at least sometimes time aligned (within ≃10 μs) with sferics tens to hundreds of microseconds long. The pulse amplitudes of the sferics have been found to match the temporal variations of the TGF photon intensity (Cummer et al., 2011; Lu et al., 2011; Pu et al., 2019), indicating that the sferic is produced by the TGF-generating discharge process (Cummer et al., 2011; Pu et al., 2019). There has been speculation (Marshall et al., 2013; Stolzenburg et al., 2016) that the sferics of TGFs are energetic versions of the initial breakdown pulses (IBPs) associated with the initial stepped leader formation (Beasley et al., 1982; Karunarathne et al., 2013, 2014; Kolmasova et al., 2018; Marshall et al., 2013; Stolzenburg et al., 2013; Villanueva et al., 1994). More recently, a special class of high peak-current IC radio pulses, termed energetic in-cloud pulses (EIPs), was discovered to coincide with TGFs (Cummer et al., 2014; Lyu et al., 2015). In fact, a one-to-one correspondence has been found between EIPs and TGFs that occur within range of a spacecraft detector (Cummer et al., 2017; Lyu et al., 2016). In addition to the associated sferics, EIPs likely produce detectable optical emissions in the lower ionosphere (Liu et al., 2017) due to their large current moments. In fact, Neubert et al. (2020) recently confirmed that optical emissions can accompany TGFs.

Table 1. Salient Features of Relevant in-Cloud Processes for Comparison With the EIP

	Description	Sferic and VHF
EIP	High peak-current (>150 kA) rel-	Sferic evolves indepen-
(energetic	atively wide (∼50 μs) sferic, time-	dently of VHF activity.^∗
in-cloud	aligned with a subset of high-fluence
pulse)	TGFs; occurs after initial upward
	negative leader develops for several
	milliseconds and kilometers^1–3.
NBE	Relatively narrow (∼10 μs) bipolar	VHF onset simultaneous
(narrow	sferic; occurs in isolation or is a	with sferic.
bipolar	flash-initiating event; associated with
event)	lightning initiation; the most powerful
	natural terrestrial emitter of VHF^4–7.
FPB	Fast-propagating (10⁷–10⁸ m/s) positive	VHF onset simultaneous
(fast	breakdown; consists of a system	with sferic.
positive	of streamers; produces most NBEs^6–8.
breakdown)	FPB is somehow involved in producing
	the EIP discharge^∗.
FNB	Fast-propagating (10⁷–10⁸ m/s) negative	VHF onset simultaneous
(fast	breakdown; consists of a system of	with sferic.
negative	streamers; produces a small subset of
breakdown)	NBEs^7,8. FNB is somehow involved in
	producing the EIP discharge^∗.
IBP	Relatively narrow (∼10 μs) bipolar	VHF onset simultaneous
(initial	sferic, sometimes superimposed by	with sferic.
breakdown	narrower (∼1 μs) subpulses; IBPs occur
pulse)	in trains starting about 1 ms after
	flash initiation and trains can continue
	for several milliseconds; associated
	with initial leader development^9–11.

Note. The events are largely defined by their recorded sferics (≃3 kHz to 1 MHz electromagnetic waveforms), and in the case of NBEs and IBPs, the sferic waveforms can be similar, but the context of the flash is important in distinguishing between them—NBEs occur at the very beginning of flashes, or even without the development of lightning, while IBPs occur some time after flash initiation and indicate that lightning will ensue. Statements marked with a ^∗ indicate new results determined herein.
^a ¹Lyu et al. (2015).
^b ²Lyu et al. (2016).
^c ³Cummer et al. (2017).
^d ⁴Willett et al. (1989).
^e ⁵Rison et al. (1999).
^f ⁶ Rison et al. (2016).
^g ⁷Tilles et al. (2019).
^h ⁸Liu et al. (2019).
ⁱ ⁹Krider et al. (1979).
^j ¹⁰Rhodes and Krehbiel (1989).
^k ¹¹Stolzenburg et al. (2013).

There are currently two main theories for the physical mechanism of TGFs (Dwyer, 2008; Dwyer et al., 2012), and intense investigations are being carried out to determine how each theory might work independently or together to produce the large number of energetic (MeV) runaway electrons produced inside thunderstorms. The first theory is known as the cold runaway mechanism and is based on conventional electrical discharge processes—leaders and streamers (Bazelyan & Raizer, 1998)—that are constituents of lightning. It suggests that the free electrons produced by leaders and streamers are accelerated to the required energies in a compact region of extremely strong electric field (about 10 times the conventional breakdown field (Dwyer, 2004, 2008)) immediately ahead of an advancing powerful lightning leader (Celestin et al., 2012; Moss et al., 2006). The other theory describes a new type of self-sustained electrical discharge, termed a relativistic feedback discharge (RFD) (Dwyer, 2012; Liu & Dwyer, 2013), as a physical mechanism for TGF generation. The key process of this mechanism is the relativistic positive feedback mechanism introduced by Dwyer (2003), where generations of relativistic runaway electron avalanches repeatedly go through the same electric field region, driven by positron and energetic photon feedback. Since in situ measurements of the TGF source process are nearly impossible, investigation of how each mechanism may produce the remotely measured radiofrequency signals of TGFs has been the focus of recent research.

Here we present broadband VHF (14–88 MHz) radio interferometric observations, LF (≃1–300 kHz) and fast-antenna (≃3 kHz to 20 MHz) electromagnetic sferics waveforms, and Lightning Mapping Array data of a relatively close (≃30 km) EIP. Although no satellite-borne gamma-ray instrument was in view of the event, EIPs are known to be reliable producers of a high-fluence subset of TGFs (Cummer et al., 2017; Lyu et al., 2016). We find that the sferics and the VHF radiation developed independently of each other during the EIP, in contrast to observations of other in-cloud breakdown processes, including narrow bipolar events (NBEs) (Liu et al., 2019; Rison et al., 2016; Tilles et al., 2019). Table 1 summarizes the salient properties of NBEs, fast positive breakdown and fast negative breakdown (FPB and FNB, respectively), IBPs, and EIPs (including the results herein) for reference. In particular, we show that the EIP sferic began well before the onset of a strong NBE-like VHF event, comparable in power (50.6 dBW or 115 kW) to the highest-power NBEs. Moreover, the sferic peaked at about the same time as the onset of the strong VHF, apparently triggering the NBE-like event. The observations support the idea that the large amplitude sferic of EIPs is generated by the relativistic discharge responsible for an accompanying TGF, rather than by streamer or leader activity. In particular, the relativistic avalanching appears to develop during the occurrence of multiple, repeated kilometer-length streamer events within localized upper positive charge in the storm, indicative of a complex coupling between the conventional and relativistic processes.

2 Instrumentation and Observations

On 24 September 2016, an intense IC lightning flash occurred off the east Florida coast near Kennedy Space Center (KSC). The flash was detected by the National Lightning Detection Network (NLDN) as having a peak current of 247.3 kA and was subsequently confirmed as being an EIP using the Duke LF magnetic field sensor located at the Florida Institute of Technology (FIT). The Duke instrument is sensitive from ≃1 to 300 kHz and acts as a dB/dt sensor below 200 kHz (Cummer et al., 2011).

The EIP flash was also observed by the 3-D VHF Lightning Mapping Array at Kennedy Space Center (KSC LMA) (Rison et al., 1999; Thomas et al., 2004) and by the New Mexico Tech broadband VHF interferometer (INTF) and fast electric field change antenna (FA) being operated at KSC in 2016–2017 (Rison et al., 2016; Stock et al., 2014). Seven LMA stations were situated within the confines of KSC and Cape Canaveral Air Force Station, and three outlying stations were located 60–100 km inland and southward along the Florida coast to provide a wide coverage area. The LMA locates impulsive events above threshold in successive 80 μs time windows in a 60–66 MHz passband, utilizing time-of-arrival measurements having a timing accuracy of 25–30 ns rms. In addition to showing the overall structure and development of the parent flash, the LMA observations provided good estimates of the 3-D location and VHF source power of the EIP (see Figures A1 and A2 in the Appendix), as well as important contextual information on the electrical structure and other lightning activity of the parent storm.

The INTF utilized three broadband VHF (14–88 MHz) flat-plate receiving antennas in a 100-m equilateral triangle baseline configuration to accurately determine the two-dimensional direction of arrival of VHF radiation events continuously with submicrosecond time resolution. The time series waveforms from each receiver and from the FA were synchronously digitized at 180 MSps with 16-bit resolution. The INTF waveforms were postprocessed to generate 1.4 μs (256 samples) exposure VHF images, with a 0.35 μs (64 samples) shift between images. The centroid or brightest pixel from each image was mapped in space and time to determine the two-dimensional, high-speed (0.35 μs) development of the EIP flash. The FA waveforms were similarly wideband, being sensitive from 3 kHz to >20 MHz and having a 100 μs decay time constant. The combination of LMA, INTF, and FA data observations provide a detailed picture of the altitude, physical extent, propagation speed (see Figure A3 in the Appendix), and polarity (Uman et al., 1975) of the EIP-associated breakdown, as well as information about the storm context in which it occurred.

3 Results

3.1 EIP Detection

The flash that produced the EIP was initiated by a high-power NBE that had an LMA-detected VHF power of 46.6 dBW (46 kW) and an NLDN-estimated peak current of 17 kA. The EIP occurred 3.25 ms into the flash with a much larger peak current of 247.3 kA and an associated peak VHF power of 50.6 dBW (115 kW). Note that the NLDN tends to underestimate the peak current associated with in-cloud discharges such as NBEs (Nag et al., 2011) and TGFs/EIPs (Mailyan et al., 2020). A detailed listing of the LMA and NLDN data for the initial ≃4.5 ms of the flash is presented in Table A1 of the Appendix. Figure 1a shows 4.5 ms of the FA electric and LF magnetic field waveforms, spanning from the initiating NBE through the time of the EIP. Figures 1c and 1d show expanded views of the E(t) and dB/dt waveforms, along with time-integrated estimates of B(t) (blue waveforms). For electromagnetic radiation, the two are related by B(t) = E(t)/c and, thus, should have matching waveforms. Due to the FA having a broader bandwidth than the magnetic sensor, and also providing a direct measure of the electric field change, E(t) has better temporal resolution and clarity than the B(t) estimate. Nevertheless, for the longer-lasting and slower EIP waveforms of Figure 1d, the B(t) estimate reproduces the three positive peaks of the FA sferic, as well as the negative undershoot at the end of the EIP. Because the magnetic sensor is a slightly imperfect detector of dB/dt at higher frequencies (Cummer et al., 2011), its time-integrated waveform in Figure 1d exhibits unphysical offsets at the completion of the NBE and EIP. This is exacerbated by the magnetic sensor saturating during the EIP, producing the sawtooth-like integrated waveform.

Details are in the caption following the image — **Figure 1**
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Observations of the Florida EIP, showing (a) the fast E(t) and Duke (∼dB/dt) waveforms for the first 4.5 ms of the flash and (c, d) expanded views of the waveforms for the initiating NBE and EIP event. The panels also show the time-integrated estimate of B(t) (blue waveforms) and their comparison with the directly-measured E(t) waveforms (black). Panels (e) and (f) show the corresponding current- and charge-moment changes, M_I (orange) and M_Q (pink), obtained by integrating the E(t) waveform (black). The changes are superimposed on the VHF waveform from the INTF, along with the times of the LMA and NLDN detections (“o” and “x” symbols, respectively). The plan view map of panel (b) shows the offshore locations of the NBE and EIP by the LMA and NLDN relative to the INTF at KSC (black triangle), and the Duke sensor at FIT (black “+”), along with the locations of four of the KSC LMA stations (green squares).

According to the criteria established in Lyu et al. (2015), the sferic of Figure 1d is characterized as an EIP due to its long “pulse width” (54 μs); its less-than-unity “peak ratio” (<0.9), which indicates the secondary peak is higher amplitude than the initial peak; and its fairly low “isolation ratio” (18 dB), which is a logarithmic ratio of the sums of sferic magnitudes prior to the EIP and during the EIP. The pre-EIP activity can be seen in the dB/dt and Bfield waveforms of Figure 1a. In contrast, the sferic of the initiating NBE in Figure 1c is typical of NBE events, having a short pulse width (14 μs), a greater-than-unity first to second peak ratio (1.3), and a high isolation ratio (73 dB).

The NBE and EIP were sufficiently far away so that the radiation field dominated the FA measurements (da Silva & Pasko, 2015). Hence, the current- and charge-moment changes M_I(t) and M_Q(t) as a function of time are obtained by successively integrating the FA waveforms of the NBE and EIP, then multiplying by the appropriate proportionality constant (viz., $urn:x-wiley:jgrd:media:jgrd56523:jgrd56523-math-0001$ , where ϵ₀ is the permittivity of free space, c₀ is the speed of light in vacuum, R is the slant range from the FA to the event of interest, and D is the plan distance (da Silva & Pasko, 2015)). M_I(t) and M_Q(t) are shown in Figures 1e and 1f, and the resulting numerical values are summarized in Table 2. For the NBE, the peak current moment was $urn:x-wiley:jgrd:media:jgrd56523:jgrd56523-math-0002$ s) = −7.7 kA-km and was generated by downward FPB similar to that observed by Rison et al. (2016). For the EIP, the integration started at t = 3.2 ms, a few tens of microseconds before the EIP onset, and gives a peak current moment M_I(t = 3.31 ms) = −293.0 kA-km. Note that this is remarkably consistent with the NLDN peak current estimate of 247.3 kA and the INTF observations showing a ≃1-km vertical extent of the EIP discharge (see section 6), given that the NLDN tends to underestimate the peak current associated with in-cloud discharges (Mailyan et al., 2020; Nag et al., 2011). The charge-moment change M_Q(t) is obtained by twice integrating the FA waveforms, giving a value of M_Q(t = 30 μs) = −0.15 C-km for the NBE, comparable to the values obtained for NBEs by Rison et al. (2016). For the EIP, M_Q(t = 3.38 ms) = −16 C-km, 2 orders of magnitude larger than that of the NBE.

Table 2. Summary of the EIP and NBE Characteristics, Namely, the NLDN Peak Current I_pk, Peak FA Sferic ΔE_pk (at Plan Distance d ≃ 30.5 km), Peak Current-Moment M_I, pk, Total Charge-Moment Change M_Q, LMA Peak Power P_pk, Rise Time τ_rise of INTF VHF Power, and Vertical Extents Δz of the Flash-Initiating NBE and the EIP

	NLDNI_pk	ΔE_pk	M_I, pk	M_Q	LMAP_pk	τ_rise	Δz
	(kA)	(V/m)	(kA-km)	(C-km)	(dBW, kW)	(μs)	(km)
NBE	17.0	24	−7.7	−0.15 (t = [0, 30 μs])	46.6, 46	0.25	0.6
EIP	247.3	123	−293.0	−16.0 (t = [3.2, 3.38 ms])	50.6, 115	1.2	1.5

Note. The peaks in I, ΔE, M_I, and P are not necessarily simultaneous for each event. M_I and M_Q are obtained by once and twice integrating the FA signal, respectively. The integration starts at time t = 0 for the NBE and at t = 3.2 ms for the EIP. τ_rise is determined by fitting a line to the natural log of the squared INTF VHF signal for each event. The vertical extent of each event is determined from the INTF elevation observations and the plan distance determined by the LMA locations and depicts the span of INTF sources from the integration start time up to the peak in M_I.

Figure 1b shows the plan location of the NBE and EIP relative to the INTF and FIT sites. LMA and NLDN observations show that the two events occurred in close proximity to each other, about 30.5 km south-southeast of the INTF/FA and at a similar distance north-northeast of the FIT magnetic field sensor. As typically happens, the initiating NBE was mislocated by the LMA (see Figure A2 of the appendix). The mislocation is a consequence of the FPB being VHF noisy during the strong radiation, causing different LMA stations to detect slightly different peaks. This is a characteristic feature of NBEs that is useful in identifying their occurrence and the streamer nature of the breakdown (Rison et al., 2016; Tilles et al., 2019). In addition to being mislocated, the LMA obtained two solutions for the NBE, both having the same VHF powers but substantially different locations and goodness of fit values (see Table A1 of the Appendix). The two solutions were separated in time by ≃1 μs and resulted from the NBE's VHF radiation straddling a boundary between successive 80 μs time windows at some of the LMA stations, which caused large-amplitude peak values on both sides of the boundary, providing two independent sets of arrival times and solutions. Both solutions were mislocated relative to the weaker, more impulsive, and accurately located LMA sources immediately following the NBE, which were tightly clustered and in good agreement (to better than 200 m) with the NLDN location (see Figure A2b in the appendix). Consequently, while the NLDN timing (“x” in Figure 1e) agreed well with the NBE sferic (better than 1 μs after taking into account the travel time from the NLDN-determined NBE location to the INTF/FA), the NBE timing was poorly determined by the LMA (double circles in Figure 1e), with the LMA sources appearing to occur about 4 μs before the onset of the NBE. In contrast, the LMA solution for the EIP was relatively well fitted (reduced chi-square of 0.21), and its timing was in good agreement with the peak in the VHF waveform of the EIP (circle in Figure 1f). Importantly, and unlike the NBE, both the onset of the 247 kA FA sferic and the NLDN detection of the sferic occurred well before the onset of strong VHF radiation during the EIP, by ≃6–12 μs. The fact that the EIP sferic led the VHF emissions by 12 μs will be revisited in more detail in section 6.

3.2 EIP-Generating Flash

Figure 2 shows an overview of the spatial structure and temporal development of the EIP-generating flash. Figures 2a and 2b show the LMA source locations for the flash (white dots) superimposed on the LMA-determined storm charge structure (Hamlin, 2004; Krehbiel et al., 2008; Marshall et al., 2005; Rust et al., 2005) of the parent storm. The storm had a normal-polarity tripole charge structure (Krehbiel, 1986), consisting of dominant midlevel negative (blue) and upper positive (red) charges, and a lesser lower positive charge. The storm had a low average flash rate of 1.4 min⁻¹ over its 21-min lifetime between 00:48:15 to 01:09:15 UT. The EIP flash occurred at 00:55:12.7, about 7 min into the storm, and was in a new, convectively vigorous cell on the eastern side of the storm that started producing lightning about 3 min earlier. It was a normal-polarity IC flash that developed vertically upward in the storm between negative charge at 6–8 km altitude above mean sea level (MSL) and upper positive charge between 10 and 12 km MSL, as seen in the LMA and INTF observations of Figures 2a–2c. As discussed in more detail in section 7, the EIP flash was preceded by a nearly identical IC flash 97 s earlier, which was also initiated by a high-power (51.1 dBW, 129 kW) NBE. In turn, the EIP flash was followed 65 s later by a negative cloud-to-ground (CG) flash, whose initial return stroke had an exceptionally strong peak current of 136 kA. Combined with the EIP flash, this activity shows that the new cell was strongly electrified.

More detailed INTF observations of the flash are shown in Figures 2c and 2d. The near-vertical trajectory of the sources between about 15° and 21° elevation (≃8 and 12 km MSL) in Figure 2c was produced by the upward negative leader propagating toward and into the upper positive charge, while the horizontally extensive portion of the flash between about 12° and 15° elevation is indicative of positive breakdown propagating through midlevel negative charge. In Figure 2d, two distinct levels of activity are clearly visible, attributed to breakdown in the upper positive and midlevel charge regions, typical of normal-polarity IC flashes (Rison et al., 1999; Shao & Krehbiel, 1996). The EIP flash was unusual, however, in that the upward negative leader did not continue to propagate through horizontally distributed upper positive charge, as previous and subsequent IC flashes did. As a result, nearly all of the negative channel development took place during the first 3–4 ms of the flash, ending just after the EIP (see section 5), though the EIP flash continued for another several hundred milliseconds. In particular, the upward channel was repeatedly retraced by multiple K events (Akita et al., 2010; Shao & Krehbiel, 1996), which started in the negative charge region (near 12° elevation), traveled back along the previously ionized leader path (Ogawa & Brook, 1964), and terminated in the upper-positive charge region (near 21° elevation) without extending the channel significantly further. The K events are seen in Figure 2d as vertical columns of INTF sources, traveling a large elevation (9° or ≃4.5 km) over short time periods (≃300 μs), or with speeds on the order of 1.5 × 10⁷ m/s. The absence of recorded INTF and FA data between 60 and 160 ms following an early K event was due to the VHF radiation being weak and not retriggering the INTF recording until later in the flash. Even then, the LMA and INTF observations show that the negative channel had not developed further into upper-positive charge region. Instead, the ensuing, subsequent K events repeatedly stopped in a relatively localized upper positive charge at the upper extent of the vertical channel established in the first 3–4 ms of the flash.

The EIP occurred about 3 ms into the flash and repeatedly discharged a region of localized positive charge at the uppermost end of the flash. The flash-initiating NBE and EIP are depicted in Figure 2d by the two groups of high-power INTF sources (large yellow diamonds) near 14° and 18° elevation, respectively. In Figure 2c, the NBE and EIP locations are roughly indicated by arrows and correspond to the two large FA pulses and saturated INTF signals seen in Figures 1e and 1f.

3.3 Pre-EIP Breakdown

Figure 3 shows an expanded view of the first 3.8 ms of the flash, starting before the NBE and ending about a half millisecond after the EIP. Figure 3a shows the upward development of the negative breakdown versus time, while Figures 3b–3h show the development during successive time intervals in elevation-azimuth projection. The complete elevation versus azimuthal development is shown in Figure 3i. The NBE that initiated the flash, Figure 3b, was produced by downward FPB that descended ≃400 m in 4 μs, corresponding to a speed of ∼10⁸ m/s, at the upper end of observed FPB speeds (Rison et al., 2016). Expanded views of the flash-initiating NBE are shown in Figure A4 of the Appendix, which also shows that the NBE breakdown exhibited little horizontal spread relative to its vertical extent. The NBE produced a 24 V/m peak electric field change (8 V/m range-normalized to 100 km), and a fast ( $urn:x-wiley:jgrd:media:jgrd56523:jgrd56523-math-0003$ s) exponential rise in VHF power, that quickly saturated the VHF signal. It also initiated breakdown ≃200 m in vertical extent directly above the NBE starting point.

Despite the strength of the NBE, and instead of launching the upward leader, the discharge appeared to die out after about ≃100 μs, causing the flash to become relatively quiescent. For ≃1.4 ms, occasional INTF and LMA sources (Figures 3c and A2 and Table A1) continued to occur immediately above the NBE in the flash start region, which eventually strengthened and launched an upward negative breakdown about 1.53 ms into the flash (Figure 3d). The speed of the upward breakdown was initially fast, ≃3 × 10⁶ m/s, slowing down to ≃5 × 10⁵ m/s by the time of the downward step at 2.6 ms (Figure 3e). The step was signaled by a transient FA sferic (Figure A5) that appears to be produced by new breakdown several hundred meters back down and off to the left side of the slowed-down activity of interval (d). The new breakdown continued to progress up the left side of the (d) activity before reaching the previously attained altitude (interval f), at which point a second, stronger downward FA and INTF transient occurred that initiated exceptionally fast (≃1.2 km in 200 μs, or ≃6 × 10⁶ m/s) upward negative breakdown into virgin air. In the process, the VHF power of the breakdown increased exponentially with distance by a factor of 6 or so, culminating in the EIP.

3.4 EIP Detailed Observations

Figure 4 shows an expanded view of the temporal and spatial evolution of the EIP activity, corresponding to interval (h) of Figure 3. As seen in Figures 4a and 4c–4f, the breakdown leading up to and during the EIP consisted of a complex sequence of repeated downward and upward breakdown events of increasing vertical extent, back and forth along the path traversed by the fast 6 × 10⁶ m/s upward breakdown at the end of the pre-EIP interval. The pseudo-oscillatory breakdown behavior was accompanied by a sequence of three large-amplitude sferic pulses, each lasting ≃20 μs between 3.25 and 3.31 ms, with a NLDN-determined peak current of 247 kA. The polarity of the sferics was positive, indicative of downward currents being produced by downward positive or upward negative charge motion. The EIP culminated in a strong burst of VHF radiation produced by a particularly high power downward/upward sequence of the INTF sources during the final part of the EIP. From the LMA observations of the burst (red circle in Figure 4a), the peak power of the burst reached ≃115 kW.

The INTF sequences preceding the EIP are shown by the black sources at the beginning of Figure 4a. The propagation speeds during this time were on the order of one to a few times 10⁷ m/s, typical of streamer-based FPB and FNB (Rison et al., 2016; Tilles et al., 2019). As discussed above, the repeated sequences were of increasing vertical extent and occurred back along the same path as the preceding 6 × 10⁶ m/s upward breakdown, indicating the absence of a leader along the path. Rather, both the 6 × 10⁶ m/s upward breakdown and repeated sequences were likely streamer based and were presumably involved in initiating the EIP. Indeed, the black sources were followed by the initial sferic pulse of the EIP, between 3.255 and 3.272 ms and, at the same time, the largest vertically extensive (≃1.3-km) and fastest downward/upward sequence up to that point in the flash (colored sources propagating downward in Figure 4c and upward in Figure 4d, centered on 3.262 ms in Figure 4a). The apparent propagation speeds of this complex event are difficult to ascertain but were on the order of 10⁸ m/s and even approaching the speed of light, making it unclear if some of the altitude changes represented a physically propagating breakdown front.

The 1.3 km event was followed by the onset of the main EIP pulse, starting at 3.272 ms in Figure 4a. The first half of the main pulse was accompanied by downward FPB having a propagation speed of ≃5.7 × 10⁷ m/s (the mostly blue sources in Figure 4e) but was otherwise relatively weak in VHF. In particular, it was much less strong than the flash-initiating NBE and would not have accounted for the highly energetic main sferic of the EIP. Instead, the weaker VHF of the first-half FPB event was overridden by the stronger VHF of a second, much more powerful FPB event during the second half of the sferic, which the sferic apparently initiated. The second-half event is seen as the increasingly yellow symbols in Figure 4a and the white sources in Figure 4e, which started about ≃500 m back up along the preceding FPB, near the top of the preceding breakdown, and descended ≃700 m in 5.5 μs, corresponding to a speed of ≃1.2 × 10⁸ m/s. In the process, the VHF radiation increased exponentially with time, causing the VHF signal to saturate within a few microseconds. As is typically observed for initial pulses of NBEs (Rison et al., 2016; Tilles et al., 2019), the downward FPB was immediately followed by upward FNB that propagated back up and beyond the same channel. The FNB lasted 50–60 μs, extending the breakdown up to 20.5° elevation (≃11.5 km). Its propagation speed was ≃4.2 × 10⁷ m/s initially, slowing down to ≃1.3 × 10⁷ m/s by the end.

Figure 5 shows the EIP observations in more detail, both in support of the above results and to illustrate how the EIP compares with similarly scaled NBE observations. Several features of interest are seen in the plots. The first feature, and as also seen in Figures 4a and 4b, is that the EIP sferic peaked noticeably before the VHF. Rather than the two being closely correlated, as for the NBE, the EIP peak occurred about ≃7 μs before the LMA-indicated VHF peak. Significantly, the onset of the strong VHF emissions, and corresponding INTF sources, began at the same time as the sferic peak. This provides clear support for the idea that the relativistic avalanching responsible for the sferic actually initiated the high-power, NBE-like event of the EIP. The second feature is that the sferic associated with the NBE-like event is seen as a perturbation on the falling edge of the otherwise smoothly varying sferic of the EIP. The two field changes are superimposed upon each other, further indicating they are separate physical processes. Using a simple envelope technique, we identified and approximately separated the two components (see Figure A6 of the appendix), with the NBE-like perturbation shown explicitly in Figure 5d (red waveform). Similar to the flash-initiating NBE in Figure 5c, the NBE-like perturbation was initially spike like and became more gradual with time, and its onset was closely correlated with the VHF onset. We further separated the NBE-like sferic from the EIP sferic by utilizing Ensemble Empirical Mode Decomposition (EEMD) (Fan et al., 2020), shown in Figure A7 of the Appendix, and determined the peak current moment (−26.1 kA-km) and charge-moment change (0.62 C-km) of the NBE-like event, which is consistent with other NBE observations (Liu et al., 2019; Rison et al., 2016; Tilles et al., 2019). The resulting filtered EIP sferic gives a slightly higher peak current moment (−298.3 kA-km) and smaller charge-moment change (13.1 C-km) than the unfiltered values given in Table 2.

Taken together, the above observations provide a clear indication that the smooth component of the EIP sferic was produced separately from that produced by the VHF-radiating fast breakdown processes. The smooth component was presumably produced by relativistic electron avalanching, which would not have radiated strongly in VHF (Dwyer & Cummer, 2013), whereas the VHF is generally associated with streamer activity (Rison et al., 2016; Shi et al., 2016, 2019). The fast streamer events were undoubtedly involved in initiating the avalanching breakdown, but the opposite would also appear to be true. In particular, the avalanching that produced the main EIP peak appears to have also initiated the breakdown of the final, strong downward/upward NBE-like streamer event.

3.5 Storm Context

The observations raise interesting questions about the storm conditions that lead to EIP production. Of particular interest is why the EIP-producing flash consistently and repeatedly discharged a relatively localized region of upper positive charge in the storm. The localized nature of the breakdown in the upper positive charge region during the EIP flash is seen in the overlays of Figure 2, both before and after the EIP, while previous and subsequent IC flashes propagated more extensively through the upper positive charge region.

Figure 6 shows LMA observations that help to answer the above question. Figure 6a shows the lightning activity over a ≃3-min period around the time of the EIP flash, and Figure 6b shows the LMA-inferred charge density over a broader 10-min time interval. Here, LMA source density serves as a proxy for storm charge density since breakdown propagates more extensively in higher-density charge regions (Hamlin, 2004; Krehbiel et al., 2008; Marshall et al., 2005; Rust et al., 2005), and the regions are colored according to the LMA-determined storm charge polarity. Four flashes are shown in Figure 6a, with the EIP flash shown in red. The EIP occurred during the fourth flash in a new cell that developed on the eastern edge of the relatively small and localized storm. Leading up to the EIP, the lightning activity increased from a maximum altitude of ≃10 km to a new maximum of ≃13 km over a ≃5-min time period. Of particular interest is the second preceding flash before the EIP, labeled IC2 and shown in blue in Figure 6a. IC2 was almost identical to the EIP flash, in that it occurred between midlevel negative storm charge (blue region in Figure 6b) and the upper positive charge (yellow-orange region above the negative charge) in the newly formed cell. Both flashes were initiated by high power NBEs (51.1 and 46.6 dBW, respectively), and both discharged remnant, horizontally distributed negative charge toward the end of their development in the older part of the storm to the west. In the process, however, IC2 propagated horizontally through the upper part of the upper positive charge region, whereas the EIP flash did not.

Comparing the vertical projections of the red and blue LMA sources in Figure 6a, it appears that IC2 had an effect on the development of the EIP flash. Namely, IC2 discharged a region of upper positive charge that restricted the upper part of the EIP flash to a small localized region that had not been traversed by IC2. The two flashes were separated in time by 97 s, a substantially longer interval than the average flash rate of 1.4 min⁻¹, or every 43 s. The relatively long time difference allowed for additional charging to occur (Hendry & McCormick, 1976; Krehbiel et al., 1996) and for the EIP flash to be as energetic as its predecessor. Ordinarily, this would also have allowed the upper positive region discharged by IC2 to be replenished. But for some reason, this appeared not to happen, and the positive charge was highly localized by the time of the EIP flash. The anomalously localized nature of the upper positive charge is also seen as the intense red-orange area over the 10-min charge density plots of Figure 6b.

The observations provide a possible explanation for why the EIP flash was confined in the upper positive charge region, while at the same time explaining why the discharges were highly energetic, as being due to the low flash rate and relatively long time interval between the two flashes in question, allowing strong electrical forces to build. That the storm was strongly electrified is further indicated by the next discharge in the storm, occurring 65 s after the EIP flash, labeled CG5 and shown in brown in Figure 6a. CG5 had an initial return stroke of unusually large peak current (136 kA) for a negative CG flash (Nag & Cummins, 2017).

4 Discussion

In an effort to understand how EIPs are produced and gain insight into TGF generation, we have presented sub-microsecond VHF radio mapping of an EIP, providing over an order of magnitude finer temporal detail than previously reported TGF-related VHF observations (Lu et al., 2010; Lyu et al., 2016, 2018; Mailyan et al., 2018). Given that EIPs can serve as proxy for a subpopulation of TGFs (Cummer et al., 2017; Lyu et al., 2016), and that the observed EIP sferic developed independently from the VHF emissions generally associated with streamer activity (Liu et al., 2019; Rison et al., 2016; Shi et al., 2016, 2019), our study provides strong evidence that the EIP sferic was not produced by conventional lightning processes (i.e., streamers and leaders), but by the relativistic electrons and associated ionization of a TGF-producing discharge. The VHF and sferics development contrasts the EIP with other lightning processes, including NBEs and IBPs, whose sferics and VHF emissions are closely correlated in amplitude and time, appearing to initiate and evolve near simultaneously (see Liu et al., 2019; Rison et al., 2016; Tilles et al., 2019 for NBE emissions, and Kolmasova et al., 2018; Krider et al., 1979; Stanley et al., 2018; Stock, 2014; Wu et al., 2016 for IBP emissions). Together with recent observations that downward TGFs occur during IBPs (Abbasi et al., 2019; Krehbiel et al., 2019), the contrasting development of the EIP and IBP emissions suggests that the energetic photons produced in each case may be due to different mechanisms. The large amplitude of the EIP sferic and consequently the large currents (≃247 kA) involved point to RFDs (Dwyer, 2012; Liu & Dwyer, 2013) as the EIP production mechanism. In addition, RFDs can produce a substantial current without necessarily emitting strongly in VHF (Dwyer & Cummer, 2013), and RFD-generated currents can influence streamer development, as has been described both conceptually (Dwyer, 2005; Petersen et al., 2008) and suggested based on detailed modeling work of RFDs (Liu & Dwyer, 2013). The high-power (50.6 dBW) NBE-like event that was triggered during the peak-amplitude EIP sferic pulse was likely an instance of RFD-initiated streamer development. In contrast with the MeV gamma rays generated during EIPs (Lyu et al., 2016), the ∼100 keV X-rays observed during negative stepped leaders to ground are likely generated by cold runaway (Dwyer et al., 2003, 2005), in which relativistic electrons avalanche ahead of advancing stepped leaders, causing the accompanying sferics and VHF radiation to be correlated.

It is not clear how the activity preceding the EIP would initiate a RFD, but the activity likely played a role in generating and accelerating electrons to the required energies and fluences. Our observations are summarized as follows: (1) The EIP flash was initiated by a high-power (46.6 dBW) NBE. (2) The negative leader started about 1.53 ms into the flash and propagated vertically upward at an unusually fast speed (5 × 10⁵ to 3 × 10⁶ m/s) compared with typical IC negative leader speeds of 1–3 × 10⁵ m/s (Shao et al., 1995; Shao & Krehbiel, 1996; van der Velde & Montanya, 2013). (3) Faster, 6 × 10⁶ m/s negative breakdown was initiated ≃200 μs before the EIP, which propagated vertically upward more than 1 km and was accompanied by increasing VHF power. (4) The EIP was immediately preceded and accompanied by a succession of fast (10⁷–10⁸ m/s) downward/upward breakdown sequences, each lasting 10 to 20 μs and growing in extent leading up to the EIP. Each downward/upward sequence retraced the same >1-km altitude volume as the preceding 6 × 10⁶ m/s negative breakdown. Given that leaders can maintain their conductivity for tens of microseconds up to milliseconds (Bazelyan & Raizer, 1998, p. 226), the volume could not have contained a hot, compact, highly conductive leader, else the repeated breakdown could not have occurred there in such quick succession. Thus, the EIP was preceded by and appeared to be triggered by repeated large-scale streamer activity. (5) The EIP occurred about 3 ms into the flash and lasted ≃60 μs, having an associated peak current of 247 kA, and consisting of three sferic pulses, presumably caused by RFDs. Fast downward/upward streamer sequences of kilometer extent continued to occur in the same volume during the EIP, but the VHF emissions were weak and apparently not correlated with the sferics. (6) Shortly after the EIP sferic peak, a high-power (50.6 dBW) NBE-like event initiated. As in previous observations of NBEs (Rison et al., 2016; Tilles et al., 2019), the NBE-like event consisted of downward FPB followed immediately by upward FNB that propagated vertically upward back along a path previously traversed by FPB, and beyond that into virgin air. By definition, the sferic peak corresponded to the peak in dM_I/dt, the time derivative of the current moment. Hence, it appeared that the peak rate of change of the current moment of a relativistic discharge triggered the NBE-like event. (7) The same volume that was discharged by the pre-EIP and EIP activity was further discharged in its entirety by at least nine fast-propagating (∼10⁷ m/s) K events during the remaining ≃300 ms of the flash. The K events did not extend the channel significantly further than during the EIP, terminating instead in the same enhanced upper-positive charge region that was discharged during the EIP.

The unusual lightning flash that generated the EIP resulted from an equally unusual thunderstorm. The storm experienced relatively long charging intervals between lightning flashes, and a particularly long interflash interval (200% longer than the mean interflash interval of the storm) immediately preceded the EIP flash, providing further evidence for extended charging periods prior to TGF generation (Larkey et al., 2019). The storm somehow produced a locally enhanced region of upper positive charge, seen as the concentrated (intense red-orange) charge density region in Figure 6b. The concentrated positive charge was repeatedly discharged by the preceding streamer activity, the EIP discharge activity, and subsequent K-events. One question is whether or not a concentrated region of positive charge is a controlling factor in EIP generation. In order for a RFD to take place, the relativistic runaway electron avalanche (RREA) threshold field (2.8 × 10⁵ V/m at sea level) must be exceeded over a large volume so that the relativistic feedback threshold will be crossed (Dwyer, 2003, 2012). The repeated streamer sequences before the EIP indicate that the electric field was at least as high as the critical field for positive streamers (4.4 × 10⁵ V/m at sea level (Qin & Pasko, 2014)) for at least several tens of microseconds over a large (>1 km altitude) volume. It is likely that RREAs took place in the same volume and possibly beyond, so long as the electric field was above the RREA threshold field. The concentrated positive charge would have enhanced the electric field, and this may have increased the feedback factor (Dwyer, 2012; Liu & Dwyer, 2013). Additionally, the 6 × 10⁶ m/s negative breakdown would have enhanced the field ahead of it, possibly pushing the RREAs above the feedback threshold and triggering a RFD, which would become the dominant discharge mode, producing the EIP and masking the sferics of lesser discharges. It is unclear if the repeated streamer sequences immediately preceding the EIP played a critical role in triggering a RFD by providing localized field enhancements within the volume. Alternatively, the repeated sequences may just be an indication that the volume was not discharged uniformly by the 6 × 10⁶ m/s negative breakdown or might otherwise be caused/influenced by RFD-generated currents (Dwyer, 2005; Liu & Dwyer, 2013; Petersen et al., 2008). It also remains to be investigated if EIPs tend to trigger high-power VHF emissions, as in the high-power NBE-like event that occurred in the latter stage of the EIP. We have shown that perturbations due to streamers can be differentiated from the smooth sferics produced by avalanching electrons, and, together with our observations, this shows a complex interdependence between storm activity, streamer development, and relativistic discharge processes, giving important insight into EIP generation.

Acknowledgments

This research was supported in part by NSF Grants AGS-1552177, AGS-1613260, and AGS-1720600 and AFOSR FA9550-16-1-0396 and FA9550-18-1-0358. This work complies with the AGU data policy.

A

Figure A1 shows a plot of LMA and NLDN data for the entire EIP flash, with the LMA data colored by time. Both the flash-initiating NBE and the EIP constitute high-peak-current events that were detected by the NLDN in the first few milliseconds of the flash and are shown in more detail in Figure A2. Table A1 lists the LMA and NLDN output corresponding to Figure A2, starting from the flash-initiating NBE and ending about 1 ms after the EIP.

Table A1. (continued)

Selected NLDN Events, sources = 2, date = 2016-09-24, start time = 00:55:12.704868565 UT, duration = 3.272039 ms
t (μs)	I_pk (kA)	pulse type	lat	lon	t (seconds)
4.895	+17.0	C	28.3085	−80.4688	3,312.704868565
3276.934	+247.3	G	28.3033	−80.4739	3,312.708140604

Note. The LMA data include the source time in microseconds since the flash-initiating NBE LMA source; the LMA-determined peak VHF power; the $urn:x-wiley:jgrd:media:jgrd56523:jgrd56523-math-0005$ goodness-of-fit value; the number of stations participating in a LMA source solution; the LMA source latitude, longitude, and altitude; the time in seconds since midnight; the LMA source plan distance from the INTF/FA; and the LMA source azimuth and elevation with respect to the INTF/FA. Note that the average LMA plan distance before and after the EIP remains around 30.6 km. For comparison, the NLDN data include the time in microseconds since the flash-initiating NBE LMA source, the pulse peak current and polarity, the determined pulse type (either “C” for in-cloud or “G” for cloud-to-ground), the longitude and latitude of the pulse, and the time of the pulse in seconds since midnight.

Figure A3 demonstrates how the INTF data were used to determine the propagation speeds of breakdown events leading up to and during the EIP. In particular, Figure A4 shows the detailed INTF and FA data for the flash-initiating NBE, showing the speed determination for the fast positive breakdown that caused the NBE. Moreover, the coincident onset of the FA and VHF signals for the NBE is shown. Similarly, Figure A5 shows the detailed INTF and FA data of an apparent step that preceded the EIP–the downward-then-upward fast breakdown is reminiscent of the downward-then-upward breakdown during the EIP, but of much shorter extent and with a clear correlation between the FA and VHF signals, unlike the EIP (cf. Figure A3, bottom panel).

The EIP sferic and VHF emissions instead evolve independently, with a VHF burst that lags the onset of the sferic peak by about 12 μs. The VHF burst is indicative of a NBE-like event, with the sferic of the NBE-like event superimposed on the EIP sferic. The NBE-like perturbation is approximately separated from the EIP sferic using a simple envelope function in Figure A6, and the NBE-like sferic amplitude is more realistically determined using Ensemble Empirical Mode Decomposition (EEMD) in Figure A7.

Open Research

Data Availability Statement

The data are available online (at https://doi.org/10.6084/m9.figshare.11833488.v1).

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Citing Literature

Volume125, Issue20

27 October 2020

e2020JD032603

Radio Interferometer Observations of an Energetic in-Cloud Pulse Reveal Large Currents Generated by Relativistic Discharges

Abstract

Key Points

1 Introduction

2 Instrumentation and Observations