Shape of Thunderstorm Ground Enhancement and Radon Progeny Radiation

Thunderstorm ground enhancements (TGEs), are intensive and prolonged particle fluxes registered on the earth's surface. TGEs measured by particle detectors are correlated with thunderous occurrences and the high strength of the atmospheric electric field. Historically, TGEs on Aragats were measured with detectors having a high energy threshold (>3 MeV). The principal engine initiating TGEs with energies above 3 MeV was established to be Relativistic Runaway Electron avalanche (RREA, [1-3]), the most powerful natural electron accelerator operating in the earth's atmosphere, which accelerates and multiplies seed electrons from the ambient population of cosmic rays (CR).  Simultaneous measurements of the electron, gamma ray, and neutron fluxes on Aragats [4], and in-situ observation of RREAs [5,6], as well as measurements of the energy spectra of electrons and gamma rays [7], proved that RREA is a robust and realistic mechanism for electron acceleration up to 50 MeV (see right side of Fig. 1). However, the high-energy flux duration does not exceed a few minutes, and the recently discovered flux enhancements that last for hours [8]   can be explained by another process in the atmosphere, namely, the radiation of the Radon progeny lifted upward by the near-surface electric field (see right part of Fig. 1, details can be found in [9,10]). 238U and its first five daughter products are solids and remain in the ground, however, the sixth daughter product, the 222Rn, is a monoatomic noble gas with a density of 9.73 kg/m3, which is ≈10 times heavier than air on Aragats station altitudes. The half-life of 222Rn (3.82 d) is long enough to go out into the atmosphere. The well-known effects of the Rn progeny attachment to aerosols and aerosol charging mechanisms enable the uplift of gamma emitters to the atmosphere and consequent gamma ray emission which gives a significant contribution to overall TGE count rate enhancement in the low energy domain.
Network of large NaI crystals (6 units, 12 x 12 x 24 cm each) can reliably recover energy spectra from 0.3 to 50 MeV with resolution (FWHH) ~50% (minute count rate is ~ 50,000). Aragats Solar Neutron Telescope (ASNT) comprises 5 cm and 60 cm thick plastic scintillators with an area of 4 m2. ASNT measures energy release histograms in the energy range 4-100 MeV every 20 seconds (minute count rate is ~300,000). Electronics allow to measure intensities of electrons and gamma rays in 6 incident directions and estimate their energy spectrum. Gamma spectrometer produced by ORTEC firm measures gathe mma ray spectrum in the energy range 0.3 - 3 MeV with resolution ~7.7%; minute count rate is ~12,000. High resolution of ORTEC spectrometer allows us to resolve the 222Rn progenies radiation lines. All spectrometers operate 24/7 and can be cross-checked. Energy spectra are measured and stored at a sampling interval of 1 s (ORTEC), 20 s (ASNT), and 1 min (NaI network). Particle fluxes are registered in coincidence with atmospheric discharges registered by electric mills EM-100 of Boltek firm (the network of 4 electric mills also monitors near-surface electric field with 50 ms resolution) and by antennas attached to high-frequency digital oscilloscopes (capture length is 1 s, including 0.2 s before triggering flash and 0.8 after it). Thus, particle spectrometers with unprecedented wide energy range (0.3 -100 MeV) and high energy resolution in the low energy range (< 3MeV) provide observation of spectral lines of 222Rn progeny gamma radiation, as well as a continuous spectrum of gamma rays and electrons of TGE up to 100 MeV.  
One of the possible TGE initiation scenarios (realized mostly in the Spring season on Aragats) is shown right side of Fig.1 and explained in detail in [11]. With approaching thundercloud, the emerged near-surface electric field started to lift charged aerosols with attached Rn progenies. After several minutes the concentration of Radon progenies in the atmosphere becomes sufficient to add its overwhelming share to low energy cosmic ray flux (below 2 MeV). When electrified cloud approaches particle detector site and, if the strength and spatial extent of electric field satisfy the conditions for the RREA initiation, electrons are accelerated up to tens of MeV, and produce an avalanche. RREA is a threshold process that is triggered when the potential drop in the atmosphere reaches a threshold value that depends on the air density.  When the atmospheric electric field exceeds this threshold, CR electrons become "runaway"; instead of wasting all energy to ionization, runaway electrons produce knock-on electrons, bremsstrahlung gamma rays, etc. Avalanches comprise a hardcore of TGE - a few minutes of an intense flux of electrons and gamma rays with energies up to tens of MeV.  If cloud height is low above the earth's surface, particle detectors register an abrupt increase in the time series of count rate lasting a few minutes. 
During thunderstorms, the concentration of charged aerosols near the earth's surface is highly enhanced [12]. Radon progenies attached to charged aerosols and lifted by the near-surface electric field enlarge concentration of gamma emitters above the gamma spectrometers. Therefore, TGE continues for hours with much lower energies s. 

    

  Figure 1.  A schematic view of the natural radiation enhancement during thunderstorms.

However, the electric field can rise again and sometimes we observe several episodes of high-energy particle appearance and elimination after consequent lightning flashes. Normal intracloud flash (IC+) occurs between the MN and main positive charge layers, and the inverted intracloud flash (IC-) occur between the MN and the LPCR. Negative cloud-to-ground flashes (-CG) occur between MN and the ground. Lightning flashes headed to LPCR can be continued to the ground and become -CG [13]. 

Particle fluxes made enough ionization in the lower atmosphere to provide a path to the lightning leader and very often lightning flash terminates the TGE [14]. As the storm stops the RREA process completely disappear and only low-energy (<3 MeV) particles can be found in the flux. Although the near-surface electric field returns to fair weather values and, consequently, the Radon progenies updraft drops, the long-lived isotopes (214Pb - the half-live ≈27 minutes and 214Bi - the half-live ≈20 minutes) continue to emit gamma rays. After 60-90 minutes TGE finally stops and particle fluxes intensities return to fair weather value. The whole development of TGE included high-energy and low-energy parts lasting for 3-5 hours; sometimes continuous storms can enlarge this time span significantly. 

 2-COMPONENT MODEL OF THE TGE 

May 2018 was extremely rich with strong TGEs, in contrast with 2019 and 2020, when we observed no strong TGEs. On May 22 a large storm approaches Armenia from the South-West; during ≈3 hours of the storm, numerous episodes of particle flux enhancements occurred. 

  Figure 2. Time-series of disturbances of the near-surface electric field (black curve) and time series of the count rate of NaI spectrometers with energy threshold 0.3 MeV (blue curves). In the inset the time series of the count rate of NaI spectrometer with energy threshold 4 MeV.

In Fig. 2 we show the time series of count rate of NaI spectrometer with a low energy threshold (E > 0.3 MeV) measured during the storm. Detector with low energy threshold shows ~ 5 hours long particle flux enhancement with the largest peak coincided with the excursion of the near-surface electric field in the deep negative domain at ≈ 19:20 UT. The same TGE was measured by NAI detector with energy threshold 3 MeV, see inset in Fig.2. The time-series of the detector with a high energy threshold drastically differ from the NaI time series with a 0.3 MeV threshold. High energy particles are related to the RREA development in the atmosphere above the detectors. The runaway process requires a rather stringent condition of the strength and extension of the atmospheric electric field. Thus, in the count rate of high energy particles, we can see several short episodes only; the largest ones prolonged from 19:18 to 19:22. The differential energy spectra of the particle flux, which corresponds to the maximum intensity is shown in Fig.3.     

  

  Figure 3. The differential energy spectra of the TGE flux corresponding to the maximal intensity minute.

 We can see that the energy spectra consist of 2 distinct parts. The first one from -.3 to 2 MeV rather well is fitted by the exponential function, the second, from 3 MeV to 50 MeV demonstrates the power low dependence. 2-part energy spectrum was observed only during the large intensity peaks when the RREA was developed above particle detectors, whereas, during most time of the TGE duration particle detectors register Rn progeny radiation only, maximal energy does not exceed 2 MeV. 

 Thus, the shape of the TGE can be rather sophisticated, it is controlled by the intracloud and near-surface electric fields, and depends on the interplay of the sporadic RREA process and more-or-less continuous gamma ray radiation of Radon progeny. After the decay of the near-surface electric field, the count rate of NaI scintillators (E>0.3 MeV) does not immediately stop because of radiation of Radon progeny with a large half-life time (20:15-22:15). Such a characteristic long tail of the decaying TGE is common for all TGEs.  

ENHANCEMENT OF THE OF NATURAL GAMMA RADIATION DURING THUNDERSTORMS 

 Thus, radon progenies radiation significantly contributes to the count rate enhancements in the energy range below 3 MeV. However, the mechanism of this phenomenon remains unknown until we learn from the early work [15] that "Radon-daughter ions are found to disappear almost completely at ground level under an active thunderstorm due to upward migration of the ions under the influence of strong electric fields." In [16] was measured the strong correlation between gamma ray levels, precipitation and vertical component of the near-surface electric field. In many other studies was observed that radon and its progenies are very mobile and, readily attach to aerosols surfaces. Thus, emanated radon progenies become airborne and immediately attach to the dust particles and aerosols existing in the atmosphere and are lifted by the near-surface electric field upward providing isotropy radiation of low energy gamma rays (see right side of Fig. 1). Owing to their long half-life (27 and 20 minutes) 214Pb and 214Bi are the most abundant radon progenies in the atmosphere and candidates for the NGR at low energies. In Summer 2019 we perform several simple experiments with NaI spectrometers to reveal the contribution of Rn progenies by covering some of spectrometers with lead filters. First of all, we put spectrometers on the lead to prove that the TGE flux comes from the top and sides of the crystal, and not from the bottom. Then, covering spectrometers from the top, we prove that the low energy portion of TGE comes under large zenith angles. The high-energy portion of TGE comes only from the near-vertical direction due to the vertical alignment of the atmospheric electric field. Spectrometer with the lead filter on the top measures only isotropic inclined flux from 222Rn progeny gamma radiation. As storm finishes, the electric field strength returns to fair-weather value, and the boosted uplift of Rn progenies stops. The half-life of count rate decay (20-35 minutes) well fits the half-life of the most-abundant gamma emitters from the Rn chain, namely 214Pb (half-live -27 minutes) and 214Bi (half-live -20 minutes). Sure, we cannot expect exact coincidence of TGE half-life and isotope half-life: different isotopes appear in the atmosphere in a slightly different time, there are various decay modes with different branching ratios; processes in the atmosphere are very dynamic, dependent on precipitation, wind, temperature, and electric field fast changes due to lightning flashes.

In Fig. 4 we show the time series of count rates measured by NaI spectrometers N 2 (upper curve) and N 4 (lower curve, 4 cm lead on the top). Between these curves, the disturbances of near-surface electric field measured by electric mill EFM-100 are shown. In the insets to the left (a and c) we demonstrate time series of maximal energies of the recovered differential energy spectra for each minute of TGE. In the right insets (b and d) we demonstrate the examples of these one-minute energy spectra for both spectrometers.  
  

 

Figure 4. One-minute time series of TGE measured on September 4 (see Fig 2c) by NaI spectrometers with the lead filter on top (bottom blue curve) and without lead (top blue curve). The disturbances of the near-surface electric field are shown between these curves (black). In inset a) and c) we show the histogram of maximal energies of energy spectra measured each minute by both spectrometers and in insets b) and d) - examples of measured energy spectra.

50 MeV peak near 21:00 seen in insets 4a and 4b corresponds to high energy gamma rays from RREA developed in the thunderous atmosphere above the detector. Both RREA and MOS processes produced a near-vertical flux of gamma rays. The maximal energies measured by the spectrometer with lead on the top (isotropic gamma rays from radon progenies decay, see Figs 4c and 4d) never exceed 2 MeV. THE RADON PROGENY WASHOUT FROM THE ATMOSPHERE The static electric field in the lower atmosphere is modulated by the mobile particles carrying electrical charges, i.e., different types of hydrometeors, aerosols, small ions, and progeny of radioactive isotopes. The charge separation initiated by the updraft of moisture generates an electric field between differently charged layers emerging in the thundercloud; potential drop (voltage) in the cloud can reach hundreds of megavolts. Emerging near-surface electric field lifts charged aerosols with attached 222Rn isotope and its progeny to the atmosphere. Correspondingly, the concentration of 222Rn at the surface decreases 10 times [15, 17] (Wilkcning et al., 1966, Roffman, 1972); the small ions and aerosols with attached 222Rn are lifted up in seconds to tens of meters due to their large mobility. These gamma emitters significantly enhance low-energy natural gamma radiation measured by spectrometers located several meters above the ground. The rain returns long-lived progeny to the Earth recovering and somewhat enhancing the surface radiation (washout process, [18-22]. To check the details of the washout process and confirm the Radon circulation during thunderstorms, we measure the intensity of the different 222Rn progenies in the rainwater to estimate the percentage of isotopes returned by the rain to the Earth surface. For measurements, we use the precise ORTEC firm gamma spectrometer (NaI (Tl), FWHM ∼7.7% at 0.6 MeV, see details in [23]) surrounded with lead filters. Simulations of the cosmic radiation, radon progeny radiation, and detector response function calculation were performed with the aid of the EXPACS code [24]. Gamma radiation measured on the earth's surface comes from the ground and from the atmosphere. The largest surface contribution is from gamma rays originating in the mineral grain, in their crystal lattices, and in the construction materials.  The radiation is stable because the concentration of radionuclides in minerals and construction materials is constant due to long half-lives of their parent isotopes (40K, 238U, 232Th, see details in[25]). Therefore, to investigate Radon progeny circulation (lifted by the near-surface electric field and returned through precipitation from rain) in the atmosphere we need to take into account and filter as much as possible this more-or-less stable contribution of the radionuclides from the surface. Gamma spectrometers are positioned on Aragats in the experimental hall which is 3 meters high and located under a metallic tilt roof of 0.6 mm thickness. By surrounding the ORTEC spectrometer with the 4-cm thick lead filter (see Fig. 5) we suppress the Radon progeny gamma radiation ≈12 times; the count rate of the spectrometer decreases from 12600 ± 112 to 1080 ± 34. In 2020 the first rain on Aragats was in June and rain showers were only during July, when it became possible to collect rainwater in the special container in a few minutes and then expose it to the crystal of ORTEC spectrometer fully covered by 4-cm thick lead bricks. 

     

Figure 5. ORTEC firm gamma spectrometer (NaI (Tl), FWHM ∼7.7% at 0.6 MeV, see details in (Hossain et al., 2012), surrounded by 4 cm thick lead filters. The spectrometer is positioned in the experimental hall on Mt Aragats (3200 m MSL) which is 3 meters high and located under a metallic tilt roof of 0.6 mm thickness

In Fig. 6 we show spectrograms of atmospheric radiation of Radon progeny and of radiation of the Radon progenies from the collected rainwater. In Table 1 we show the corresponding count rates of gamma emitters including radioactive isotopes, positron annihilation, and continuous spectrum of secondary cosmic rays (mostly muons) and gamma rays scattered in the body of the NaI crystal (continuum to the right of each spectral line). 

    

Figure 6. Spectrograms of gamma-emitters of atmospheric and rainwater origin.


Table 1. The shares of gamma emitters of atmospheric and rainwater origin including radioactive isotopes, positron annihilation,
511 keV line, and continuous spectrum of secondary cosmic rays (mostly muons) and gamma rays scattered in the body
of the NaI crystal (continuum to the right of each spectral line). For each event, the share of each group is calculated
and in the last line, the mean of the 4 evetns is shown.

    Atmospheric 222Rn progeny radiation                                                          Rainwater 222Rn progeny radiation
  Sum    [0.3-3] 214_Pb [0.33-0.38] MeV 214_Bi [0.56-0.66] MeV Sum radionuclide (others) CR+ Compton scatter   Sum [0.3-3] MeV 214_Pb [0.336-0.38] MeV 214_Bi [0.56-0.66] MeV Sum radionuclide (others) CR+ Compton scatter
11:09:2019 at Time [11:05 - 12:05] count rate[1/min] 1818 415 291 489 623 21:07:2020 at Time [14:27 - 15:07] count rate[1/min] 133 31 24 37 41
%   22,83 16,01 26,90 34,27 %   23,31 18,05 27,82 30,83
28:09:2019 at Time [08:45 - 09:45] count rate[1/min] 681 174 112 167 228 23:07:2020 at Time [12:31 - 12:51] count rate[1/min] 629 147 112 149 221
%   22,83 16,01 26,90 34,27 %   23,37 17,81 23,69 35,14
01:11:2019 at Time [15:30 - 16:30] count rate[1/min] 749 186 115 180 268 23:07:2020 at Time [18:26 - 18:46] count rate[1/min] 554 119 101 166 168
%           %   21,48 18,23 29,96 30,32
27:11:2019 at Time [14:40 - 15:40] count rate[1/min] 847 190 132 207 318 24:07:2020 at Time [17:26 - 17:46] count rate[1/min] 853 185 155 243 270
%   22,43 15,58 24,44 37,54 %   21,69 18,17 28,49 31,65
Mean%   23,91 15,85 24,97 35,27 Mean%   22,46 18,06 27,49 31,99

As it was expected from previous measurements the most pronounced peaks are 214Pb and 214Bi and the share of different gamma-emitting isotopes in the atmosphere measured by the same spectrometer well coincides with the spectra measured from the rainwater. The concentration of the most abundant gamma emitters in the rainwater 214Pb, 214Bi(609keV), 214Bi (1.12 MeV) was 25.3 ± 0.8%, 19.5 ± 1%, and 7.5 ± 0.2% in the first minute of the exposing of the rainwater to the ORTEC spectrometer. In the last, 150-th minute of exposition, the concentration of these isotopes changed to 13.5 ± 0.7%, 25.6 ± 1.8%, and 17.1 ± 2.8% accordingly due to radioactive decay.  As we see from the overall composition of the 222Rn progeny in rainwater coincides well with one recovered from the registered gamma radiation of the atmospheric origin. Rainwater share of the 214Pb is a bit less and the share of 214Bi is larger due to the spend from collecting the rainwater to exposing it to the ORTEC NaI crystal. The 214Bi isotope is originated from the 214Pb. Thus, the near-surface electric field lifts the 222Rn and its progeny up in the atmosphere, and the rain return it backward in this way providing the circulation of the radioactive isotopes and enlarging surface radioactivity during thunderstorms.

We analyzed the TGE development according to the main physical processes responsible for TGE origination, namely RREA and Radon progenies radiation. We explain the impact of both processes on the TGE shape and energy spectrum. We conclude that TGE is a rather complicated phenomenon having roots in at least 3 physical processes related to thunderous atmospheres. These processes are controlled by the electric field emerging in the thundercloud and near the earth's surface. RREA is a triggered process started in thundercloud only when the electric field surpasses the threshold value specific for the particular atmospheric density. Gamma radiation of Radon origin starts when the updraft of aerosols (with attached radiated isotopes) provides a sufficient concentration of gamma ray emitters at heights above particle detectors.   RREA radiation is near-vertical, whereas the isotope radiation is isotropic (see Fig. 1) and can be registered at large zenith angles. 
 We demonstrate that there are several signatures (tracers, tags) of the RREA occurrences within the long-lasting TGE: 

1. An abrupt surge of particle flux intensity for several minutes;  
2. Presence of gamma rays/electrons with energy above 3 MeV in the energy spectra; 
3. Detection of the individual electron avalanches by the distributed surface array; 
4. Abrupt decline of high energy species (> 3 MeV) of TGE caused by lightning flashes; 
5. Origination of LPCR evidenced by reversal of polarity of the near-surface electric field and by detection of the graupel fall; 
6.  Detection of the enhanced fluxes from the near-vertical direction. 

We separate "pure" Radon progenies radiation as a continuous part of hours lasting TGE. The shape of the TGE time-series is rather complicated and is controlled by the intracloud electric field and near-surface electric field and by decay time of most frequent 214Pb (0.354 MeV) and 214Bi (0.609 MeV) isotopes of the Radon decay chain. After the fast rise, the TGE continues by a long decaying "tail". Thus, the shape of the TGE can be separated into 3 species:  
1. Induced by relativistic runaway electron avalanches in the thundercloud - large, reaching several hundred percent peaks above background lasting few minutes with particle energies reaching tens of MeV; fluxes are usually interrupted by lightning flash. Particles come from the near-vertical direction.
 
2. Radon progenies radiation - low energy (< 2MeV) hours continued radiation never interrupted by lightning; particles come isotropic; 

3. The decay phase - decay of Radon progeny that still concentrated in the air after the storm finished. The half-life time of TGE decay is consistent with the half-life time of 214Pb (~300keV peak) and 214Bi- (~600 keV peak) isotopes from the Radon chain. 

REFERENCES:

1.    A.Gurevich, G. Milikh, and R. Roussel-Dupre, Runaway electron mechanism of air breakdown and preconditioning during a thunderstorm, Phys. Lett. A 165, 463 (1994).

2.    L. Babich, E. Donskoy, I. M. Kutsyk, A. Yu. Kudryavtsev, R. A. Roussel-Dupré, B. N. Shamraev, and E. M. D. Symbalisty, Comparison of relativistic runaway electron avalanche rates obtained from Monte Carlo simulations and from kinetic equation solution, IEEE Trans. Plasma Sci. 29, 430 (2001). 

3.    J. Dwyer, A fundamental limit on electric fields in air, Geophys. Res. Lett. 30, 2055 (2003).

4.    A.Chilingarian, A. Daryan, K. Arakelyan, A. Hovhannisyan, B. Mailyan, L. Melkumyan, G. Hovsepyan, S. Chilingaryan, A. Reymers, and L. Vanyan, Ground-based observations of thunderstorm-correlated fluxes of high-energy electrons, gamma rays, and neutrons, Phys. Rev. D 82, 043009 (2010).

5.    A.Chilingarian, G. Hovsepyan, and A. Hovhannisyan, Particle bursts from thunderclouds: Natural particle accelerators above our heads, Phys. Rev. D 83, 062001 (2011).

6.    A.Chilingarian G.Hovsepyan, B.Mailyan, In situ measurements of the Runaway Breakdown (RB) on Aragats mountain, Nuclear Inst. and Methods in Physics Research, A 874,19 (2017).

7.    A.Chilingarian, B. Mailyan, and L. Vanyan, Recovering of the energy spectra of electrons and gamma rays coming from the thunderclouds, Atmos. Res. 114-115, 1 (2012).

8.    A.Chilingarian, G. Hovsepyan, S. Soghomonyan, M. Zazyan, and M. Zelenyy, Structures of the intracloud electric field supporting origin of long-lasting thunderstorm ground enhance- ments, Phys. Rev. D 98, 082001 (2018).

9.    Chilingarian, A. Avetisyan, G. Hovsepyan, T. Karapetyan, L. Kozliner, B.Sargsyan, et al., Origin of the low-energy gamma ray flux of the long-lasting thunderstorm ground enhancements, Phys. Rev. D 99, 102002 (2019).

10.  A.Chilingarian, Reply to "Comment on ‘Long lasting low energy thunderstorm ground enhancements and possible Rn-222 daughter isotopes contamination, Phys. Rev. D 99, 108102 (2019).

11.  A.Chilingarian, G. Hovsepyan, A. Elbekian, T. Karapetyan, L. Kozliner, H. Martoian,  and Sargsyan, Origin of enhanced gamma radiation in thunderclouds, Physical review research, 1, 033167 (2019).

12.  Hong-Ku Lee, Kang-Ho Ahn, Charging Effect on the 80-200 nm Size Atmospheric Aerosols during a Lightning Event, Aerosol and Air Quality Research, 17, 2624, (2017).

13.  A.Nag, and V. Rakov (2009), Some inferences on the role of lower positive charge region in facilitating different types of lightning, Geophys.Res. Lett., 36, L05815.

14.  A. Chilingarian, S. Chilingaryan, T. Karapetyan, et al., On the initiation of lightning in thunderclouds, Scientific Reports 7, Article number: 1371, (2017).

15.  M. Wilkening, M. Kawano & Carlton Lane, Radon-daughter ions and their relation to some electrical properties of the atmosphere, Tellus, 18:2-3, 679-684, DOI: 10.3402/tellusa. v18i2-3.9199, (1966).

16.  Y.Reuveni, Y.Yair, C.Price and Gideon Steinitz, Ground level gamma-ray and electric field enhancements during disturbed weather: Combined signatures from convective clouds, lightning and rain, Atmospheric Research 196 142 (2017).

17.  Roffman, A. (1972). Short-lived daughter ions of radon-222 in relation to some atmospheric processes, J. Geophys. Res., 27, 5883.

18.  McCarthy, M., & Parks, G. K. (1992). On the modulation of X-ray fluxes in thunderstorms. Journal of Geophysical Research, 97(D5), 5857-5864. https://doi.org/10.1029/91JD03160.

19.  Reuveni Y., Yair Y., Price, c., and Steinitz, G., (2017). Ground level gamma-ray and electric field enhancements during disturbed weather: Combined signatures from convective clouds, lightning and rain, Atmospheric Research 196, 142-150.

20.  Barbosa S.M., Miranda, P., Azevedo, E.B. (2017). Short-term variability of gamma radiation at the ARM Eastern North Atlantic facility (Azores), Journal of Environmental Radioactivity 172, 218.

21.  Fabró, F., J. Montanyà, N. Pineda, et al. (2016). Analysis of energetic radiation associated with thunderstorms in theEbro delta region in Spain, J. Geo- phys. Res. Atmos., 121, 9879.

22.  Chilingarian, A., Hovsepyan, G., Karapetyan, T., et al., (2020). Structure of thunderstorm ground enhancements, PRD 101, 122004.

23.  Hossain, I., Sharip,N., and Viswanathan, K.K. (2012). Efficiency and resolution of HPGe and NaI(Tl) detectors using gamma- ray spectroscopy, Sci. Res. Essays 7, 86.

24.  Sato, T. (2018). Analytical Model for Estimating the Zenith Angle Dependence of Terrestrial Cosmic Ray Fluxes, PLOS ONE, 11(8): e0160390, http://phits.jaea.go.jp/expacs/.

25.  Chilingarian, A., Avetisyan, A., Hovsepyan, G., et al. (2019). Origin of the low-energy gamma ray flux of the long-lasting thunderstorm ground enhancements, Phys. Rev. D 99, 102002.