1 Introduction

Lightning processes often occur in repeating patterns with rates ranging from units of microseconds to fractions of a second. Among these processes, the most explored ones are parts of lightning flashes, which take place below the thundercloud, as the Return Strokes (RSs), stepped leaders, dart leaders, dart-stepped leaders, and M-components in cloud-to-ground (CG) discharges, which have been investigated for many decades. Both optical and electromagnetic records confirm that individual lightning strokes within multi-stroke flashes are typically separated by several tens of milliseconds (Poelman et al., 2021). The repetition rate of stepped leader pulses is about several tens of kHz (Lu et al., 2008) and the dart-stepped leader pulses occur in a succession, which is as short as several microseconds (Jiang et al., 2014). The incloud processes, as lightning initiation or propagation of intracloud (IC) leaders, are usually not visible for high-speed cameras. When exploring them, we have to rely on electromagnetic measurements. Sequences of initial (or preliminary) breakdown (IB) pulses are believed to accompany the initiation of majority of CG and IC discharges in their electromagnetic records (Marshall et al., 2014). The IB pulses are bipolar, separated by several tens to a few hundreds of microseconds in CG flashes and by several hundreds of microseconds in normal IC flashes (Kolmašová et al., 2019; Marshall et al., 2013; Scholten, Hare, Dwyer, Liu, Sterpka, Kolmašová, et al., 2021; Smith et al., 2018; Yang et al., 2023).

After the initiation of a flash, positive and negative leaders propagate through the thundercloud forming hot and conductive plasma channels. Positive and negative leaders behave differently. The space stem mechanism of extension of negative leaders causes their stepping manifested by the presence of pulses in the electromagnetic records. The channels of positive leaders develop more continuously and thus are poorly detectable in electromagnetic recordings (Visacro et al., 2017). Nevertheless, recent observations provided evidence of stepping also during the prolongation of positive leaders (Jiang et al., 2020).

Sometimes new leaders retrace the channels previously established by slower leaders propagating in a virgin air. These leaders can travel a significant distance through both former positive and negative leader channels. The terminology used for leaders following the previously established plasma channel is unfortunately somewhat inconsistent. The leaders occurring within CG flashes below the cloud base are called dart or dart-stepped leaders (Biagi et al., 2010; Dwyer & Uman, 2014; Petersen & Beasley, 2013; Stolzenburg et al., 2019; D. Wang et al., 2016; J. Wang et al., 2022). Leaders, which do not reach the ground and stay inside the thundercloud, were named K-leaders, recoil leaders, and also dart leaders (Jensen et al., 2021). Ogawa and Brook (1964) originally defined negative recoil leaders as leaders traveling along the preceding positive leader channels toward their origin. This behavior was confirmed by optical observations (Saba et al., 2008). Mazur et al. (2013) suggested using a term “dart leader” only for recoil leaders, which reach the ground. Jensen et al. (2021) tried to consolidate the terminology suggesting to use “dart leader” as a general term for all leaders (both retrograde leaders on positive channels and prograde leaders on negative channels), which travel in already ionized channels at a higher speed than previous leaders propagating in a virgin air. As not all the leaders investigated in our study fit the original definition of recoil leaders by Ogawa and Brook (1964), we will follow Jensen et al. (2021) and use a term “dart leader” to describe our observations.

One of the poorly understood in-cloud phenomena are the trains of regularly distributed unipolar microsecond-scale pulses, which occur in electromagnetic measurements conducted during the evolution of both CG and IC flashes. These trains were for the first time described by Krider et al. (1975), who suggested that observed pulse trains could be produced by K-changes developing in a stepped manner. Rakov et al. (1992) found that only 24% of observed K-changes were accompanied by microsecond-scale pulses. Davis (1999), Krider et al. (1975), and Y. Wang et al. (2021) found that duration of an average interpulse interval in regular pulse trains occurring within IC flashes was about 5 µs. The pulse repetition rates and peak pulse amplitudes tend to decrease toward the end of the train (Kolmašová & Santolík, 2013; Rakov et al., 1992, 1996). Rakov et al. (1996) noted rare reversals of the polarity of pulses within several observed trains and attributed this effect to the changes of the channel geometry. Based on the evolution of pulse spacing and pulse polarity changes Y. Wang et al. (2010) divided the regular pulse trains into four categories (normal, back, symmetry, and reversal trains) and showed a temporal correspondence of pulses observed by a broadband (0–10 MHz) instrument and power peaks detected by a Very High Frequency (VHF) receiver (267–273 MHz). Zhu et al. (2014) investigated a convective storm in Shanghai, and found that over 98% of observed K changes (from more than one thousand cases) were associated with a microsecond-scale pulse activity. The pulses were grouped in regular trains only in 9% of events. Y. Wang et al. (2021) found that the leaders generating regular pulse trains occurred usually in the middle of an IC flash, and propagated at a velocity of 1.2–3 × 10⁶ m/s, slower than both the dart leaders or dart-stepped leaders in CG flashes. Using an array of 12 electric field antennas, Shi et al. (2020) found that a majority of pulse trains propagated through the main negative charge region. Jiang et al. (2022) combined optical images and mapping of VHF radiation sources, and hypothesized that long dart leaders (referred to as recoil leaders in that work) activated negative breakdown at the opposite end of a corresponding channel network at the time when the regular pulse trains were observed.

Using the radio telescope Low Frequency Array (LOFAR), Hare et al. (2023) recently showed that the propagation speed of five investigated dart leaders (again referred to as recoil leaders in that paper) varied from 5 × 10⁶ to 2.5 × 10⁷ m/s, the intensity of the emitted VHF radiation usually decreased when the leader speed slowed down, and that the dart leaders had meter-scale tortuosity but without any evidence of stepping.

In the present study, we for the first time combine broadband magnetic field measurements with the data provided by LOFAR during the observational campaign conducted in summer 2021, in order to bring new information about regular microsecond-scale pulse trains and provide new constraints to future modeling of incloud dart-stepped leaders. In Section 2, we introduce our instrumentation and data set. In Section 3, we describe our observations. In Sections 4 and 5, we discuss and summarize our findings.

2 Instrumentation and Data Set

3 Observations

As the first step, we analyzed the properties of magnetic field pulse trains. The pulses in the trains were unipolar, regularly distributed, with a pulse width of about 1 microsecond. Similarly, as in Kolmašová and Santolík (2013), each individual pulse was considered to be unipolar, if the immediately following overshoot of the opposite polarity does not exceed one half of the peak amplitude of the original pulse. The magnetic field waveforms are plotted in Figure 1a (event C1), Figure 2a (event C9-1), in Figure S2a in Supporting Information S1 (event C5), and Figure S3a in Supporting Information S1 (event C9-2). Duration of the trains varied from 91 to 277 µs. There were 19 pulses in the shortest train and 96 pulses in the longest one. The median interpulse interval varied from 4 to 7 µs. The interpulse interval was increasing toward the end of trains C5, C9-1, and C9-2. During event C1, we observed both trends, the interpulse spacing was increasing during the first half of the train and then decreasing up to the end of the train. The results are summarized in Table 1. Based on the criteria of Y. Wang et al. (2010) trains C5, C9-1, and C9-2 can be classified as regular trains, while train C1 was a symmetric train. The peak amplitude of pulses decreased toward the end of train C1. There was no clear evolution of the pulse peak amplitude within the other three trains.

Using the LOFAR impulsive imager, we were able to estimate location of the leaders, which generated observed regular trains of magnetic field pulses. We chose the LOFAR stations closest to the emitting sources (CS002 for event C1; CS003 for event C5; RS508 for events C9-1 and C9-2), and we thoroughly corrected the timing of the LOFAR data recorded at these stations for the propagation delay. We similarly corrected the timing of the corresponding broadband magnetic field waveforms. We found that the magnetic field pulses plotted in panel (a) (Figures 1 and 2; Figures S2 and S3 in Supporting Information S1) perfectly line up with the VHF power peaks plotted in panel (b) in the same figures. This correspondence is more clearly visible in details indicated in panel (a) by a blue rectangle and plotted in panel (f). The average propagation velocity of the leaders was calculated from the moving mean position of sources along a track (see Scholten, Hare, Dwyer, Liu, Sterpka, Kolmašová, et al., 2021) and plotted in panel (c). For all events, the velocity was on the order of 10⁶ m/s and decreased toward the end of the trains. Note that this average velocity is being calculated over groups of steps and that the formation of individual steps might be faster. The sources of VHF radiation localized by the LOFAR impulsive imager and color coded by their time of occurrence are displayed in panel (d). The leader was propagating down from 8.7 to 7.5 km during event C1 (Figure 1d), traveling up from 6.1 to 6.4 km during the short event C5 (Figure S2d in Supporting Information S1), and up from 6.5 to 6.9 km during event C9-1 (Figure 2d), and traveling down from 6 to 5.5 km during event C9-2 (Figure S3d in Supporting Information S1). Based on the impulsive imager data we estimated the length of individual leader steps to be of the order of a few tens of meters. When using the new LOFAR TRI-D imaging procedure, which includes both strong and weaker VHF sources, each broadband pulse was clearly accompanied by an isolated burst of VHF radiation sources as it is illustrated in panel (f) in Figures 1 and 2; Figures S2 and S3 in Supporting Information S1. The spread of sources for each broadband pulse has a width in space around 100 m, which is due to a combination of physical source spread and LOFAR imaging inaccuracies. Unfortunately, it is difficult to separate the two effects, since LOFAR's imaging accuracy depends highly on pulse sub-structure (Scholten et al., 2022).

By combining the location of the leaders, direction of their motion, and the relative orientation of antennas to the leader position with the polarity and relative amplitude of magnetic field pulses in both broadband antennas, we obtain a very consistent picture corresponding to negative leaders (with negative current in the direction of their motion) in all investigated cases.

To interpret our observations, we also looked at the placement of the other detected stepping leaders within the flashes imaged by the LOFAR impulsive imager. The overview plots are provided in Figures S4–S7 in Supporting Information S1, for events C1, C5, C9-1, and C9-2 respectively. The gray scale is used for the evolution of flashes outside the pulse trains episodes, which, in turn, are plotted on a color scale. The time intervals displayed by both scales are shown at the bottom of the figures. It is clear, that all imaged events can be characterized as complex and extensive IC flashes, and the stepping leaders occurred well inside their time interval, close to the boundary between the in-cloud negative and upper positive charge regions. Detailed images shown in panel (e) in Figures 1 and 2; Figures S2 and S3 in Supporting Information S1 reveal that all leaders exhibiting the microsecond scale stepping were dart-stepped leaders following the previous path of positive (events C1, C5, and C9-1) or negative leaders (event C9-2) with a delay of 13–81 ms after them, while the total duration of their parent flashes was 0.25, 0.3, and 0.4 s, respectively, as indicated in Table 1.

4 Discussion

Owing to the limited duration of the broadband magnetic field records (168 ms), which covered only about 40%–60% of the three investigated IC flashes observed by LOFAR on 18 July 2021, we were unable to inspect all dart leaders occurring within these flashes for the presence of regular microsecond-scale pulse trains. However, the collected data allowed us to concentrate on a detailed analysis of several recorded sequences. The four investigated pulse trains possess the same temporal properties as previously reported sequences of microsecond-scale pulses measured in various geographical and meteorological conditions (Kolmašová & Santolík, 2013; Krider et al., 1975; Rakov et al., 1992, 1996; Y. Wang et al., 2010; Zhu et al., 2014). It indicates that the fundamental process, which triggers the observed regular pulse bursts, might be the same as in all other published events. Because of the lower frequency limit of our instrumentation at 5 kHz, we were unable to verify the presence of slow K-changes accompanying the analyzed pulse trains.

The pulses within the trains investigated in our case study were not extremely strong, only those, which occurred during event C1 had peak amplitudes comparable to peak amplitudes of typical IB pulses (a few tens of percent of the corresponding (RS amplitudes) normalized to similar distance from the source discharge (Kolmašová et al., 2018). In other three cases the pulse amplitudes were similarly strong as the stepped leader pulses in CG flashes. It is thus possible that the processes generating the regular pulse trains occur more frequently, but the pulses might be too small to be recognizable in electromagnetic recording at larger distances. As regards the power of the VHF sources, these were, in all observed events, by one to two orders of magnitude stronger than intensely radiating negative leaders (IRNL) reported by Scholten, Hare, Dwyer, Liu, Sterpka, Kolmašová, el al. (2021).

We discovered that all stepping leaders generating regular pulse trains were negative dart-stepped leaders (in agreement with Shi et al., 2020) following pre-existing plasma channels after several tens of milliseconds (C1: 52 ms; C5: 81 ms; C1-9: 13 ms, and C9-2: 54 ms). Estimation of these delays is based on the location of the previously occurring sources imaged by the LOFAR impulsive imager. We cannot rule out that these delays were shorter because of poorly imaged parts of the path of preceding positive leaders. Most delays between the dart leaders and their predecessors reported by Hare et al. (2023) ranged from 15 to 32 ms, and were thus comparable to our observations with one exception of a very long delay of 170 ms in their records. The dart-stepped leaders described in our study propagated at a slightly smaller speed than usual dart leaders reported by Hare et al. (2023). The leader propagation speed was decreasing within the trains while the propagation steps approximately kept their spatial scale during the time intervals manifested by the presence of regular pulse trains. This was reflected by increasing interpulse time intervals, similarly as in the studies by Kolmašová and Santolík (2013) or Rakov et al. (1996).

We do not see any correlation between the pulse peak amplitudes and power of corresponding VHF pulses. Kolmašová et al. (2019) also reported the lack of correlation between amplitudes of broadband IB pulses and the peak power of the corresponding VHF pulses. It implies that the strength of streamers occurring at the beginning of the step formation (reflected in the power of sources imaged by LOFAR) does not correlate with the magnitude of currents flowing in these steps (measured by the magnetic loops).

There are nearly no other reports describing properties of dart-stepped leaders in IC flashes, then those reporting similar pulse trains (Rakov et al., 1996; Shi et al., 2020; Y. Wang et al., 2010; Zhu et al., 2014). As concerns comparison with dart-stepped leaders in natural or triggered CG lightning, Stolzenburg et al. (2019) investigated a transition between the dart leader and subsequent stepped leader preceding subsequent lightning strokes in negative CG flashes. Just a millisecond before the transition from the dart leader traveling in an existing path to the stepped leader forming a new path, a train of relatively intense unipolar pulses similar to our observation occurred in the displayed electric field records (their Figure 12b). This indicates that changes in the conditioning of the existing channels control the stepping and that the time delay between the observed dart-stepped leaders and the preceding leaders does not seem to be the only parameter controlling the initiation of the stepping process. The dart-stepped leaders in triggered CG lightning in the study by Wang et al. occurred 25, 50, and 127 ms after the preceding stroke, in a similar broad range of values as found by Hare et al. (2023), and as we also obtained in the present study.

In a study of rocket and wire triggered flashes, the dart-stepped leader propagated downward at an average speed between 2.7 × 10⁶ and 3.4 × 10⁶ m s⁻¹ (Biagi et al., 2010), very close to the propagation speeds of incloud dart-stepped leaders observed in our study. The propagation velocity of dart-stepped leaders fluctuated without any clear trend in the study of J. Wang et al. (2022), in contrast with the deceleration of the dart-stepped leader velocities in our study. The pulses generated by CG dart-stepped leaders were not regularly distributed in measurements of the time derivative of electric field in Dwyer and Uman (2014, their Figure 4.10) and the larger ones were found to be accompanied by X-ray bursts. Such observation was not reported for regular pulse trains in IC dart-stepped leader up to now.

Finally, measurements of microwaves at 1.57 GHz radiated by a dart-stepped leader in natural CG flashes, as reported by Petersen and Beasley (2013), showed power peaks approximately every 5 μs, the pulses were quite regularly spaced and interpulse noise was much lower than in case of regular step leaders. The authors explain the interpulse noise in step leaders by a presence a corona streamer zone which might have been absent in case of dart-stepped leaders. This is exactly what we can see in our case study: isolated VHF power bursts lined up with broadband pulses, separated by about 5 μs with no or very weak VHF activity between pulses.

5 Conclusions

These properties of observed incloud dart-stepped leaders, which emitted regular pulse trains, and a relative rareness of their observations with respect to their CG counterparts lead us to an assumption that suitable conditions for formation of dart-stepped leaders are fulfilled more often below the cloud base than inside the thundercloud. We thus hypothesize that a favorable combination of the conditioning of decaying plasma channels, their geometry on a meter scale (Hare et al., 2023), and a strength of the ambient electric field is required to trigger the stepping process manifested by regular pulse trains. We assume that the thunderstorm severity might play a significant role in the formation of these suitable conditions, as severe thunderstorms are known for very strong updrafts, which are heavily involved in distribution of hydrometeors and their electrification (Baker et al., 1999). Indeed, the thunderstorm, which hosted the events for this case study, was extremely severe (very high CAPE of 2400 J/kg and a very large wind shear of 18 m/s) when compared with several thousands of severe European convective storms occurring during the warm seasons in 2006 and 2007 (Kaltenböck et al., 2009). Extended data set of dart-stepped leaders coming with pulse trains, as well as relevant meteorological contexts of their observations are needed to verify our hypotheses. Nevertheless, this case study can provide new constraints to future modeling of incloud dart-stepped leaders.