Volume 03 Issue 03-2023
58
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
I
SSUE
03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
The ionosphere is so named because it is a region in the atmosphere where ions exist. In most areas of the
atmosphere, molecules are in a combined state and remain electrically neutral. In the ionosphere, however, solar
radiation (mainly ultraviolet light) is so intense that when it strikes gas molecules they split-ionize and an electron is
set free. What remains is a positive ion (a molecule that is “missing” an electron) and a free electron. Although io
ns
give their name to the region, free electrons actually affect radio waves. The number of electrons starts to increase at
an altitude of about 30 km, but the electron density isn’t sufficient to affect radio waves until about 60 km. We often
think of the ionosphere as having a number of distinct layers.
KEYWORDS
Lonosphere, conductivity, dielectric constant, atmosphere
Research Article
STUDY OF DIELECTRIC PERMITTIVITY AND CONDUCTIVITY IN THE
IONOSPHERE
Submission Date:
March 21, 2023,
Accepted Date:
March 26, 2023,
Published Date:
March 31, 2023
Crossref doi:
https://doi.org/10.37547/ajast/Volume03Issue03-11
Eshquvatov Husan Eshtemirovich
Ulugh Beg Astronomical Institute, Tashkent, Uzbekistan National University Of Uzbekistan, Tashkent,
Uzbekistan Tashkent Institute Of Irrigation And Agricultural Mechanization Engineers” National Research
University, Department
“Physics And Chemistry”, Tashkent, Uzbekistan
Asatov Uralbay Toshniyozovich
Tashkent Institute Of Chemical Technology, Tashkent, Uzbekistan
Xolboyev Yunusali Xasanovich
National University Of Uzbekistan, Tashkent, Uzbekistan
Shukurov Ahmadjon Raxmatovich
Academic Lyceum Under Tashkent Textile And Light Industry Institute, Tashkent, Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 03 Issue 03-2023
59
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
I
SSUE
03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
INTRODUCTION
The ionosphere, like any medium, is characterized by
dielectric constant ε, magnetic permeability μ and
conductivity σ. The magnetic permeability of
the entire
atmosphere with a sufficiently high degree of accuracy
is assumed to be constant and equal to the magnetic
permeability of the vacuum, that is, the relative value
μ=1. The remaining two parameters are derived based
on the physical processes occurring in the ionosphere
and depend on the state of the ionosphere, the
frequency of the propagating wave, and other
parameters. One very important distinction of the
dynamics of the ionospheric plasma below 400 km
altitude from the dynamics of the magnetospheric
plasma is that the ionospheric plasma is embedded
into the dense neutral gas. Collisions between neutral
and charged particles significantly affect the
electromagnetic
processes
occurring
in
the
ionosphere. In particular, collisions provide a finite
conductivity of the ionospheric plasma, connecting
currents and the electric field in the ionosphere.
The field of a propagating wave in the ionosphere
induces a displacement current of free space and a
current due to the movement of free electrons under
the action of the field. The density of these currents is:
0
e
j
i
E
j
=
+
(1)
The current density due to the movement of free electrons,
e
э
j
eN
=
e
ύ
, (2)
where
e
ύ
is the average speed of the ordered motion of electrons, which is determined from the equation of
electron motion:
e
e
d ύ
m
t
+
e
e
m v ύ
=
е Е
,
(3)
where
e
m
is the electron mass;
e
is the charge of an electron.
The electric force acting on the charge from the side of the field
F
=
eE
is balanced by the force
particle inertia
e
e
d ύ
m
t
and friction force
e
e
m v ύ
. We seek the solution of equation (3) in the form
Volume 03 Issue 03-2023
60
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
I
SSUE
03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
exp(
)
e
e
ύ
ύ
i t
=
(4)
Expression (4) is substituted into (3) and after simple calculations the speed of movement of free electrons and
the current density (2) are found. Next, the total current density in the ionosphere (1) is compared with the total
current density in a medium with losses
0
(
/ )
j
i
i
E
=
−
The Pedersen conductivity is responsible for the
Pedersen currents flowing in the ionosphere in the
direction of the electric field (Fig.1). This current is
carried mostly by ions. It causes dissipation of the
electric field energy in the ionosphere and the
ionospheric heating. The Hall conductivity is
responsible for the Hall current flowing in the
ionosphere in the direction perpendicular to the
electric field and mostly carried by electrons.
Both conductivities result from the fact that collisions
with neutrals demagnetize ions in the ionosphere, and
they start to move in the direction of the electric field
instead of participating in the E×B drift. Electrons
remain magnetized, and they continue to move
perpendicular to E with the velocity of the electric drift.
Thus, collisions effectively separate electrons from
ions, the ions carry Pedersen current in the direction of
the electric field, and the electrons carry Hall currents
in the direction perpendicular to E.
The Hall and Pedersen currents arise from the
peculiarities of the electric drift motion in the
collisional media. They both depend on the orientation
of the background magnetic and electric field relative
to each other. These fields are oriented differently at
high and low latitudes. At high latitudes, the magnetic
field has a large angle with the ionosphere and with the
electric field produced in the ionosphere. At low
latitudes, the magnetic field in the south
–
north
direction is parallel to the ionosphere and, if there is an
electric field in the east
–
west direction in the
ionosphere, then the E×B drift pushes electrons in the
vertical direction and creates a vertical component of
the electric field. Comparison makes it possible to
determine the dielectric permittivity and conductivity
of the ionosphere [1, 2, 3].
=
+
−
=
2
2
0
2
1
1
e
e
m
N
e
3,19∙10
-9
2
2
+
e
N
(5)
2
2
2
2
2
2
2
10
82
,
2
+
=
+
=
−
e
e
e
N
m
N
e
(6)
Volume 03 Issue 03-2023
61
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
I
SSUE
03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
Fig.1. Example of distribution of Pedersen (σP), Hall (σH), and Cowling (σC) conductivities with altitude.
Expressions (5) and (6) are substituted with numerical
values
e
,
0
,
e
m
and
;
frequency of the
propagating wave,
e
N
(
3
/
cm
el
)
- concentration of
free electrons,
(1/sec) - frequency of collision of
electrons with heavy particles.
The resulting formula (5) for the permittivity allows us
to draw the following conclusions.
RESULTS AND DISCUSSION
The presence of free electrons leads to the fact that
the dielectric constant of the ionosphere is always less
than the dielectric constant of free space. Free
electrons have a negative charge and, moving against
the field, they create an opposite polarization and
thereby reduce the total field [4, 5]. The permittivity
depends on the electron concentration, which has a
main maximum at altitudes of 300
–
400 km.
Consequently, ε first decreases, and then, above
the
ionization maximum, increases with height, and the
ionosphere is an electrically inhomogeneous medium
(Fig. 2).
Volume 03 Issue 03-2023
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American Journal Of Applied Science And Technology
(ISSN
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VOLUME
03
I
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03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
Fig.2. Height relation of the atmosphere and ionosphere.
The permittivity also depends on the frequency of the
propagating
electromagnetic
wave,
and
the
ionosphere is a dispersed medium. The ionosphere has
an unequal influence on the propagation of radio
waves of different ranges. The frequency dependence
is explained by the fact that an electron, having a finite
mass, manifests its inertial properties in different ways.
At high frequencies, due to inertia, the average velocity
of electrons decreases, and the properties of the
ionosphere at high frequencies approach the
properties of free space, this occurs at frequencies f >
100 MHz The ionosphere practically has the main
influence on radio waves of frequencies
f < 100 MHz (
λ
> 3m) [6, 7].
At frequencies f > 3 MHz, condition
2
2
is satisfied and in expression (5) one can neglect
2
compared to
2
.
The permittivity (5) of the ionosphere takes on a simpler form
)
(
)
/
(
81
1
3
kHz
f
cm
el
N
e
−
(7)
Volume 03 Issue 03-2023
63
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
I
SSUE
03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
Simplified formula (7) can be used at frequencies above 3 MHz, i.e. in the HF and VHF bands. Depending on the
frequency, the permittivity varies over a wide range, taking both zero and negative values. For a given electron density
e
N
, we find the frequency at which
= 0
)
/
(
9
)
(
3
0
cm
el
N
kHz
f
e
=
(8)
The frequency at which
= 0 is called the natural frequency of the ionosphere or the Langmuir frequency.
Taking into account (8), the permittivity takes the following form:
2
0
2
1
f
f
= −
(9)
At frequencies
0
f
f
, the permittivity takes negative values
< 0. Propagation of radio waves of the indicated
frequencies is impossible. Figure 2 shows the case when for some frequency
f
3
at heights from
h
1
to
h
2
< 0. A wave
with frequency
f
3
cannot propagate in the indicated region of the ionosphere [8, 9, 10].
This is explained by the fact that the propagation constant
a
a
k
=
at
a
<0 and the absence of losses
becomes the imaginary value
k
i
= −
and the field amplitude decreases exponentially
Е
=
Е
0
0
2
r
e
−
, and there is no
energy transfer.
Without taking into account losses for a wave propagating in the ionosphere, one can use the known calculation
formulas.
с
ph
=
,
с
gr
=
(10)
CONCLUSIONS
The phase velocity is considered in matters of
reflection, refraction of waves, determining the shape
of the trajectory of the wave propagation path. The
group velocity determines the speed of energy
propagation, it is necessary in the evaluation of signal
distortion, when measuring the delay time of radio
waves reflected in the ionosphere. Pulse distortion is
Volume 03 Issue 03-2023
64
American Journal Of Applied Science And Technology
(ISSN
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2771-2745)
VOLUME
03
I
SSUE
03
Pages:
58-64
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
significant if the carrier frequency is close to the
natural frequency of the ionosphere.
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