GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 4067–4073, doi:10.1002/grl.50742, 2013

Properties of the thundercloud discharges responsible for terrestrial gamma-ray flashes Joseph R. Dwyer,1 Ningyu Liu,1 and Hamid K. Rassoul1 Received 13 June 2013; revised 10 July 2013; accepted 11 July 2013; published 8 August 2013.

[1] The source of terrestrial gamma-ray flashes (TGFs) has followed by observations by the Reuven Ramaty High been an active area of research since their discovery by Energy Solar Spectroscopic Imager (RHESSI) [Smith et al., Compton Gamma-Ray Observatory/Burst and Transient 2005; Grefenstette et al., 2009; Gjesteland et al., 2012], Source Experiment in 1994. These intense bursts of Fermi [Briggs et al., 2010, 2013], and AGILE spacecraft gamma rays originate within thunderclouds via the rapid [Marisaldi et al., 2010a, 2010b; Tavani et al., 2011]. production of relativistic runaway , accelerated [3] TGFs have been shown to be associated with the initial by thundercloud/ electric fields to multi-MeV stage of moderately strong positive intracloud (+IC) light- energies. Recent studies have shown that electrical ning [Cummer et al., 2005; Williams et al., 2006; Stanley discharges within thunderclouds caused by these runaway et al., 2006; Lu et al., 2010; Shao et al., 2010; Cummer electrons can generate currents that rival those of et al., 2011; Østgaard et al., 2013], presumably during the lightning and so could serve as an alternative discharge time when the negative is in the process of bridging path for thunderclouds. In particular, the discharges the gap between the negative and positive charge regions in- responsible for TGFs produce some of the largest side the thundercloud. amplitude VLF-LF radio pulses from thunderstorms and, [4] Spacecraft measurements, along with modeling of the indeed, were previously misidentified as lightning. In this propagation of the gamma rays up and out of the atmosphere, article, we shall provide a brief review of TGFs have found that the source altitudes of the gamma rays must and present calculations of their electrical properties be below about 20 km [Dwyer and Smith, 2005; Carlson inside thunderclouds and their gamma-ray and optical et al., 2007; Gjesteland et al., 2010; Xu et al., 2012], within emissions. We shall show that the lightning-like events the altitude range of thunderstorms. The spectra of TGFs responsible for TGFs emit relatively little visible light (up to a few tens of MeV) are consistent with and, thus, are inherently dark. Citation: Dwyer,J.R., emissions from energetic electrons accelerated by strong N. Y. Liu, and H. K. Rassoul (2013), Properties of the thundercloud electric fields within the thunderclouds [Dwyer and Smith, discharges responsible for terrestrial gamma-ray flashes, Geophys. 2005; Carlson et al., 2007; Xu et al., 2012], although there Res. Lett., 40,4067–4073, doi:10.1002/grl.50742. is currently some debate about the spectra at very high energies (~40–100 MeV) [Tavani et al., 2011; Celestin et al., 2012]. Calculations based upon RHESSI observations 1. Introduction show that at the source, for each recorded TGF, the thunder- 17 [2] Terrestrial gamma-ray flashes (TGFs) are intense storm must have produced about 10 high-energy electrons bursts of gamma rays that originate from thunderstorms (average energy is 7 MeV), in order to account for the fluence [Fishman et al., 1994]. They have durations ranging from a of gamma rays recorded at the spacecraft many hundreds of few tens of microseconds to a few milliseconds [Fishman kilometers away, although it is possible that some observed et al., 2011; Briggs et al., 2013] and produce the highest TGFs occur deeper in the atmosphere, requiring more high- energy emission of natural phenomena originating from energy electrons at the source (see example in section 4 within the Earth’s atmosphere, with particle energies typi- below) [Dwyer and Cummer, 2013]. cally reaching several tens of MeV [Dwyer and Smith, [5] It is a challenge to develop models that can explain 2005; Tavani et al., 2011; Dwyer et al., 2012]. TGFs are how large numbers of high-energy electrons are generated relatively common, with a thousand or more produced so rapidly deep within the atmosphere [Dwyer, 2008]. In around the planet each day [Østgaard et al., 2012; Briggs recent years, two main explanations have emerged: One et al., 2013]. Paradoxically, even though they originate from involves ordinary lightning, and the other involves an exotic deep within the atmosphere, at altitudes where aircraft kind of discharge generated by X-rays and high-energy routinely fly, the vast majority of TGFs that have been positrons. In this paper, we shall review these models and recorded so far were almost all observed by spacecraft in show that the latter generates lightning-like electric currents low Earth orbit, starting with the Compton Gamma-Ray while producing little visible emission. Observatory in the early 1990s [Fishman et al., 1994],

1Department of Physics and Space Sciences, Florida Institute of 2. Runaway Physics Technology, Melbourne, Florida, USA. [6] To understand the underlying mechanism for produc- Corresponding author: J. R. Dwyer, Department of Physics and Space ing high-energy electrons in air and their accompanying Sciences, Florida Institute of Technology, 150 W. University Blvd., X-ray and gamma-ray emissions, the rate that electrons lose Melbourne, FL 32901, USA. (jdwyer@fit.edu) energy while traveling through air must be considered. The ©2013. American Geophysical Union. All Rights Reserved. energy loss per unit length, predominantly from 0094-8276/13/10.1002/grl.50742 (solid curve) and bremsstrahlung losses (dashed curve), is

4067 DWYER ET AL.: PROPERTIES OF TGF DISCHARGES

1000 Hard scattering events, either Møller scattering (electron- electron elastic scattering) or bremsstrahlung, can be seen eEc as sudden drops in the energy in the individual electron trajectories (black). 100 [8] The simulation shown in Figure 2 was initiated by eE injecting one 5 MeV positron (upper blue trajectory) at the right side of the plot. Like the energetic electrons, the posi-

(keV/cm) tron gains energy and runs away, but in the opposite direction F 10 of the electrons, eventually reaching almost 50 MeV on the left side of the figure. As positrons propagate, they experi-

eE ence hard scatters with atomic electrons (Bhabha scattering), b producing energetic secondary electrons that may also run 1 -2 0 2 4 6 away. These secondary electrons generate the runaway 10 10 th 10 10 10 seen in the figure. As the runaway elec- kinetic energy (keV) trons propagate through air, they produce bremsstrahlung Figure 1. Energy loss per unit length experienced by a free X-rays and gamma rays, some of which may escape and be electron (or positron) moving through air at STP as a function observed as a TGF. Others will pair-produce within the of kinetic energy. Figure from Dwyer [2004]. avalanche region, creating additional positrons that may also run away. Such a secondary positron is seen in Figure 2 (lower blue trajectory). In this way, a positive feedback loop plotted in Figure 1 versus the kinetic energy of the energetic may occur, with more making more electron (or positron). When a moderately strong electric positrons, which make more runaway electrons, etc. This field is applied (e.g., Figure 1, horizontal line), for energetic mechanism is called positron feedback [Dwyer, 2003]. A particles with kinetic energies below εth, the rate of energy similar feedback cycle may be also created via the loss is greater than the rate of energy gain, causing the Compton backscattered X-rays, called X-ray (gamma-ray) electrons to decelerate and stop. However, above εth, the feedback [Dwyer, 2003, 2007; Babich et al., 2005]. electrons will gain more energy from the field than they lose Together, these mechanisms are called relativistic feedback to the air. These are the so-called runaway electrons, first [Dwyer, 2007]. Relativistic feedback allows the production described in Wilson [1925]. Monte Carlo simulations have of the high-energy particles to be self-sustaining, resulting shown that the minimum electric fieldrequiredforelec- in an explosive growth of energetic radiation on the time trons to run away and propagate long distances is scale, typically, of tens of microseconds. Relativistic feed- 5 Eth =2.8×10 V/m × n [Dwyer, 2003; Babich et al., back discharges (RFDs) may be viewed as a novel form of 2004], where n is the density of air relative to that at sea , analogous to the Townsend breakdown level at standard conditions. This is slightly higher than at low energies [Brown, 1966; Dwyer, 2007]. Unlike conven- the so-called breakeven field, Eb, which corresponds to tional electrical breakdown, which requires strong electric 6 the minimum of the curve in Figure 1. At a very large field, fields greater than Ek ~3×10 V/m × n, RFDs only require 7 Ec ~3×10 V/m × n, virtually all free electrons may gain moderate electric field strengths, on the order of Eth, albeit energy and run away [Gurevich, 1961; Moss et al., applied over large length scales with large electric potentials. 2006]. This “thermal runaway” mechanism, operating in the high fields associated with lightning leaders and streamer tips, is thought to be responsible for the X-ray 3. TGF Models emissions observed from lightning near the ground [9] There are currently two main classes of TGF models [Moore et al., 2001; Dwyer et al., 2003; Dwyer, 2004; under active investigation: lightning leader models and the Moss et al., 2006]. As will be discussed below, this relativistic feedback discharge model. A third class of models mechanism has also been proposed as an explanation for involves atmospheric cosmic rays seeding RREAs in large TGFs [Dwyer, 2008; Celestin and Pasko, 2011; Celestin et al., 2012]. 105 [7] As energetic electrons ionize the air, some of the E = 1000 kV/m secondary electrons can be energetic enough to also run away. These secondary electrons will gain energy and 104 generate additional electrons that will run away and so on. The result is an avalanche of energetic runaway electrons that 103 grows exponentially with time and distance. This mecha- (keV) nism, which was first described by Gurevich et al. [1992], is commonly called the relativistic runaway electron ava- 102 lanche (RREA) mechanism and has been investigated in many papers [e.g., Symbalisty et al., 1998; Lehtinen et al., 101 1999; Gurevich and Zybin, 2001; Dwyer, 2003; Babich 0 10 20 30 40 50 60 et al., 2004, 2005; Coleman and Dwyer, 2006; Roussel- Z (m) Dupré et al., 2008; Celestin and Pasko, 2010; Dwyer, 2010; Dwyer and Babich, 2011; Babich and Bochkov, Figure 2. Monte Carlo simulation of (black) electrons and 2011]. Such an avalanche can be seen in Figure 2, which (blue) positrons moving through air at STP for an electric shows the results of a detailed Monte Carlo simulation. field strength of 1000 kV/m.

4068 DWYER ET AL.: PROPERTIES OF TGF DISCHARGES electric fields that may appear above thunderclouds after IC or cloud-to-ground (CG) lightning [e.g., Lehtinen et al., 1999; Gurevich and Zybin, 2001; Babich et al., 2008a, 2008b]. Because TGFs are observed to occur during the initial stage of +IC lightning, before a large amount of charge is transferred within the cloud, these models do not appear to explain most TGFs (for more discussion on this topic, see Dwyer [2008]). [10] In contrast, lightning leader models are based upon the observations that negative lightning leaders emit hard (hundreds of keV) X-rays as they approach the ground [Dwyer et al., 2004], possibly caused by thermal runaway electron production [Dwyer, 2004; Moss et al., 2006]. Because the potential difference available to the runaway electrons in front of the lightning leaders near the ground apparently never reaches the tens of megavolts needed to generate RREAs, the resulting X-ray energy spectra are much softer than TGFs [Saleh et al., 2009; Schaal et al., 2012]. However, it has been conjectured that for lightning Figure 3. Average energy spectrum of TGFs as measured leaders within thunderclouds, the potential differences by the (circles) RHESSI spacecraft along with (solid and available to the runaway electrons in front of the lightning dashed lines) model fits. The inset shows the dependence of leaders could be much larger than near the ground, perhaps the spectra on source altitude. The RFD model will produce large enough to produce a TGF [Dwyer, 2008]. Calculations the same energy spectrum as the RREA model and so also based upon the production rate of runaway electrons from agrees with the RHESSI TGF data. Figure courtesy of Xu lightning near the ground and reasonable assumptions about et al. [2012]. thunderstorm electric fields show that this mechanism could account for the number of gamma rays in a TGF [Dwyer, 2008; Saleh et al., 2009; Dwyer et al., 2010; Dwyer et al., RHESSI data match the RREA spectrum shows that rather 2012]. On the other hand, it is unclear if this mechanism is large potential differences must be involved in the production consistent with the radio emissions observed in association of TGFs, with several RREA avalanche lengths present. with TGFs [Dwyer and Cummer, 2013], and so, more work [12] Alternatively, the RFD model of TGFs assumes that a is needed on this topic. Several papers have modeled self-sustaining relativistic feedback discharge is created in various aspects of the lightning leader mechanism, espe- the large-scale electric field region inside the thundercloud. cially with the scenario that the runaway electron’senergy This model also involves large electric potentials with several gain occurs primarily in the electric fields generated by the RREA avalanche lengths and so also produces a RREA lightning leaders [Gurevich et al., 2007; Carlson et al., energy spectrum (black curve) consistent with the RHESSI 2009, 2010; Celestin and Pasko, 2011; Celestin et al., data, as seen in Figure 3. 2012; Mallios et al., 2013]. [13] According to the RFD model, as a thundercloud [11] Figure 3 shows TGF model results for thermal run- charges, the amount of runaway electron avalanche multi- away electron emission from lightning leaders inside thun- plication may increase until the system approaches the derstorms as calculated by Xu et al. [2012], plotted with self-sustaining feedback threshold. Once the feedback TGF data measured by RHESSI. The RHESSI data are the threshold is crossed, the electric current produced by the average spectrum for many TGFs, recorded with a range of runaway electrons grows very rapidly, partially discharging spacecraft positions relative to TGF source location [Dwyer that region of the storm [Dwyer, 2012; Liu and Dwyer, and Smith, 2005; Xu et al., 2012]. Two different thunder- 2013]. One possible mechanism for rapidly pushing the storm potential differences are shown (red and dashed green system above the feedback threshold is for +IC lightning to curves), along with the results for the standard RREA calcu- discharge part of the avalanche region, enhancing the field in lation (black curve). As can be seen, the three curves and the the remaining part. Detailed, self-consistent simulations data all agree at low energies. However, at high energies show that when a thundercloud and IC lightning are modeled (e.g., >107 eV), the spectrum predicted by the lightning in this way, a large RFD occurs, which naturally has many leader model with a 100 MV thundercloud potential (red of the same properties as TGFs, including similar time struc- curve) rolls over much quicker than the TGF data. Better tures, gamma-ray fluences, RF emissions, and association agreement is achieved with the 200 MV thundercloud poten- with +IC lightning. A prediction of the RFD model is that tial difference (dashed green curve), but the RREA model large current-moment pulses (many tens of kiloamperes- gives the best fit to the RHESSI TGF data. At even larger kilometer) are generated by the runaway electrons and their potentials, the lightning leader model will produce the same accompanying ionization, which track the time profile of spectrum as the RREA model since the runaway electrons the gamma-ray emission [Dwyer and Cummer, 2013]. created by the lightning leader will undergo a large amount [14] These large current-moment pulses, in turn, produce of additional RREA multiplication. The X-ray emission from strong radio pulses in the LF-VLF range, which have been lightning seen near the ground, which rarely extends beyond measured. The connection between TGFs and large radio a few MeV, is an extreme example of the soft spectra that can pulses has been known for many years, but the radio pulses be generated by lightning leaders when only small potential were previously interpreted as resulting from normal light- differences are present. In contrast, the fact that the ning discharges closely associated with the TGFs [Inan

4069 DWYER ET AL.: PROPERTIES OF TGF DISCHARGES

+ et al., 1996, 2006; Cohen et al., 2006, 2010; Lu et al., 2011; 2PN2 and 1NN2 are about 0.0312% and 0.46%, respectively, Connaughton et al., 2010]. In fact, it is possible that many of which are obtained by combining measurements of the + these radio pulses associated with TGFs were not actually fluorescence efficiency for 0-0 bands of 2PN2 and 1NN2 from normal lightning. Instead, it now appears that many of [Keilhauer et al., 2006] and the spectra derived from aurora these observations may have been measuring the currents measurements [Vallance-Jones, 1974]. The efficiency is τ produced by the TGFs directly [Cummer et al., 2011; reduced by a factor of 1 þ 0 at pressure p, where τ is the τc 0 Connaughton et al., 2013; Østgaard et al., 2013]. inverse of the Einstein coefficient, and τc is the inverse of the collisional quenching frequency. The term Fdnrev is 4. Optical Emissions the total energy deposited per unit volume per unit time by runaway electrons. The friction force Fd = eEdn, where e is [15] As discussed in section 3, it is possible that some or all 5 the elementary charge, Ed = 2.76 × 10 V/m [Dwyer, 2012], TGFs are produced by thermal runaway electron production and n is the density of air with respect to its value at sea level. in association with lightning leaders. In that case, these fi The symbol nre is the runaway electron number density, and TGFs are closely connected to speci c lightning processes v is the average speed of runaway electrons. The function f and may be viewed as a by-product of lightning. However, (p) characterizes the dependence of E on the pressure, because we do not yet know what the specific lightning opt where pQ is the pressure where τ0 = τc. The quenching processes are, it is difficult to calculate the optical emissions + altitudes of 2PN2 and 1NN2 are about 30 and 48 km, respec- associated with these TGFs, as there may be substantial tively, which are lower than 53 km for 1PN [Liu et al., 2006, lightning leader and streamer components. In this section, 2 2009], so that the 1PN2 emission intensity is negligible for we shall instead calculate the optical emissions produced the fluorescence emission. At thundercloud altitudes, the by relativistic feedback discharges, which are at least distribution of the fluorescence emission intensity follows partially decoupled from the lightning processes within that of the runaway electron density. the thundercloud. [18] In addition to the fluorescence emission from runaway [16] In addition to TGFs, early studies have attempted to electrons, low-energy electrons created by the RFD can model transient luminous events (such as blue jets, gigantic also excite N2 through collisions. At thundercloud jets, and red sprites) by calculating the optical emissions from altitudes, the lifetimes of the upper excited states of RREAs above thunderstorms [Lehtinen et al., 1999; Babich 1PN , 2PN , and 1NN + are very short, with the longest et al., 2008c, 2008d]. RFDs also involve RREAs, although 2 2 2 being those of 1PN2, a few tens of nanoseconds. Steady state they are created by a different mechanism and occur in a solutions of the model discussed in Liu and Pasko [2004] can different environment than in the previous studies. Unlike be used to find the emission intensity due to low-energy normal lightning, the RFD does not produce hot channels; electrons. therefore, there is no bright incandescent light. The main fl [19] Figure 4 shows the optical emissions from an RFD mechanisms for producing light by RFDs are the uores- producing a single-pulse TGF, which was studied in detail cence from runaway electrons and excitation of neutral previously [Dwyer, 2012; Liu and Dwyer, 2013]. The RFD molecules by low-energy electrons generated by the RFD. is driven by an upward propagating +IC lightning discharge To calculate the fluorescence emission intensity, we apply initiated at 0 ms between the lower negative and upper posi- an approach that has been used to study the fluorescence tive thundercloud charge layers (Q = ±36.5C) centered at 10 emission from extensive air showers [e.g., Keilhauer et al., 2006]. The main fluorescence emission consists of two and 15 km, respectively. The RFD becomes self-sustaining + at 0.36 ms and reaches its peak around 0.6–0.65 ms, and it emission band systems: 2PN2 and 1NN2. Their spectra are dominated by strong blue and UV lines. However, instead is quenched by the subsequent self-produced ionization. of using band-resolved Einstein coefficients and deactivation Even though the RFD is initiated by lightning in this case, constants [Keilhauer et al., 2006], we use the lumped values it may be viewed as a discharge path that is distinct from for each band system, as was done previously for modeling the lightning. At t = 0.65 ms, the runaway electron density 6 3 the optical emission of conventional streamers [Liu et al., has a maximum value of 9 × 10 m at an altitude of 14 km. The horizontal radius of the RFD discharge is about 2006, 2009]. With this approach, our calculations show that τ fl 500 m, and the ratio 0 is about 12 and 86 for 2PN and the uorescence yield in the wavelength between 300 and τc 2 + 400 nm produced by a minimum ionizing 0.85 MeV electron 1NN2, respectively. The results shown in Figure 4 can be in air is 1.9–2.4 photons/m near the ground, which agrees verified by using those numbers and equation (1). The with 2.5–4 photons/m calculated by Keilhauer et al. [2006] gamma-ray pulse shape, width, and magnitude shown in and 4 photons/m in the wavelength range between 300 and Figure 4a agree with a typical TGF observed by Fermi 430 nm measured by Lefeuvre et al. [2007]. These values [Briggs et al., 2010; Fishman et al., 2011]. change only slightly with altitude below 20 km. [20] The volume integrated optical intensity pulses [17] Here we focus on calculating the intensity of the emis- (Figures 4b–4d) coincide with the TGF pulse produced by sion produced by RFDs in the visible range of 390–700 nm. the RFD. Figures 4b and 4c show the intensities of the The volume emission rate in this wavelength range can also fluorescence emission generated by the runaway electrons, be calculated with the approach used by Keilhauer et al. [2006]: and Figure 4d shows the optical emission intensity of 1PN2 0 due to the low-energy electrons, assuming that an average ∑λϵ 1 E ¼ λ ðÞF n v ∝fpðÞn ; fpðÞ¼ : (1) opt τ0 d re re 1 1 wavelength of 1PN2 photons in the visible spectrum is 1 þ τ þ c p pQ 650 nm. The low-energy electrons do not have sufficient + energy to produce 2PN2 and 1NN2. The intensity pulse in 0 The quantity ∑λϵλ is the total fluorescence efficiency in Figure 4d is about 3 orders of magnitude smaller than those the visible spectrum without quenching, and its values for in Figures 4b and 4c. As a result, the RFD is purplish blue.

4070 DWYER ET AL.: PROPERTIES OF TGF DISCHARGES

2 (a) W) 8 t = 0.65 ms (R) 1 15 109 (10 (e) Gamma rays 0 (b) 14 2 2 W)

5 108

2PN 1

(10 13

6 (km)

+ (c) 12 2 W) 4 107 5

1NN 2 (10 11

8 (d) 6

2 6 10 10 W) −2 −1 0 1 2 1 4

1PN (km)

(10 2

0.4 0.5 0.6 0.7 0.8 0.9 1 Time (ms)

Figure 4. The optical emissions from a relativistic feedback discharge (RFD) producing a single-pulse TGF. (a) The + gamma-ray intensity. (b–d) The volume integrated optical emission intensities of 2PN2, 1NN2, and 1PN2 as a function of time. The right panel shows the total emission intensity distribution in rayleigh at the moment of the TGF peak produced by the RFD.

The total optical energy radiated is approximately 40 J, which the sum of path lengths of all the runaway electrons in the is many orders of magnitude smaller than that of normal thundercloud at 13 km is 3.9 × 1020 m for that event [Dwyer lightning [Uman, 2001]. Therefore, the RFD is relatively and Cummer, 2013], about 1.75 larger than the average dark compared to normal lightning. Although there may be TGF, making it a particularly strong discharge. Indeed, from lightning activity in parts of the thundercloud at the time of the RF data, the inferred current moment for the 3 August the RFD, which may produce some amount of visible light, event was 90 kA-km with a peak current of roughly 160 unlike normal lightning, the RFD would produce a very large kA, which is large even compared with typical lightning first current pulse [Liu and Dwyer, 2013] that would not be return strokes. In the visible range, calculations find that the accompanied by significant visible light emission. Østgaard fluorescence yield per unit length traveled by each runaway et al. [2013] reported space-based optical measurements at electron is about 0.7 photons/m or about 3.5 × 1019 J/m, the time of a TGF and found that detectable optical emission valid for all altitudes below about 20 km. Combining this occurred after but not during the TGF, suggesting that the fluorescence yield with the sum of runaway electron path processes that generate the gamma rays do not simulta- lengths for this TGF gives a total emission of only 135 J in neously produce bright optical emission. the visible range associated with this very large current pulse. [21] Figure 4e shows the total intensity distribution from all three emission band systems in rayleighs, assuming that + 5. Discussion the average wavelength of the 2PN2 and 1NN2 photons is 400 nm. The distribution is similar to that of the runaway [23] In this paper, we have discussed two main mecha- electron density [see Liu and Dwyer, 2013, Figure 3], and nisms for generating TGFs within thunderstorms. At this the size of the luminous region is about 1 km across. The time, it is not clear which mechanism describes most TGFs, intensity is about an order of magnitude higher than sprite but both are extremely interesting: If TGFs are produced by streamer heads that have a much smaller size. Therefore, lightning leader emissions, then spacecraft are directly although weak, the optical emission of the RFD may be observing lightning in gamma rays many hundreds of detectable, although further calculations on the propagation kilometers away, illustrating that we have much to learn of the light through the cloud are needed [Koshak et al., about ordinary lightning. On the other hand, if TGFs are + 1994]. In addition, the 1NN2 emission is stronger than produced by relativistic feedback discharges, then this means 2PN2, which is quite different from streamer discharges. that a new and different kind of electrical breakdown At altitudes of 70–75 km, the 2PN2 emission intensity of commonly occurs inside ordinary thunderstorms. sprite streamers is about a factor of several tens larger than [24] Following Uman [2001], lightning can be defined as a + 1NN2 [Liu et al., 2006, 2009]. This factor is even larger at transient, high-current with length scales thundercloud altitudes because the quenching altitude of generally measured in kilometers. RFDs are also transient, 2PN2 is much smaller. This means that the RFD emission high-current electric discharges with length scales measured may be effectively differentiated from the streamer discharge in kilometers. In particular, RFDs produce large, lightning- emission by considering the relative strength between these like current pulses that generate radio emissions similar to two emission band systems. lightning, causing lightning detection networks such as the [22]Asafinal example, a model fit of the radio measure- World Wide Lightning Location Network (WWLLN) to ments of a Fermi TGF recorded on 3 August 2010 shows that identify the sources of these signals as lightning. However,

4071 DWYER ET AL.: PROPERTIES OF TGF DISCHARGES these discharges involve a novel mechanism of air break- Connaughton, V., et al. (2010), Associations between Fermi Gamma-ray Burst Monitor terrestrial gamma ray flashes and sferics from the World down that produces little visible light compared with normal Wide Lightning Location Network, J. Geophys. Res., 115, A12307, lightning and so would appear dark to the human eye. The doi:10.1029/2010JA015681. , which is the low-energy analog of the Connaughton, V., et al. (2013), Radio signals from electron beams in terres- fl – relativistic feedback discharge, is sometimes called a dark trial gamma-ray ashes, J. Geophys. Res. Space Physics, 118, 2313 2320, doi:10.1029/2012JA018288. discharge. Therefore, relativistic feedback discharges may Cummer, S. A., et al. (2005), Measurements and implications of the relation- be viewed as a kind of “dark lightning,” with TGFs being ship between lightning and terrestrial gamma ray flashes, Geophys. Res. one possible by-product. Lett., 32, L08811, doi:10.1029/2005GL022778. Cummer, S. A., G. Lu, M. S. Briggs, V. Connaughton, S. Xiong, G. J. Fishman, and J. R. Dwyer (2011), The lightning-TGF relationship [25] Acknowledgments. This work has been supported in part by on microsecond timescales, Geophys. Res. Lett., 38, L14810, DARPA grant HR0011-1-10-1-0061. doi:10.1029/2011GL048099. [26] The Editor thanks Abram Jacobson and Nikolai Ostgaard for their Dwyer, J. R. (2003), A fundamental limit on electric fields in air, Geophys. assistance in evaluating this paper. Res. Lett., 30(20), 2055, doi:10.1029/2003GL017781. Dwyer, J. R., et al. (2003), Energetic radiation produced during rocket- triggered lightning, Science, 299, 694–697. Dwyer, J. R. (2004), Implications of X-ray emission from lightning, References Geophys. Res. Lett., 31, L12102, doi:10.1029/2004GL019795. Babich, L. P., E. N. Donskoy, R. I. Il’kaev, I. M. Kutsyk, and Dwyer J. R., et al. 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