2.1 VHF Broadband Interferometry System

Lightning discharges emit electromagnetic radiation over a broad range of the electromagnetic spectrum from extremely low frequency (ELF) to gamma-ray energy. In particular, in the VHF band (30–300 MHz) the nature of this emission is characterized by pulses of variable duration from some nanoseconds to a few microseconds. Due to their short duration, it is possible to consider, in first approximation, these pulses as stationary point sources. This assumption allows to locate the VHF sources evaluating the different time-of-arrival (TOA) or the phase difference of the electromagnetic waves detected by a system of antennas.

A VHF broadband lightning interferometer (INTF) is an instrument that allows to map these VHF sources with an interferometric technique called generalized cross-correlation.

Computing the geometric delay δt_ij between pairs of antennas with baseline d, it is possible to determine the direction of the point source through two angles: Azimuth and elevation.

(1)

An illustration with the basic geometry of the lightning interferometer is depicted in Figure 1b.

An excellent description of this kind of instrument and the processing technique was presented by the New Mexico Tech researchers (Stock et al., 2014). Our system and processing technique is clearly inspired by their work and we refer further details on the overall operation of the interferometer to their report (Stock et al., 2014).

Two almost identical interferometers were built and developed in order to lead this investigation. Each interferometer consists of three antennas (aluminum disks of radius 20 cm) deployed along two orthogonal baselines (d = 22 m). The antenna’s output signal is connected to a bandpass-filter (20–80 MHz) and then preamplified. All the antennas are connected using three identical high-quality coaxial cables (l = 30 m) to the acquisition system. The hardware of the acquisition system is primarily made by a digitizer and a workstation with sufficient CPU and memory requirements. The digitizer board used is the GaGe Razor Express 1604: 4 channel with 16-bit of resolution and 200MS/s of sampling rate and 8 GB of memory. In order to maximize the chance to record interesting events, we developed the acquisition system software to get a continuous recording in streaming mode, filling a circular buffer in the RAM memory. We set our acquisition time duration at 2.5 s with 0.5 s of pre-trigger and less than 20 s of dead time after the triggered event.

Both interferometers were online and could be turned on remotely when a storm was approaching. Once activated, the acquisition system can be triggered by an E-field flat plate antenna installed nearby. The flat-plate antenna measures the environmental electric field along the vertical axis. In order to study the high-energy emissions, we were interested in close lightning CG strokes in a 10 km area. For this reason, the gain of the antenna was set properly to avoid saturation and the trigger threshold was adjusted to avoid to collect too remote events. The nominal calibration of the antenna is 16 kV/m on output volt with a time-constant of 1 s. The E-field signal was acquired in the fourth channel of the GaGe digitizer and by a Picoscope PS4424 to synchronize the high-energy detector output with the VHF signals (further details in 2.2).

In the data processing, we applied a window-based cross-correlation method in frequency domain, with up-sampling and parabolic interpolation of the cross-correlation peak. The window length was set to 128 samples (∼640 ns) with a sliding step of a single sample. To mitigate the effect of the strong window overlapping, a clustering algorithm was applied. We selected all the compatible values within 1 nanosecond and then averaged them together. Several thresholds were applied to improve the accuracy and the noise reduction: An amplitude threshold of the cross-correlation peak of 0.8, a threshold on the closure parameter of 0.6 ns and a minimum size of the cluster of 8 windows. Further details on the data processing and especially a discussion on the imaging efficiency are available in Supporting Information.

2.2 High-Energy Detector

The high-energy detector was installed nearby the INTF-1 (Figure 1a) and it is composed of a NaI(Tl) cylindrical scintillator 76 × 76 mm (Scionix: Type 76B76/3M-E2-X2) with a photomultiplier tube (PMT). The detector contained a voltage divider and a preamplifier in a magnetic shielded housing and the scintillator is enveloped in an aluminum body (thickness 0.5 mm). The nominal decay constant is 0.23 ms and the rise time 0.5 μs, in good agreement with measured values. The detector was calibrated in energy at the nuclear physics laboratory in the Physics department at the Polytechnic University of Catalonia (UPC) with a ¹³⁷Cs and a ⁶⁰Co radioactive sources. The linear calibration in the range (0–1332 keV) provided a scale factor of m = 4.63 ± 0.02 keV/mV. This calibration was used, as well, at higher energy assuming a linear response. The output signal was acquired by a Picoscope PS4424 with 12-bit resolution and a sampling rate of 10 MS/s and triggered by the E-field flat plate antenna. Therefore, the acquisition system has two different digitizers with two different sampling rates: The GaGe Board with 4 channels at 200MS/s (3 VHF antennas, E-field flat plate antenna) and the Picoscope 4 channels at 10 MS/s (E-field flat plate antenna, high-energy detector, GPS signal). The E-field signal provides the trigger of both acquisition system and allows an accurate synchronization (∼0.1 μs) during the post-processing phase. Other systematic instrumental uncertainties were evaluated, all of them are dominated by the rise time of the detector and the synchronization accuracy.

From the signal processing, two relevant quantities are estimated: The X-ray energy and the time-of-arrival t0. The energy is evaluated by computing the ΔV of the signal at the pulse rise and then using the calibration factor. This method underestimates the energy when the time interval between two successive pulses is less than the decay time (Bolic et al., 2009). In contrast, an energy overestimation occurs when it is not possible to resolve multiple photons. The resolution to exclude the photon pile-up is dominated by the rise time δt_rt ∼ 0.5 μs. Both cases are very common in the physical phenomenon investigated; therefore, with our instrumentation, a very accurate measurement of the energy is out of our scope. On the other hand, an accurate evaluation of the t0 is crucial for the discussion of the results. For this reason, we applied an algorithm to compute the t0 using a linear interpolation of the rise time (further details are available in the Supporting Information), this simple procedure ensures a good accuracy and objectivity of the results. Another relevant observation concerns the environmental background. The probability of observing k background pulses in a given time interval Δt can be estimated using the Poisson distribution (e.g., Tran et al., 2019):

(2)

where λ is the average rate of background events and Δt is expressed in milliseconds. We evaluated λ in the field during the campaign and we estimated a mean value of λ = 0.20 ± 0.05 events/ms, almost the double of the Mallick et al. (2012) measurements. For example, the probability to have more than 2 background events in the last millisecond before a lightning return stroke is P (k > 2, 1) ≈ 0.001. Therefore, when a X-ray burst is observed, there is no doubt that those emissions can be related to lightning activity. On the other hand, a single pulse emission has to be evaluated more carefully considering the probability of a false coincidence with lightning activity. (e.g., the chance to have a background pulse in 1 ms before the return stroke is P (1, 1) ≈ 0.18 and in 0.1 ms is P (1, 0.1) ≈ 0.02).

2.3 LINET

Complementary data and information to our measurements were provided by the Colombian Total Lightning Detection Network, operated by Keraunos company since 2011. This network is composed of 19 low frequency (VLF/LF) sensors of LINET type (Betz et al., 2009) deployed with baselines of approximately 100 km. Further details on this network can be found in Aranguren et al. (2017).

3.1 Overall Data Analysis

In this paper, an “X-ray burst” is defined as a sequence of three or more X-ray pulses related with the same lightning event. Each X-ray pulse is not necessarily a single photon and the choice of three as the minimum size of an X-ray burst is discussed in Section 3. In the literature, it is equally common to define an X-ray burst as the sub-microsecond emissions of multiple energetic photons (e.g., Dwyer et al., 2005). We call “X-ray pulses” the detection of these emissions, as they appear in our measurements (e.g., Mallick et al., 2012).

The observed events can be divided into four categories: (1) Events where an X-ray burst was observed; (2) Events where one or two X-ray pulses were observed (we call these events “single X-ray pulses” as discussed in Section 3.); (3) Events in which no X-ray emissions were observed; (4) Events that did not trigger our data acquisition system, but they were recorded by LINET.

In Figure 2 we combined the high-energy detections with the lightning locations provided by LINET. The map is centered in the INTF-1 system of reference and allows to evaluate in particular the radial distance between our detection system and the lightning strokes. It can be observed that all the X-ray bursts detected are within an area delimited by a radius of about 1.2 km, and the majority of the events observed in this area have produced detectable high-energy radiation.

Table 1 summarizes the overall X-ray bursts data combining the high-energy measurements with the LINET data. Seven X-ray bursts were observed, corresponding to a total of 84 X-ray pulses. Unfortunately, for some events, we only have some partial data, due to the failure of the trigger in the acquisition system or to the detection efficiency of the lightning network.

Figure 3 shows the energy distribution and the time distribution of the X-ray pulses belonging to the X-ray bursts. The energy distribution has the most frequent count in the range 100–150 keV and the median value is approximately 280 keV. It is possible to observe that the vast majority of the X-ray pulses has an energy below 1 MeV. Higher values of energy have been observed from 2 MeV up to 8 MeV, but these results have to be discussed. Although energies of some MeV can actually be achieved and therefore observed, it is important to underline that our instrument has a rise time of 0.5 μs and therefore, as explained in Section 3, we cannot exclude that some of these values may be due to a pile-up phenomenon caused by the detection of multiple photons (Dwyer, 2004). This energy spectrum is consistent with earlier lightning observations (e.g., Arabshahi et al., 2015; Dwyer et al., 2004) and it is softer than a typical TGF spectra detected from space (e.g., Marisaldi et al., 2014; Østgaard et al., 2012). The time distribution shows a clear increase in X-ray detection approaching the return stroke (RS), as previously observed by Mallick et al. (2012). Unfortunately, with our instrumentation, we are not able to say if this effect is mainly due to the leaders’ approach to the ground or due to the decreasing distance between leaders and the high-energy detector. We cannot separate efficiently the two contributions. The maximum duration of the observed X-ray bursts was about 900 μs and the mean duration ∼600 μs. Taking into account the time distribution of all X-ray pulses belonging to the X-ray bursts observed, the median value was 150 μs before the return stroke.

3.2 Negative Downward Leaders: 2019-11-11 06:39:06

On November 11, 2019, a tropical thunderstorm passed through Barrancabermeja during the night and several lightning events were recorded. Six X-ray bursts and five X-ray single pulses were detected from lightning activity. In this section, we present the most energetic burst associated with a negative downward leader and subsequently a dart leader event that occurred 4 ms later.

The first relevant observation is that all the X-ray bursts detected were associated with negative downward leaders with several branches. In particular, in this case, it is possible to distinguish two main leader branches: The first one at a lower elevation, probably farther away from the INTF or with lower speed, and the second one at a higher elevation probably closer to the INTF or faster. This ambiguity is due to the two-dimensional imaging of a three-dimensional development of a lightning event. We will focus especially on this second main leader branch because the high-energy radiation detected seems to be associated with its propagation.

Figure 4 and Figure 5 show the negative downward leader evolution during the last 3 ms before the RS. The lightning map is 2D and it is described by the angular coordinates: Elevation and azimuth defined in Section 2 and in Figure 1b. The timestamp in UTC time is the proper time of the RS detected by LINET. In order to better appreciate the evolution in time, especially when the X-ray emissions were detected, we provide an animation of Figure 4 in the supplementary material.

For this event, it was possible to obtain a relatively accurate location of the radial distance comparing the LINET location with pictures and satellite images of the struck area and likely this distance is 430–450 m, two high-buildings are the most likely striking point. In Figure 5 it is possible to appreciate the detailed evolution of the downward leader and the most likely location of the X-ray sources.

In order to describe the procedure by which the most likely X-ray sources were located, a few comments on the E-field signal, the X-ray signal, and VHF sources are needed.

Figure 6a shows the output signals of the flat plate antenna and the high-energy detector in the last 1 ms before the RS. The electric field increases due to the approaching of the downward leader to the ground until the dramatic drop at the RS. The high-energy detector signal shows the overlap of the X-ray pulses due to the long decay constant of the detector. This pile-up effect can be resolved for time intervals greater than 0.5 μs. The time-of-arrival t0 of each X-ray pulse was evaluated and numbered.

Figure 6b allows us to clarify the terminology used in this work. We use the term “VHF sources” to indicate the set of all solutions provided by the interferometer data processing.

In general, the VHF sources detected by a broadband lightning interferometer can be due to continuously radiating or impulsive events (Stock et al., 2014). We are especially interested in a subset of these VHF sources that we call “the most intense VHF pulses.” We define this subset considering a local maximum condition and a threshold condition on the VHF amplitude. The local maximum condition on the amplitude, generally defines a “VHF pulse,” instead, the threshold condition on the amplitude, based on the median or the third quartile (top 25%), allows to define in a robust way the “most intense VHF pulses.” More details are available in the Supporting Information.

With only one high-energy detector, it was not possible to obtain an independent measurement to locate the X-ray sources. Therefore, our initial assumption was to associate each X-ray t0 with the closest VHF sources in time domain and infer the X-ray source location from the associated VHF source location. Following this procedure, we realized that several VHF sources could be associated with the same X-ray in our uncertainty range, dominated by the rise time of the high-energy detector. For this reason, in order to express this uncertainty in the location of the high-energy radiation, a good strategy consists in plot all the possible X-ray sources in a time interval δt with respect to X-ray t0. We have chosen δt = ±1 μs because it is the double of our uncertainty range, and assuming a normal random distribution, it would correspond to a 95% of confidence interval.

Figure 7a shows the density plot of VHF sources in this interval; it is probably the most effective way to show all the possible locations of the X-rays detected together with their location uncertainty. Despite that, this figure is integrated over a long time compared to the single X-ray emission and it is not allowed to evaluate the location uncertainty of each X-ray pulse detect. Therefore, we provide in Figure 7 two example of the location uncertainty related to the X-ray pulses number 18 and 19 (all the other cases can be find in supplementary material). Figure 7b shows an unique location of the X-ray source, instead, Figure 7c shows an ambiguous location.

Despite this occasional ambiguity on the X-ray source location, we were not sure that the VHF emissions and the high-energy radiation were related until we observed a clear correspondence between the X-ray t0 and the most intense VHF pulses.

3.2.1 Temporal Correspondence Between the High-Energy Emissions and the Most Intense VHF Pulses

In this section, we present the evidence of a temporal correspondence between the high-energy emissions and the most intense VHF pulses. We compare the time-of-arrival of the high-energy emissions t0, computed by the algorithm described in Section 3, with the time-of-arrival of the VHF sources, computed by the interferometer. Further details on the data processing and the quantitative definition of the VHF source amplitude are described in the Supporting Information.

Figure 8 shows a clear example of this temporal correspondence. On the background, it is possible to observe the VHF signal of the central antenna (gray line). The black spline connects all the VHF sources obtained by the INTF processing and in particular, the most intense VHF pulses marked with black dots. The output signal of the high-energy detector and the dE/dt signal are respectively the blue and the red line.

It is possible to observe how the black spline presents several peaks, which correspond to the most intense VHF pulses. Superimposing a vertical reference related with t0 (blue lines) emerges the correspondence with VHF peaks. A blue star mark represents the matching.

As already mentioned, there are several VHF sources that could be associated with the same X-ray pulse in our uncertainty range, but usually only one intense VHF pulse. Nonetheless, to prove the goodness of this correspondence, we performed two complementary analyses.

The first test consists in computing the discrete cross-correlation between the X-ray time-of-arrivals t0 and the VHF pulses timestamps, considering the temporal uncertainty of ± 0.5 μs as the width of the t0 pulses. The result shows a correlation peak compatible with zero, therefore, we can state that high-energy pulses and VHF pulses are temporally correlated. Furthermore, following a similar approach we computed the cross-correlation between the X-ray time-of-arrivals t0 and the most intense VHF pulses (top 25%) and we compared it with the cross-correlation with the other VHF pulses (bottom 75%). Figure 9a shows that there is a clear correlation between the X-ray time-of-arrivals t0 and the most intense VHF pulses, instead there is no correlation with VHF pulses with lower amplitude.

The second test we performed is a Monte Carlo simulation to evaluate the p-value in the case of study illustrated in Figure 8. We considered all the most intense VHF Pulses (top 50%) and we simulated the X-ray t0* assuming a random uniform distribution in the time range [−180:0] μs, then we evaluated the absolute deviation Δt = |t0* − t_VHF|. The probability to have a single random correspondence is actually quite high p (k = 1, Δt < 0.5) < 0.366, but the probability to have several random correspondences decrease rapidly.

We evaluated the average absolute deviation for 16 correspondences. The probability density function is shown in Figure 9b. The probability for a random correspondence in the uncertainty range is less than 0.4% but the p-value of our event is lower than 0.02% and if we consider the average VHF amplitude as well, the probability to have a random association with overall higher VHF amplitude is absolutely low (p < 2.6 × 10⁻⁶).

After that, we evaluated the deviation Δt = t0 − t_VHF of the measured X-ray t0, where t_VHF is the time related to the VHF pulse associated. This quantity Δt was computed for all the X-ray bursts observed and shows that both processes could be considered simultaneous within an accuracy of 0.5 μs (see Figure 10a).

Despite the definition of “the most intense VHF pulses” provided is generally clear, we studied the relation with the VHF amplitude more thoroughly. We computed the 20-quantiles in all the X-ray bursts observed in order to compare the relative magnitude of the VHF amplitude of the pulses associated with the high-energy emissions.

The overall distribution is shown in Figure 10b, the most intense VHF pulses (top 50%) correspond to more than 96% and the top 25% correspond to the 82% of the distribution.

In conclusion, we can state that a temporal correspondence between the high-energy emissions and the most intense VHF pulses was observed and it is statically significant. This temporal correlation allows a more accurate location of the X-ray sources and could suggest a shared production mechanism.

It is relevant to note that also the peaks of the electric field derivative (dE/dt) are in correspondence of the X-rays pulses, as observed for the first time by Dwyer et al. (2005) and with the majority of the VHF pulses. This “triple” correlation between high-energy radiation, VHF pulses and electric field derivative dE/dt is discussed in Section 13.

3.2.2 High-Energy Emissions and Leader Speed

In this section we investigate the relation between the high-energy radiation and the VHF leader speed. The goal of these measurements is not intended to provide an accurate absolute value of the leader speed, but rather to investigate whether it is possible to observe some correlation or change in speed in correspondence with the high-energy emission. Assuming a good accuracy in the radial distance (≈450 m) and a leader development, essentially vertical, it is possible to quantify the 2D speed of the leader.

The attempt to calculate the speed between two consecutive VHF sources has failed, this procedure produces unreliable values of the leader speed. The reason for that could be due to the fluctuations or likely because the VHF pulses measured by the INTF are associated with the streamers’ propagation (and therefore, two consecutive streamers can be randomly directed and unrelated in terms of their propagation). To overcome this problem, we selected nine leading branches (LBs) by visually separating the VHF sources through polygons in the 2D image and then we averaged the VHF sources together in a fixed time interval of 10 μs.

Figure 11 shows the 2D speed of the selected branches, the areas of great interest are delimited by a border obtained from the previous density plot. To allow better visualization, it was decided to saturate speeds above 4.0 × 10⁶ m/s, this threshold was chosen considering the overall speed distribution.

It seems possible to observe a variation in the 2D speed in correspondence with the X-ray emissions (see the arrows in Figures 11, for example, LB2, LB3, LB5, LB8, and LB9). This speed variation can be identified by the color change, especially in the presence of red dots or warm colors, but it could also be due to multiple branching in the third dimension or in smaller scale, high streamer activity or simply random fluctuations. Therefore, although there is an indication of correspondence between the X-ray location and the 2D speed variation, such correlation is not strong enough to be statistically significant.

Despite the averaging procedure, several outliers, essentially due to fluctuations or secondary branching, compromise the measurement of the overall 2D speed of a single leader branch. For this reason, in order to get more reliable speed values for each single branch, we preferred to calculate them using an 1D linear fit (see Figure 12). We take advantage of the 2D imaging to select the branches and compute the 1D speed in both components (vertical and horizontal) and then obtain the 2D speed by combining both.

In conclusion, although we investigated the relation between the high-energy radiation and the VHF leader speed, we did not observe a clear correlation. It is possible to report that high-energy radiation was observed in negative downward leader propagation in the 2D speed range 0.4–1.2 × 10⁶ m/s. Further implications are discussed in Section 13.

3.3 Dart Leader: 2019-11-11 06:39:06

After 4 ms from the previous negative downward leaders, we observed dart leader event with X-ray emissions. In Figure 13, it is possible to appreciate the development of the dart leader along the main channel of the previous event (in gray). Two X-ray pulses were observed in coincidence, both with an energy of about 100 keV. The total duration of the event is about 100 μs.

Figure 14 shows the vertical evolution of the dart leader during the last 50 μs before the return stroke. We used linear interpolation to calculate the 1D speed in both components (vertical and horizontal) to determine the 2D speed. The average speed seems constant for the last 800 m with a value of 2.0 × 10⁷ m/s. We did not observe measurable increase of the speed in the proximity of the X-ray emissions. A strong VHF signature was observed, typical of dart leaders. The elapsed time between the VHF pulses is much less than the negative downward leaders. Further implications are discussed in Section 13.

3.4 Negative Downward Leaders: 2019-11-11 06:38:16

A similar analysis to the one described for the event 2019-11-11 06:39:06 is conducted on all observed X-ray bursts, but in less detail due to the larger uncertainty on the distance and a smaller number of X-rays detected. For completeness and further considerations, we briefly present another case of negative downward leaders: 2019-11-11 06:38:16.

Figure 15a shows the location of the high-energy sources with their uncertainty expressed by the density plot. This case is characterized by three simultaneous distinct leaders’ main branches all around our INTF station (note azimuth scale). The duration of the X-ray burst is about 1 ms with 23 X-ray single pulses detected. We observed many X-ray sources in correspondence with the unconnected leader tips.

LINET provides a unique location for this event (likely related to LB4 the channel where the return stroke occurred), the approximate distance from the INTF station is 550 m. Assuming this value for all the LBs, we calculated the 2D speed: 0.8–1.0 × 10⁶ m/s for LB1, LB2, LB3, and 1.2 × 10⁶ m/s for LB4.

As a final remark, we would like to point out that an X-ray burst can have multiple sources belonging to different leader branches, that could be hundreds of meters apart. Therefore, an extensive origin of the X-ray burst should be considered, the same also in downward TGFs like those observed by Abbasi et al. (2019) and maybe, we hypothesize, in TGFs detected from space.

4.1 Implications on the Origin of the Most Intense VHF Pulses

A recent study has established that VHF emissions from stepping negative leaders in lightning is most likely due to streamer formation around the region of the step (Hare et al., 2020). It is interesting to note that observations in laboratory experiments (Kochkin et al., 2014; Montanyà et al., 2015), models (Gurevich et al., 2007) and simulations (Celestin & Pasko, 2011; Chanrion & Neubert, 2010) agree that the high-energy radiation is associated with streamers development and in particular, the tip of the streamer provides the high electric field needed to initiate the electron runaway.

Therefore, the association between high-energy radiation and VHF pulses observed suggests that the origin of the VHF pulses could be due to the runaway electrons mechanism, or more in general, to the high-energy electron acceleration. It is well known that accelerated electrons produce an intense electromagnetic radiation field, whose emitted power is proportional to the square of the acceleration according to the Larmor formula. It is possible to show that the radiation spectrum in frequency domain justifies the VHF signature observed. In particular, it is relevant to note that the emitted power increases drastically in the relativistic regime.

A very high field cannot exist in air for very long, since conventional breakdown will rapidly discharge the field (Dwyer & Uman, 2014). The consequence of this fact is that the runaway electrons mechanism in lightning discharges is an impulsive phenomenon. In summary, high-energy radiation and the most intense VHF emissions likely share the runaway electrons as a common production mechanism. This could explain in particular, the intensity and impulsive nature observed in the VHF bandwidth.

4.2 Implications on the Origin of the High-Energy Radiation

High-energy radiation undergoes a strong absorption exponentially proportional to the density of the air (e.g., Hubbell & Seltzer, 1995) which plays a crucial role in the detection, especially in ground-based observations. The strong absorption explains why the X-ray detection from lightning requires to be very close to the lightning discharge as shown by the results obtained in Section 6. Furthermore, the small effective detector area (∼0.02 m²) considerably limits the chance of observation. Based on these considerations, it is reasonable to think that observed X-rays are a very small fraction compared to those actually produced by lightning leaders. This conclusion is in agreement with Monte Carlo simulations and absorption models (Berge & Celestin, 2019; Celestin et al., 2015; Østgaard et al., 2008).

In Figure 16, we considered the negative downward leaders event described in detail in Section 7 and we hypothesized that all the most intense VHF pulses are associated with sources of high-energy radiation. Assuming that, the number of high-energy radiation sources is potentially greater than the one observed, many more sources (≈10²−10³) have to be taken into account.

Clearly, high-energy radiation requires energetic electrons and a threshold has to be considered to assume the correspondence with the VHF pulses, but if we assume that runaway electrons is the shared mechanism, the amplitude of the VHF pulses is related to electrons acceleration, hence it can be considered a good criterion to infer the high-energy production.

Therefore, with reference to Figure 16b, if an X-ray detection is associated with a VHF pulse, there is no reason to think that another VHF pulse with comparable amplitude cannot be considered as a source of high-energy radiation too.

In our measurements, high-energy radiation has been detected in negative downward leaders with a 2D speed range of 0.4–1.2 × 10⁶ m/s and in a dart leader with a 2D speed of 2.0 × 10⁷ m/s. Unfortunately, we were not able to establish a strong relation between the leader speeds required for high-energy production, although we speculate that intense VHF pulses in negative leader with comparable speed could be considered as high-energy sources.

4.3 Implications on the Origin of the TGFs

Although our measurements are related to high-energy radiation in cloud-to-ground lightning, some relevant considerations could be extrapolated for TGFs detected from the space. First of all, it is evident from our analysis that the X-ray bursts detected in coincidence with negative downward leaders are originated by multiple sources of high-energy radiation. As discussed in the previous section, the number of these sources is clearly underestimated by ground measurements, essentially due to the strong absorption exponentially proportional to air density.

This suggests that the origin of TGFs could be seen as the cumulative effect of many sources, each capable of generating runaway electrons. The cumulative effect is capable of explaining the origin of TGFs observed with the duration of several microseconds (e.g., ≳ 50 μs). This is more consistent for events with longer duration. On the other hand, in shorter TGFs, since there are fewer sources in the time interval, it is not possible to state this conclusion with the same confidence. This hypothesis supported by our observations is in agreement with Celestin and Pasko (2012) simulations and Dwyer and Cummer (2013) calculations. From a spatial point of view, the multiplicity of sources translates into an extensive origin of the TGF radiation.

The association between X-ray emission and strong VHF pulses can be considered a valuable method to locate the high-energy radiation phenomena. Furthermore, it can be a crucial criterion to locate the origin of the TGFs, as recently shown in Lyu et al. (2018) two TGFs were associated with 10 μs accuracy with a strong VHF emission detected by the Lightning Mapping Array (LMA). Our measurements can suggest that likely those strong VHF emissions can be properly associated with the high-energy radiation and therefore, that could be the most accurate spatial and temporal reference of the TGFs origin.

Moreover, it is interesting to point out a very good agreement between the leader speed measured in CG negative downward leaders and a few measurements in the literature of leader speed in IC negative upward leaders associated with TGF production. In particular, the leader speed measured by Shao et al. (2010) 0.4–0.6 × 10⁶ m/s and Cummer et al. (2015), p. 0.8–1.0 × 10⁶ m/s. Although more investigations are needed to evaluate the relation between leader speed and high-energy radiation, leader speed could be another relevant observable in TGF studies from ground measurements.

Finally, we would like to compare our results with the downward TGFs observed by the Telescope Array reported by Abbasi et al. (2019) since their instrument allows unique ground measurements of the high-energy radiation from lightning discharges. We point out several analogies which their results (summarized in Section 1.) that allow us to believe that the observed phenomena are substantially the same.