Radio emission from negative lightning leader steps reveals inner meter-scale structure
B. M. Hare, O. Scholten, J. Dwyer, U. Ebert, S. Nijdam, A. Bonardi, S. Buitink, A. Corstanje, H. Falcke, T. Huege, J. R. Hörandel, G. K. Krampah, P. Mitra, K. Mulrey, B. Neijzen, A. Nelles, H. Pandya, J. P. Rachen, L. Rossetto, T. N. G. Trinh, S. ter Veen, T. Winchen
RRadio emission from negative lightning leader steps reveals inner meter-scale structure
B. M. Hare,
1, 2, ∗ O. Scholten,
1, 2, 3, † J. Dwyer, U. Ebert,
5, 6
S. Nijdam, A. Bonardi, S. Buitink,
7, 8
A. Corstanje,
7, 8
H. Falcke,
7, 9, 10, 11
T. Huege,
8, 12
J. R. H¨orandel,
7, 8, 9
G. K. Krampah, P. Mitra, K. Mulrey, B. Neijzen, A. Nelles,
13, 14
H. Pandya, J. P. Rachen, L. Rossetto, T. N. G. Trinh, S. ter Veen, and T. Winchen University of Groningen, KVI Center for Advanced Radiation Technology, Groningen, The Netherlands University of Groningen, Kapteyn Astronomical Institute, Groningen, The Netherlands Interuniversity Institute for High-Energy, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium Department of Physics and Space Science Center (EOS), University of New Hampshire, Durham NH 03824 USA CWI, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands TU/e, Eindhoven University of Technology, Eindhoven, The Netherlands Department of Astrophysics/IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands Astrophysical Institute, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium Nikhef, Science Park Amsterdam, Amsterdam, The Netherlands Netherlands Institute for Radio Astronomy (ASTRON), Dwingeloo, The Netherlands Max-Planck-Institut f¨ur Radioastronomie, Bonn, Germany Institut f¨ur Kernphysik, Karlsruhe Institute of Technology(KIT), P.O. Box 3640, 76021, Karlsruhe, Germany Erlangen Center for Astroparticle Physics, Friedrich-Alexander-Univerist¨at Erlangen-N¨urnberg, Germany DESY, Platanenallee 6, 15738 Zeuthen, Germany Department of Physics, School of Education, Can Tho UniversityCampus II, 3/2 Street, Ninh Kieu District, Can Tho City, Vietnam (Dated: July 8, 2020)We use the Low Frequency ARray (LOFAR) to probe the dynamics of the stepping process ofnegatively-charged plasma channels (negative leaders) in a lightning discharge. We observe that ateach step of a leader, multiple pulses of VHF (30 – 80 MHz) radiation are emitted in short-durationbursts ( < µ s). This is evidence for streamer formation during corona flashes that occur with eachleader step, which has not been observed before in natural lightning and it could help explain X-rayemission from lightning leaders, as X-rays from laboratory leaders tend to be associated with coronaflashes. Surprisingly we find that the stepping length is very similar to what was observed near theground, however with a stepping time that is considerably larger, which as yet is not understood.These results will help to improve lightning propagation models, and eventually lightning protectionmodels. Keywords: thunderstorms; lightning; radio emission; streamers; negative leaders
Lightning is one of the most energetic processes inour atmosphere. It is thought to initiate from a singlepoint, that then separates into positively and negativelycharged ends, called positive and negative leaders, whichpropagate away from the initiation point and into oppo-sitely charged cloud regions [1]. At the tip of each leadermany streamer discharges create weakly ionized plasmachannels through the joint action of ionization fronts andlocal field enhancement at the front of the streamer chan-nels. For positive leaders, electrons accelerate towardsthe leader, allowing the positive leader to grow fairlygradually while supported by the strong photo-ionizationin air as a source of free electrons [2–4]. We have recentlydeveloped new high-resolution VHF measurement tech-niques, and applied them to positive leaders [5].In this work we focus on negative leaders. Negativeleaders have a significantly more complex propagationmechanism where they propagate in discrete steps. Eachstep appears to be due to luminous structures, generallyassumed to be conducting (see Ref. [6] for an alternative ∗ [email protected] † [email protected] interpretation) that form in front of the main conductingchannel, called space stems in this work. After their for-mation, these structures grow backward to connect withthe main leader body, resulting in a large current pulseto equalize the electric potential. This process was firstobserved in laboratory discharges [2, 7] and later in light-ning [8–10]. However, the majority of the previous workhas been done in the optical regime, which does not di-rectly relate to electrical current (e.g. [6]), or using radioemission below 10 MHz that is only sensitive larger scaleelectrical currents (e.g. [11, 12]). The stepping processhas been observed before in VHF emission [13], howeverwith a resolution that made it difficult to draw firm con-clusions.To investigate the mechanism behind negative leaderpropagation and its VHF emission we have used LOFARto provide measurements of the meter-scale distributionof electrical currents in negative leaders using the tech-nique described in Ref. [5]. These measurements will helpto improve lightning leader modeling, which tends to relyon a large number of assumptions, inhibiting, for exam-ple, our understanding of basic lightning processes suchas attachment to ground, which is critical for improvedlightning protection [14, 15]. Furthermore, previous workhas shown that the majority of terrestrial gamma ray a r X i v : . [ phy s i c s . a o - ph ] J u l flashes (TGFs), intense bursts of gamma ray radiationwith energies up to 10 MeV, are correlated with negativeleader stepping [1], therefore our improved understand-ing of leader propagation could be used in future work tohelp understand TGFs.We show that each leader step emits a burst of multi-ple discrete VHF pulses. This is in direct contrast withwhat is expected based on previous work, which predictsone single VHF source per step [12]. We find that themajority of VHF sources in a leader step occur withinabout a meter of each other, showing that VHF radi-ation from negative leaders comes from corona flashes,which have been observed in laboratory sparks but notin natural lightning [16, 17]. This discovery could explainwhy lightning leaders tend to emit 100-500 keV X-rays,since similar X-ray bursts seen in laboratory sparks areoften associated with corona flashes [16, 18].LOFAR is a distributed radio telescope that is primar-ily built for radio-astronomy observations [19] but hasalso proven to be an excellent cosmic-ray air-shower de-tector [20, 21]. Its potential for lightning detection wasclear at the initial design [22]. We use the Dutch partof LOFAR consisting of thousands of dipole antennasspread over 3200 km in the northern Netherlands withantennas operating in the 30 – 80 MHz band. The tracesare sampled at 200 MHz and relative arrival time of eachpulse can be measured with about 1 ns accuracy. Our al-gorithm can locate sources that are at least 120 ns apart.Previous techniques could map lightning in either 3Dwith about 100 m accuracy [23], or in 2D with 1 ◦ accu-racy [24]. Our technique allows to map lightning in 3Dwith a horizontal accuracy better than 2 m and 15 mvertically with an efficiency of one source per 1 µ s [5].We analyze a lightning flash from September 29 th East-West distance [km]time [ms] N o r t h - S ou t h [ k m ] H e i gh t [ k m ] EventsMap-2017-NL-1a1WedJan29202012:21:22
FIG. 1: A section of a negative leader where each dot isthe location of a reconstructed source. Top panel showsheight v.s. emission time of the source, the bottompanel shows the projection of the source position on theground plane where distances are measured from thecore of LOFAR. The color of each dot reflects emissiontime going from yellow to green.response. We find that these radio sources on negativeleaders come in bursts. These bursts can be seen in Fig. 1,where the VHF sources tend to cluster in time. A widerview of this leader is shown in the supplementary ma-terials. These bursts are observed across all well-imagednegative leaders. The obvious interpretation is that thesebursts are due to leader stepping.
50 100 150 200 250 300010 -1
105 15 20010 Time between subsequent sources [ μ s] D i s t r i b u t i o n [ nu m b e r / μ s ] FIG. 2: The distribution of time between subsequentsources. The error bars show the lowest and largestpoisson rates that can model the data with 34%confidence (1 σ ).Fig. 2 shows a distribution of time between subsequentradio sources across 26 negative leader segments, with atotal length of about 15 km, in the 2017 lightning flash. Ifevery radio source were randomly distributed in time, thetime between radio sources would be exponentially dis-tributed. The distribution strongly deviates from an ex-ponential, in particular, there is a sharp spike below timedifferences of 4 µ s that shows that our located sourcescluster together in time significantly more than could bepossible for random chance. This spike continues down to120 ns, the smallest time differences that can be probedwith our present imaging algorithm.It is ambiguous how to precisely define which sourcesshould be clustered together in a burst. This is ex-pressed by the fact that the distribution in Fig. 2 is verysmooth. In lieu of a physics-inspired definition, we havedefined a burst such that every located source in a burstis within 2 µ s of its subsequent radio source. This timecut was chosen because: 1) it includes the majority ofVHF sources shown in the spike in Fig. 2, 2) it is shortenough that it minimizes the chance of VHF sources fromdifferent leader steps to interfere with our results, and3) the qualitative results are similar even if the time ishalved or doubled. The number of sources in a burstmay thus vary from a single one up to a maximum of 9located sources, using this prescription. Of the total of2599 bursts we have 224 bursts with 3 or more sources.Investigation of the VHF time traces shows that the ma-jority of bursts with a single located source even havemultiple VHF pulses that are not located but most prob-ably come from the same spot. If we use instead 8 µ sin the definition of a burst we obtain qualitatively verysimilar numbers (2204 bursts of which 340 have 3 or moresources). We find that the strength of the pulses within aburst varies greatly, in addition some burst may containthree strong pulses while others may have a single muchweaker one. N u m b e r point source model1 m std noisemeasured distribution FIG. 3: The histogram shows the horizontal spatialdistribution of pulses in a bursts. The orange line givesthe simulation results if the sources are at one locationwith a 1 m horizontal location accuracy and accountsfor 2/3 of the number of sources. The error barsindicate the lowest and highest poisson rates that couldmodel the data within 34% confidence (1 σ ).Fig. 3 shows the spatial distribution of sources withina burst that have three or more located sources by bin- ning the horizontal distance between each source and thegeometric center of all pulses in the burst. Note thatwe focus on the horizontal plane, since our horizontallocation accuracy (around 1 m) is significantly betterthan our vertical location accuracy (around 10 m). Alsoshown is a simulated distribution if every radio sourcein a burst came from the same location with a locationerror of 1 m. The fact that 2/3 of the data-derived dis-tribution is within the radius of our simulation showsthat our data is consistent with the majority of locatedsources in a burst coming from the same location. Thiscan also be seen from Fig. 1 where the different bursts inthe time v.s. height plot are also localized after project-ing on the ground plane. However there are also manybursts where the sources are spread over larger distances.This is expressed by the shoulder in the distribution ata distance of 3.5 m. This shoulder persists independentof changes in our quality cut, burst definition, or specificset of leaders used in the analysis. Bursts with spatialextent seem to be mostly due to simultaneous activityin close branches, and due to bursts that are extendedlength-wise along the channel (with lengths around 5 m).The supplementary material includes figures that show avariety of different bursts.The total duration of a burst (for bursts with at least2 pulses) is exponentially distributed with a median of0.5 µ s and a suppression below 0.1 µ s. Changing ourburst definition to 8 µ s increases the median consider-ably to 1.5 µ s by adding a long tail extending to 4 µ s.Even though the density of located sources in the flashis second to none, it should be realized that our imagingformalism has an efficiency of only 30%, i.e. only a thirdof the strongest pulses in a spectrum is located. Thisprobably most strongly affects the burst duration. Forexample, if a pulse in the middle of a burst is not imaged,then our simple 2 µ s definition may split that burst intwo. While, using a 8 µ s definition, may combine multi-ple bursts.The time distribution between bursts shows an expo-nential distribution, see Fig. 4, with a median at 40 µ swhich we interpret as the median stepping time. Thisnumber is not affected much by the precise definition ofa burst since using the 8 µ s burst definition yields a me-dian stepping time of 50 µ s. The horizontal distance be-tween bursts also shows an exponential distribution witha cut-off at distances below 4 m and a median of 7.5 mwhere the median shifts to 8.5 m for the 8 µ s burst defini-tion. We have taken here the distance as measured in thehorizontal plane because our vertical resolution is of theorder of 10 m and thus would confuse the picture. Opticalobservations of leader growth well below the cloud havefound that the time between negative leader steps tendsto be around 10 µ s and their length tends to be around5 m [8]. We thus observe that in the cloud the steppingtime is considerably longer than close to ground witha stepping length that is only marginally larger. Nearground level one could expect stronger electric fields thanin a cloud but how this reflects in the observed differences
250 50 75 100 125 150 175 200050100150200 Time between subsequent bursts [ μ s] N u m b e r N u m b e r FIG. 4: Time between bursts (top panel) and horizontaldistance between bursts (bottom panel), where a burstcan have only a single pulse.is not understood.A very common interpretation of the negative-leaderstepping process is that when the space stem connects tothe existing leader, there is a current pulse that equalizesthe voltage in the space stem to the much larger (nega-tive) voltage at the tip of the leader by removing positivecharge from the space stem [12]. In the process, the spacestem, which was poorly conducting, heats up due to thedissipation of the electric energy of the current, ionizesfurther and becomes a good conducting heated plasmathus forming a new leader section. This sudden voltagejump will cause the electric field to exceed breakdown( E c = 3 . ≈ × − J in our 30-80 MHz frequency band. This roughlyequates to a streamer with an order-of-magnitude of 5 × free electrons. Details of these order-of-magnitudecalculations are given in Supplemental Material, whichincludes Refs. [31–35]. This is consistent with the ideathat there are of the order of 10 steamers [18] in a coronaflash, distributed in strength of emitted VHF energy,where we are only sensitive to the extreme tail of thatdistribution. Future work is needed to find the distribu-tion of detected streamer sizes.As mentioned before, the large current pulse during astep moves the negative charge cloud over the length ofthe step. The radio emission during this step must havea wavelength of at least the spatial extent of the chargecloud (expected to be 10’s of meters) to be coherent andthus strong. Thus, the radiation from the stepping cur-rent itself has a peak intensity at frequencies well belowthe LOFAR band of 30 – 80 MHz (10 – 3.8 m) whichwould explain why this signal is not clearly visible in ourdata. It therefore would be very interesting to performsimultaneous measurements in the 100 kHz – 10 MHzband, where such current pulses are regularly observed.In this work we have established that the VHF emissionseen from stepping negative leaders in lightning are mostlikely due to streamer formation around the region of thestep. The VHF emission appears concentrated near thetip of the leader, potentially where the inception cloudbreaks up into streamers during a corona flash, whichhas not been observed in natural lightning before. Thereis also emission along the body of the step, potentiallydue to spurious streamer emission from the body of theleader. ACKNOWLEDGMENTS
The LOFAR cosmic ray key science project acknowl-edges funding from an Advanced Grant of the EuropeanResearch Council (FP/2007-2013) / ERC Grant Agree-ment n. 227610. The project has also received fundingfrom the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovationprogramme (grant agreement No 640130). We further-more acknowledge financial support from FOM, (FOM-project 12PR304). AN is supported by the DFG (NE2031/2-1). TW is supported by DFG grant 4946/1-1.This paper is based on data obtained with the Interna-tional LOFAR Telescope (ILT). LOFAR [19] is the Low Frequency Array designed and constructed by ASTRON.It has observing, data processing, and data storage facili-ties in several countries, that are owned by various parties(each with their own funding sources), and that are col-lectively operated by the ILT foundation under a jointscientific policy. 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