Inuence of hydrometeors on relativistic runaway electron avalanches D. Zemlianskaya Moscow Institute of Physics and Technology - 1 A Kerchenskaya st. Moscow 117303 Russian Federation and

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Inﬂuence of hydrometeors on relativistic runaway electron avalanches

D. Zemlianskaya

Moscow Institute of Physics and Technology - 1 “A” Kerchenskaya st., Moscow, 117303, Russian Federation and

Institute for Nuclear Research of RAS - prospekt 60-letiya Oktyabrya 7a, Moscow 117312

E. Stadnichuk

HSE University - 20 Myasnitskaya ulitsa, Moscow 101000 Russia

E. Svechnikova

Institute of Applied Physics of RAS - 46 Ul’yanov str., 603950, Nizhny Novgorod, Russia

(Dated: October 6, 2022)

Previously, all studies in this area of atmospheric physics, namely, avalanches of relativistic run-

away electrons (RREA), were carried out without taking into account the presence of hydrometeors

in thunderclouds, which could seriously aﬀect the results and their correspondence to actually ob-

served natural phenomena. This article takes into account hydrometeors in clouds. In this work,

the distribution of RREA was simulated in GEANT4 was simulated taking into account various

concentrations of ice particles. Modeling showed that accounting for the presence of hydrometeors

cannot be simpliﬁed and reduced to a change in the main substance. Two methods are considered

- modeling of volumetric hydrometeors as separate modeling objects and as a simple change in the

components of a whole substance (adding water to air with a corresponding density). These meth-

ods show completely diﬀerent results. Modeling by volumes of hydrometeors shows a decrease in the

length of the avalanche by 20 %, on the other hand, when modeling with a modiﬁed material, the

length changed only by 1 %. This suddenly proves that hydrometeors should be taken into account

in research, as they can signiﬁcantly change the growth length of an avalanche in real thunderstorm

condition.

I. KEYPOINTS

•The presence of hydrometeors contributes to the

narrowing of the beam of avalanches of relativistic

runaway electrons

•The realistic density of hydrometeors in a cloud can

reduce the avalanche growth length by 20 percent,

which leads to the signiﬁcant increase in the num-

ber of relativistic electrons in thunderstorms

•The eﬀect of runaway electrons multiplication is

connected with the geometry of the hydrometeors,

the contribution of their density and chemical com-

position proved to be neglectable

II. INTRODUCTION

Research of high-energy phenomena in atmospheric

electricity has been going on for several decades, but

there are still many unsolved mysteries. One thing is

known for sure — the main participants in all high-energy

thunderstorm processes are runaway electrons ([1], [2], [3]

[4]). Electrons in strong large-scale thunderstorm elec-

tric ﬁelds can obtain more energy from acceleration by

the electric ﬁeld than they in average lose on interactions

with air molecules. Such accelerating electrons are called

runaway electrons [5, 6]. Runaway electrons can pro-

duce additional runaway electrons by Moller scattering

on air molecules [7]. In this way, runaway electrons mul-

tiply and form a relativistic runaway electron avalanche

(RREA). Electric ﬁeld strength necessary for RREA pro-

duction is called critical electric ﬁeld and depends on the

air density [7]. RREAs are commonly studied using nu-

merical calculations [8] [9] [10] and Monte Carlo simula-

tions ([11]; [12]; [13]; [14]; [15]). Analytical solutions for

individual RREAs were described in ([4]; [16]; [12]).

Runaway electrons radiate bremsstrahlung gamma-

rays when they interact with air. These gamma-rays

are detected as high-energy component of TGE [17] [18].

Relativistic runaway electron avalanches are believed to

cause thunderstorm gamma-ray glows [19]. In addition,

RREA bremsstrahlung is considered as one of possible

sources of TGF [20], [21], [22], [23]. TGF diﬀers from

the other high-energy atmospheric physics phenomena

in its short duration and high brightness. For RREAs to

cause a TGF large number of relativistic runaway elec-

tron avalanches is required [24].

The main problem in the formation of a discharge in

thunderclouds lies in the weak electric ﬁeld, which is ob-

served experimentally. The value of the observed diﬀers

from that required for a normal discharge by an order of

magnitude ([25], [26], [27], [28]). Hence, there is a need

to consider new eﬀects that can increase the electric ﬁeld

and contribute to the formation of lightning and Thun-

derstorm Ground Enhancement (TGE).

However, it has never been possible to get enough elec-

trons for lightning and for initiation TGF [24], [4], [8].

With a large number of particles, we would observe a

decrease in the required value of the electric ﬁeld for

arXiv:2210.01916v1 [physics.ao-ph] 4 Oct 2022

breakdown due to mass character. Also, the strength

of feedback would increase many times over [8], [6]. The

key parameter of an avalanche is its growth length, and

for real conditions in a cloud, it is quite large, so there

are few high energy particles in avalanche.

Naturally, a cell (a selected area of a thundercloud with

a directed electric ﬁeld [29]) of a thundercloud cannot be

considered ideally homogeneous. The mass density of

hydrometeors in cumulonimbus clouds typically is up to

0.5 g/m3according to [30]. Approximations are usually

considered due to the small scale of the selected area.

Moreover, the presence of hydrometeors should be taken

into account.

Previously, hydrometeors were considered in streamer

physics. Studies have been carried out on the possible

role of corona discharges on ice hydrometeors [31]. A

class of hypotheses for the initiation of lightning and

sprites suggests that streamers are able to form around

the sharp tips of conducting objects (e.g., thundercloud

hydrometeors for lightning and ionospheric ionization

patches for sprites) placed in an electric ﬁeld much

weaker than the value of the electric ﬁeld at which the

electrons are accelerated rather than damped due to col-

lision [32]. That is, impurities in clouds were previously

considered as the cause of a change in the electric ﬁeld,

and not as an eﬀect due to a change in the mass fraction

of water in space, or, as the appearance of a dense inho-

mogeneity, a change in the direction of particle propaga-

tion and, as a consequence, a change in the total number

of formed particles.

In this work, we have shown that unexpectedly hy-

drometeors eﬃciently multiply runaway electrons. By

analogy with the interaction with air particles, runaway

electrons can interact with hydrometeors in thunder-

clouds. This results in a 20% reduction in avalanche

growth length for a realistic number of hydrometeors and

thus in the increase of the number of electrons.

In this article, the inﬂuence of the presence of hydrom-

eteors in thunderclouds is studied. Also, the inﬂuence of

the atomic composition of the substance is considered

speciﬁcally, without taking into account the change in

the electric ﬁeld by the particles of hydrometeors. This

article presents the analysis of RREAs development in

the cloud, based on numerical modeling. Describes two

diﬀerent modeling options taking into account hydrome-

teors. The second section ”Modeling” describes the mod-

eling of energetic particles behaviour in the media of the

cloud modeled in two diﬀerent ways: model with volu-

metric hydrometeors and model with modiﬁed material.

Section 2.2 presents the simulation results with volumet-

ric hydrometeors. A comparison is made of the number of

produced electrons with an increase in the mass fraction

of hydrometeors and one radius, as well as one mass frac-

tion and diﬀerent radius.A comparison of the spectrum

at the exit of a cell with and without a small number

of volumetric hydrometeors, and a simulation with one

hydrometeor is also presented. Section 2.3 presents the

simulation results with modiﬁed material. The results in

the section prove that the eﬀect obtained is not a con-

sequence of a change in the nuclear composition of the

substance (adding an ice component).

III. MODELING

A. General properties

Numerical modeling is one of main instruments in at-

mospheric physics, crucial in conditions of limited mea-

surement data, and useful for analyzing complex mecha-

nisms verifying the results of other studies. In present

study we carried out Monte Carlo simulation using

GEANT4 version 4.10.06.p01. GEANT4 is widely known

and used for the problems of simulating the passage of

particles through matter. Its ﬁelds of application include

high energy physics, nuclear and accelerator physics, as

well as medical and space research [33].

We used the Physics list

G4EmStandardPhysics option4. It should give ac-

curate results in electromagnetic physics simulations.

We developed two approaches to modeling the cloud

media with hydrometeors: model with volumetric hy-

drometeors and model with modiﬁed material. Within

both approaches, the modeling volume was a cube with

a side of 200 m. The cube initially consists of air with

a density of 0.414 mg/cm3, which corresponds to the

density of air at a height of 10 km. Next, depending

on the chosen approach, we add hydrometeors. In the

cube the uniform electric ﬁeld with strength 200 kV/m

is applied. The direction is chosen so that the electrons

are accelerated in the direction of launch. The minimum

step for simulation was chosen as fMinStep = 0.01 mm.

An electron with an energy of 5 MeV is launched. We

ﬁx the born particles in the entire volume using the

SensitiveDetector (the sensitive detector class in Geant4

has the task of creating hits (deposits of energy) each

time a track traverses a sensitive volume and loses some

energy).

B. Model with volumetric hydrometeors

In this simulation, hydrometeors with a radius of 1

cm were used, which is bigger than a real hydrometeor.

However, modeling smaller balls leads to an increase in

their number at the same mass fraction, which compli-

cates the calculations. In order to justify the use of parti-

cles of this size, the following additional simulations were

carried out.

A cube with a side of 50 meters was taken, since in

this case one can limit oneself to measuring the number

of electrons, and not the growth length of the avalanche.

For exact values of the growth length, one should take

the length of several the growth length of an avalanche

so that it has time to stabilize. For us, in order to

model many small-radius hydrometeoroids for a given

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InuenceofhydrometeorsonrelativisticrunawayelectronavalanchesD.ZemlianskayaMoscowInstituteofPhysicsandTechnology-1A"Kerchenskayast.,Moscow,117303,RussianFederationandInstituteforNuclearResearchofRAS-prospekt60-letiyaOktyabrya7a,Moscow117312E.StadnichukHSEUniversity-20Myasnitskayaulitsa,Moscow101000R...

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Inuence of hydrometeors on relativistic runaway electron avalanches D. Zemlianskaya Moscow Institute of Physics and Technology - 1 A Kerchenskaya st. Moscow 117303 Russian Federation and

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