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\begin{document}

\title{TGE electron energy spectra: Comment on ``Radar Diagnosis of the
Thundercloud Electron Accelerator'' by E. Williams et al. (2022)}



\author[1]{Ashot A. Chilingarian}%
\author[1]{Gagik Hovsepyan}%
\author[1]{Mary Zazyan}%
\author[2]{Balabek Sargsyan}%
\author[3]{Tigran KArapetyan}%
\author[3]{Levon Vanyan}%
\affil[1]{Yerevan Physics Institute}%
\affil[2]{Yerevan physics Institute}%
\affil[3]{yerevan physics institute}%


\vspace{-1em}



  
  \date{May 24, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Williams et al. (2022) questioned TGE electron energy spectra measured
on Aragats; they conclude that ``A more likely origin for any detected
electrons at 3.2 km MSL is Compton scattering and pair production
activated by longer-range bremsstrahlung gamma rays, themselves produced
by runaway electron encounters with nuclei in breakeven field at higher
altitude ``.

In this comment, we show that the selection criteria of ``electron''
TGEs unambiguously reject the assumption on the origination of TGE
electrons from the Compton process of the TGE gamma rays. Additionally,
comparison of recovered gamma ray and electron energy spectra allows to
estimate the height of the strong accelerating electric field above
particle spectrometers and establish 24/7 monitoring of the horizontal
profile of the atmospheric electric field during thunderstorms.%
\end{abstract}%



\sloppy


\textbf{TGE electron energy spectra: Comment on ``Radar Diagnosis of the
Thundercloud Electron Accelerator'' by E. Williams et al. (2022)}

A. Chilingarian, G. Hovsepyan, T. Karapetyan, B. Sargsyan, L. Vanyan,
and M.Zazyan

\emph{A. Alikhanyan National Lab (Yerevan Physics Institute), Yerevan
0036, Armenia}

\textbf{Key points}

The contribution of the Compton scattered electrons to TGE flux is
negligible.

The Aragats Solar Neutron Telescope (ASNT) 24/7 measures gamma ray and
electron (if any) energy spectra for [?]15 years.

If the strong accelerating electric field is low above the earth's
surface (150-200 m) TGE electrons reach ASNT and their energy spectrum
is reliably recovered.

Comparison of the energy spectra of the electrons and gamma rays allows
remote sensing of the vertical profile of the atmospheric electric
field.

\textbf{Introduction}

E. Williams et al. (2022) questioned TGE electron energy spectra
measured on Aragats; they conclude that ``A more likely origin for any
detected electrons at 3.2 km MSL is Compton scattering and pair
production activated by longer-range bremsstrahlung gamma rays,
themselves produced by runaway electron encounters with nuclei in
breakeven field at higher altitude ``.

In this comment, we show that the selection criteria of ``electron''
TGEs unambiguously reject the assumption on the origination of TGE
electrons from the Compton process of the TGE gamma rays. Additionally,
comparison of recovered gamma ray and electron energy spectra allows to
estimate the height of the strong accelerating electric field above
particle spectrometers and establish 24/7 monitoring of the horizontal
profile of the atmospheric electric field during thunderstorms.

\textbf{Electron and gamma ray propagation in the terrestrial
atmosphere}

When gamma rays and electrons multiplied in the relativistic runaway
electron avalanche (RREA, Gurevich et al., 1992, Babich et al., 2001,
Dwyer, 2003) exit the region of the strong electric field, both species
are attenuated in the dense air, but in a very different way. Electrons
lose almost a fixed portion of energy crossing each meter of air ([?]0.2
MeV at altitudes 3-4 km), whereas the gamma rays lose at each meter only
a small percent of their intensity; therefore, gamma rays of all
``primary'' energies can reach the ground. This difference in the
attenuation rates of the main species of TGE allows one to approximately
estimate the height above ground where the strong electric field
terminates. From Table 1 we can see, that if the electric field
terminates at 400 m above the ground, the TGE electrons with energies
above 64 MeV only can be registered. At exceptional atmospheric
conditions, only very few electrons can be accelerated to such high
energies. In contrast, [?]50\% of gamma rays can reach the ground and lead
to a large enhancement of intensity measured by surface detectors; the
energy spectrum of gamma rays can be reliably recovered by NaI and other
scintillation spectrometers. Sure, the gamma ray ``beam'' traveling in
the air undergoes various well-known interactions with air atoms. The
most important are the photoelectric effect, pair production, and
Compton scattering (in MeV region, the Compton scattering is the
dominant process).

\textbf{Table 1. Energy losses of electrons and attenuation of the gamma
ray flux traveling different distances in the air above Aragats station
(3200 m a.s.l.)}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Distance above Aragats station (m)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Expected gamma ray flux absorption (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Electron losses on ionization (MeV)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
50\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
8.67\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
8\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
100\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
16.6\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
16.1\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
200\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
30.44\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
32.1\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
300\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
41.98\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
48.23\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
400\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
51.62\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
64.3\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
1000\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
83.7\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
10000\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
99.99999\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

However, the number of electrons produced by RREA gamma rays is rather
small as compared to the ``parent'' gamma ray number, and their energies
are also much smaller than gamma ray energies. As we can see in Fig. 1,
the fraction of Compton scattered electrons in the TGE flux is less than
1\% relative to the gamma ray flux. Obviously, for such a small
fraction, it is not possible to reliably separate the electron flux from
the overall TGE flux. Only gamma ray energy spectrum can be recovered
from the energy release histograms in particle spectrometers operating
on Aragats.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1. The comparison of the energy spectra of the gamma rays
(parent particles) and Compton scattered electrons. The accelerating
electric field terminates at the height of 400 m above detectors.}

In Fig. 1 we show the electron and gamma ray energy spectra obtained
with GEANT4 simulations of the RREA in the atmosphere. We examined the
RREA process for various vertical profiles of the atmospheric electric
field, and on the basis of this examination, we select plausible
combinations of the field strength and extension, which support RREA
emergence (Chilingarian et al., 2021a and 2021b). Using some of these
values (electric field 1.9-2.1 kV/cm and field extension 2 km) we
simulate the RREA propagation to the earth's surface using 1 MeV
electrons as seeds. The height of the termination of the accelerating
electric field was preset to 400 m, thus no RREA electron can reach the
ground, see Table 1. Only electrons generated by the gamma rays nearby
the earth's surface can be registered. The electron content is less than
1\% for simulations of the gamma ray content for the electron energies
above 7 MeV. Under these conditions, it is practically impossible to
recover the electron energy spectrum with the ASNT spectrometer, it can
be done only if the electron to gamma ray ratio is larger than [?]10\%. A
detailed description of the ASNT spectrometer and the method of energy
spectra recovery can be found in (Chilingarian et al., 2022c). Thus, the
necessary condition of recovering of the electron energy spectrum is the
considerably large portion of electrons relative to gamma rays.

\textbf{Examples of the electron spectrum recovery}

In Fig. 2a we show the time series of count rates of two ASNT
coincidences, namely ``01'' -- signal only in the lower layer of the
ASNT spectrometer (60 cm thick scintillator), and ``11'' -- signals in
both layers of the spectrometer (also in the upper layer -- 5 cm thick
scintillator). The detection efficiency of the 5-cm scintillator is
[?]99\% for electrons and 6-7\% for gamma rays; for the 60-cm thick
scintillator, the efficiency is 99\% for electrons, and nearly 50\% for
gamma rays. Thus, particles registered by ``01'' coincidence are mostly
gamma rays, and by ``11'' coincidence -- electrons. As we can \selectlanguage{russian}сее in
Fig. 2a, during the minute 2:03-2:04 on October 6, 2021, we have a
significant enhancement of the electron flux, that allows one to recover
electron energy spectra. In Fig. 2b we show the recovered energy spectra
of both species of TGE. The electro-to-gamma ray ratio reaches 13\%,
much larger than the ``11''/''01'' ratio due to the much larger
attenuation of the electrons compared to gamma rays in the upper
scintillator of the ASNT spectrometer. To reach the lower scintillator,
electrons cross the 5 cm thick scintillators and metallic tilts of the
detector housings.

The fraction of electrons can be quite large if the strong electric
field extends almost to the ground. An example of a large fraction of
electrons is demonstrated in Fig.2c which shows an exceptional TGE that
occurred on 19 September 2009, just at the start of the TGE research on
Aragats.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2. a) 2-s time series of count rates of coincidences
registered by ASNT spectrometer, shown in percent of the count rates
measured at fair weather before TGE; b) energy spectra of both TGE
species recovered from energy release histograms; c) 1-min time series
of count rates of coincidences registered by ASNT spectrometer; d)
energy spectra of both TGE species recovered from energy release
histograms.}

In Fig. 2c we show the same ASNT spectrometer coincidences, as in Fig.
2a but for the 1-min time series of count rates (in 2009 the ASNT
electronics sampling time was 1 minute.). As we can see in Fig. 2d, the
intensities of electron and gamma ray spectra are almost equal at high
energies, and the electron to gamma ray ratio reaches 66\% at the minute
22:49-22:50. It can happen only if a strong accelerating electric field
is very low above the ground (we estimate the height to be 25-50 m) and
the electron avalanche covers a sizable area on the ground. Thus, the
fraction of electrons in the TGEs selected for energy spectra
recovering, are much larger than the fraction of Compton scattered
electrons.

\textbf{Characteristics of selected TGE events with large electron
content}

In Table 2 we show several parameters of TGEs for with we recover the
electron energy spectrum and estimate the height of the termination of
the accelerated electric field. A full set of TGE parameters is
available from the Mendeley data set (Chilingarian et al., 2022b)

In the first column of the table, we put the date of the TGE that
occurred during 3 last years (2019-2021). In the second column of the
table, we show the power-law index of the electron differential energy
spectra derived from the energy release histograms measured by the

ASNT spectrometer; in the third column - the same for the gamma ray
spectra. In the fourth column - integral electron spectra from 7 MeV, in
the fived - the same for gamma ray spectra. In the sixth and seventh
columns, maximal energies of electrons and gamma rays; in the eighth
column, we post the TGE significance - the percent of flux enhancement
relative to fair weather value measured just before TGE, count rate of
SEVAN detector upper scintillator (combination ``100'') was used (energy
threshold 7 MeV). In the ninth column, we show the approximate estimate
of the strong accelerating electric field termination height obtained by
the equation: H(m) [?] (1.2E\selectlanguage{greek}γ\selectlanguage{english}(max)- Ee(max))/0.2, where E\selectlanguage{greek}γ\selectlanguage{english}(max) and
Ee(max)) are estimates of maximum energies of gamma rays and electrons
as measured on the earth's surface and 0.2 MeV in the denominator is an
approximate value of electron energy losses in the 1 m of air
(Chilingarian et al., 2021d). We assume that the maximum energy of
electrons on the exit of the strong electric field can be approximated
by the measured on the earth's surface maximum energy of gamma rays
multiplied by a coefficient of 1.2 (this approximate equation is valid
for the electric field heights up to 200 m). Due to the fast attenuation
of the electron flux, electron spectra cannot be measured reliably by
the ASNT spectrometer if the accelerating electric field terminates
above 200 m). In the tenth column, we post the TGE duration; in the
eleventh column, we show the share of electron flux related to gamma ray
flux (above 7 MeV).

\textbf{Table 2. Parameters of electron and gamma ray energy and
estimates of the electric field heigh. Significances of peak enhancement
are larger than 5\%, Ne/Ng -- larger than 0.06}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllll@{}}
\toprule
\begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Date, (month.day. year)\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Power law Index el.\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Power law index gamma rays\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Int. Spectra el.\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Int. Spectra gamma rays\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Max energy el. (MeV)\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Max energy gamma (MeV)\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
TGE significance (\%)\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
El. Field height (m)\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
TGE duration (min)\strut
\end{minipage} & \begin{minipage}[t]{0.09\columnwidth}\raggedright\strut
Ne/ N?\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
06.14.19\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1.67\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.41\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1060\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
7570\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
16\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
70\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.14\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
06.18.19\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1.65\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.67\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1880\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
15390\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
40\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
13\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
150\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.12\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
07.07.19\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1.79\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.26\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
852\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
4810\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
34\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
50\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.18\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
06.14.20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.45\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.89\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2920\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
23410\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
18\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
39\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
140\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.12\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
06.27.20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1.61\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.61\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2150\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
11910\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
43\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
9\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
110\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
19\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.18\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
07.23.20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1.63\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.16\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1080\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
8894\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
24\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
35\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
90\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.12\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
09.25.20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.40\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.88\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
4790\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
29600\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
26\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
110\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.16\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
05.24.21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.34\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
920\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
9200\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
29\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
45\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
9\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
125\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
13\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.1\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
10.06.21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.04\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.92\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
6000\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
73200\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
43\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
45\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
46\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
55\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.08\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
09.24.21\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.18\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2.11\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2110\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3325\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
40\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.63\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
Mean\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1,92\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2,53\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2398\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
18730\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
38\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
95\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
6,8\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.19\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Averaged over 10 TGEs, the number of electrons is 2398, and number of
gamma rays is 19730. The Total number of Compton scattered electrons
according to Figure 1 will be [?]1\% of a total number of gamma rays,
i.e., 197. It will be 8.2\% of the total number of electrons only. From
Fig. 1 we can see those energies of scattered gamma electrons are much
lower than the energies of parent gamma rays, and consequently, much
lower than the energies of TGE electrons. Thus, the contamination of the
Compton scattered electron can slightly influence only lower energies of
the recovered electron energy spectrum.

\textbf{Conclusions}

If the accelerating electric field is terminated high above the ground
TGE electrons are attenuated, the contribution of the Compton scattered
electrons is negligible (less than 1\% relative to gamma ray flux) and
such TGEs never allow recovery of the electron energy spectrum. The
electron energy spectrum recovered only for TGEs with large electron
content (mean [?]20\%, see last row of Table 2 and Figure 2). The
corresponding height of the electric field termination is less than 150
m (mean[?]100 m). Only from these heights electrons from RREA above
Aragats can be reliably recovered by the energy releases histograms
measured by the ASNT spectrometer. Continuous monitoring of gamma ray
and electron energy spectra allows remote sensing of the atmospheric
electric field horizontal profile during thunderstorms.

\textbf{References}

L.P. Babich, I.M. Kutsyk, E.N. Donskoy, et al., Comparison of
relativistic runaway electron avalanche rates obtained from Monte Carlo
simulations and kinetic equation solution, IEEE Trans. Plasma Sci. 29
(3) (2001) 430--438. https://doi.org/ 10.1109/27.928940.

A.Chilingarian, T.Karapetyan, H.Hovsepyan, et. al. (2021a). Maximum
strength of the atmospheric electric field, PRD, 2021, 103, 043021.

A.Chilingarian, G. Hovsepyan, and M. Zazyan (2021b). Measurement of TGE
particle energy spectra: An insight in the cloud charge structure,
Europhysics letters, 134 (2021) 6901, https://doi.org/10.1209/0295-
5075/ac0dfa

A. Chilingarian, G. Hovsepyan, E. Svechnikova, and M. Zazyan, (2021c).
Electrical structure of the thundercloud and operation of the electron
accelerator inside it, Astroparticle Physics 132 102615
https://doi.org/10.1016/j.astropartphys.2021.102615.

A.Chilingarian, G. Hovsepyan, T.Karapetyan, et al. (2022a). Measurements
of energy spectra of relativistic electrons and gamma-rays avalanches
developed in the thunderous atmosphere with Aragats Solar Neutron
Telescope, Journal of Instrumentation, 17 P03002.

Chilingarian, Ashot; Hovsepyan, Gagik (2022b). ``Dataset for 16
parameters of ten thunderstorm ground enhancements (TGEs) allowing
recovery of electron energy spectra and estimation the structure of the
electric field above earth's surface '', Mendeley Data, V3, doi:
10.17632/tvbn6wdf85.3 https://data.mendeley.com/datasets/tvbn6wdf85/3

J.R. Dwyer, A fundamental limit on electric fields in air, Geophys. Res.
Lett. 30 (20) (2003) 2055. https://doi.org/10.1029/2003GL017781.

A.V. Gurevich, G. Milikh, R. Roussel-Dupre, Runaway electron mechanism
of air breakdown and preconditioning during a thunderstorm, Phys. Lett.
A 165 (1992) 463.

Williams, E., Mkrtchyan, H., Mailyan, B., Karapetyan, G., \& Hovakimyan,
S. (2022). Radar diagnosis of the thundercloud electron accelerator.
Journal of Geophysical Research: Atmospheres, 127, e2021JD035957.
https://doi. org/10.1029/2021JD035957

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