Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere
The problem of the disappearance of the lower hybrid cavities, which are observed in the terrestrial ionosphere, is considered. As a possible mechanism which leads to the disappearance of the cavities the anomalous diffusion of plasma, which occurs due to a drift turbulence of plasma is considered...
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| Cite this: | Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere / N.A. Azarenkov, D.V. Chibisov // Вопросы атомной науки и техники. — 2018. — № 6. — С. 117-120. — Бібліогр.: 6 назв. — англ. |
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Azarenkov, N.A. Chibisov, D.V. 2019-02-18T20:41:56Z 2019-02-18T20:41:56Z 2018 Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere / N.A. Azarenkov, D.V. Chibisov // Вопросы атомной науки и техники. — 2018. — № 6. — С. 117-120. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.35.Qz, 52.35.Ra, 94.20.wf https://nasplib.isofts.kiev.ua/handle/123456789/148868 The problem of the disappearance of the lower hybrid cavities, which are observed in the terrestrial ionosphere, is considered. As a possible mechanism which leads to the disappearance of the cavities the anomalous diffusion of plasma, which occurs due to a drift turbulence of plasma is considered. The frequency and the characteristic time of development of the drift instability in the cavity, the saturation level of the instability and the anomalous diffusion coefficient of plasma in the cavity are obtained. The cavity lifetime is also estimated, which can be greater or about 1 second. Розглянуто проблему зникнення нижньогібридних порожнин, які спостерігаються в земній іоносфері. В якості можливого механізму, який призводить до зникнення порожнин, розглядається аномальна дифузія плазми, що виникає внаслідок її дрейфової турбулентності. Отримано частоту і характерний час розвитку дрейфової нестійкості в порожнині, рівень насичення нестійкості і коефіцієнт аномальної дифузії плазми в порожнині. Також оцінюється час життя порожнини, який може становити більше або порядку 1 с. Рассмотрена проблема исчезновения нижнегибридных полостей, наблюдаемых в земной ионосфере. В качестве возможного механизма, приводящего к исчезновению полостей, рассматривается аномальная диффузия плазмы, возникающая из-за её дрейфовой турбулентности. Получены частота и характерное время развития дрейфовой неустойчивости в полости, уровень насыщения неустойчивости и коэффициент аномальной диффузии плазмы в полости. Также оценивается время жизни полости, которое может составлять больше или порядка 1 с. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Фундаментальная физика плазмы Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere Аномальна дифузія плазми в нижньогібридних порожнинах, що спостерігаються в земній іоносфері Аномальная диффузия плазмы в нижнегибридных полостях, наблюдаемых в земной ионосфере Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere |
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Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere Azarenkov, N.A. Chibisov, D.V. Фундаментальная физика плазмы |
| title_short |
Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere |
| title_full |
Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere |
| title_fullStr |
Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere |
| title_full_unstemmed |
Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere |
| title_sort |
anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere |
| author |
Azarenkov, N.A. Chibisov, D.V. |
| author_facet |
Azarenkov, N.A. Chibisov, D.V. |
| topic |
Фундаментальная физика плазмы |
| topic_facet |
Фундаментальная физика плазмы |
| publishDate |
2018 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Аномальна дифузія плазми в нижньогібридних порожнинах, що спостерігаються в земній іоносфері Аномальная диффузия плазмы в нижнегибридных полостях, наблюдаемых в земной ионосфере |
| description |
The problem of the disappearance of the lower hybrid cavities, which are observed in the terrestrial ionosphere,
is considered. As a possible mechanism which leads to the disappearance of the cavities the anomalous diffusion of
plasma, which occurs due to a drift turbulence of plasma is considered. The frequency and the characteristic time of
development of the drift instability in the cavity, the saturation level of the instability and the anomalous diffusion
coefficient of plasma in the cavity are obtained. The cavity lifetime is also estimated, which can be greater or about
1 second.
Розглянуто проблему зникнення нижньогібридних порожнин, які спостерігаються в земній іоносфері. В якості можливого механізму, який призводить до зникнення порожнин, розглядається аномальна дифузія плазми,
що виникає внаслідок її дрейфової турбулентності. Отримано частоту і характерний час розвитку дрейфової
нестійкості в порожнині, рівень насичення нестійкості і коефіцієнт аномальної дифузії плазми в порожнині.
Також оцінюється час життя порожнини, який може становити більше або порядку 1 с.
Рассмотрена проблема исчезновения нижнегибридных полостей, наблюдаемых в земной ионосфере. В качестве возможного механизма, приводящего к исчезновению полостей, рассматривается аномальная диффузия
плазмы, возникающая из-за её дрейфовой турбулентности. Получены частота и характерное время развития
дрейфовой неустойчивости в полости, уровень насыщения неустойчивости и коэффициент аномальной диффузии
плазмы в полости. Также оценивается время жизни полости, которое может составлять больше или порядка 1 с.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148868 |
| citation_txt |
Anomalous diffusion of plasma in the lower hybrid cavities observed in the terrestrial ionosphere / N.A. Azarenkov, D.V. Chibisov // Вопросы атомной науки и техники. — 2018. — № 6. — С. 117-120. — Бібліогр.: 6 назв. — англ. |
| work_keys_str_mv |
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| first_indexed |
2025-11-25T20:44:31Z |
| last_indexed |
2025-11-25T20:44:31Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №6(118)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2018, № 6. Series: Plasma Physics (118), p. 117-120. 117
ANOMALOUS DIFFUSION OF PLASMA IN THE LOWER HYBRID
CAVITIES OBSERVED IN THE TERRESTRIAL IONOSPHERE
N.A. Azarenkov, D.V. Chibisov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: dmitriychibisov@karazin.ua
The problem of the disappearance of the lower hybrid cavities, which are observed in the terrestrial ionosphere,
is considered. As a possible mechanism which leads to the disappearance of the cavities the anomalous diffusion of
plasma, which occurs due to a drift turbulence of plasma is considered. The frequency and the characteristic time of
development of the drift instability in the cavity, the saturation level of the instability and the anomalous diffusion
coefficient of plasma in the cavity are obtained. The cavity lifetime is also estimated, which can be greater or about
1 second.
PACS: 52.35.Qz, 52.35.Ra, 94.20.wf
INTRODUCTION
In the plasma of terrestrial ionosphere the axially
symmetric regions elongated along the geomagnetic
field are observed, which are characterized by a reduced
density of plasma in comparison with the environment
as well as an increased level of oscillations in the range
of the lower hybrid frequency [1]. Such regions called
the lower hybrid cavities (LHC) and another name is the
lower hybrid solitary structures (LHSS), have transverse
dimensions of a few to many thermal ion gyroradii usu-
ally from tens to hundreds of meters. The registration
and measurements of the LHC are carried out by satel-
lites as well as sounding rockets, and it occurs only
when they pass through these structures. Because of the
relatively small transverse dimensions of LHC and the
high velocities of the spacecraft, the time of measure-
ment is up to tens of milliseconds. However during this
time the cavity does not change significantly, which
indicates that LHC is sufficiently stable formation. Alt-
hough there are a number of works on the explanation
of this phenomenon which are given in the review [1],
the mechanisms for occurrence of LHC, as well as their
stability, are not completely clear. There are also no
estimates of the time of their existence and the explana-
tions of their disappearance.
This paper is devoted to the problem of disappear-
ance of LHC. As a possible mechanism for the disap-
pearance of LHC we consider the anomalous diffusion
of inhomogeneous plasma across the magnetic field. It
is known that in magnetized plasma the excitation of
various instabilities due to the radial inhomogeneity of
the plasma density is possible. One of them is the drift
lower hybrid instability due to which an increased level
of low hybrid oscillations in the LHC is believed to oc-
cur [1]. In addition, it is possible the excitation of a drift
instability with a frequency much less than the ion cy-
clotron frequency, which can lead to the lower frequen-
cy drift turbulence of plasma. In turn, due to the drift
turbulence, an anomalous diffusion of plasma across the
magnetic field occurs, which should lead to the filling of
the LHC with plasma and its disappearance. Since the
cavities have axial symmetry, then an analysis of the
development of turbulence as well as diffusion process-
es in plasma of LHC in the present work is considered
using the model of small-scale cylindrical waves [2-5].
We considered the linear as well as the nonlinear stages
of drift instability for cavities conditions, found the lev-
el of turbulence in the LHC, and also obtained the diffu-
sion coefficient of plasma and solved the diffusion
equation for given initial conditions. We also estimated
the lifetime of the cavity.
1. DRIFT WAVE TURBULENCE IN THE
LOWER HYBRID CAVITIES
In homogeneous magnetized plasma, we consider
the axially symmetric cavity whose axis coincides with
z – directed magnetic field and the dependence of the
plasma density on the radius as follows
2
0
2
0
2
exp1
r
r
anrn , (1)
which is the "inverse" Gaussian distribution. In (1) 0n
is the plasma density in the environment, a is the con-
stant which determines the depth of the cavity, 0r is the
length of the plasma density inhomogeneity. Note that
the dependence (1) was obtained by satellite measure-
ments [1]. The measurements showed that the magni-
tude of a varies up to 0.4, at altitudes of
600…1000 km, is up to 0.2 at altitudes of
1500…13000 km and does not exceed 0.05 at altitudes
of 20000…35000 km. The velocity distribution for the
components of plasma is assumed to be Maxwellian,
which is confirmed by observations. The distribution
function for the plasma in this case is [6]
2
2
2
2
2
0
2
32/3
0
0
2v
v
2
exp
2
exp1
v2
T
z
TT R
R
a
n
F , (2)
where the subscript denotes ions (i) or electrons (e),
R , and v z , are the radial coordinate of the guiding
center, Larmor radius and velocity along the magnetic
field of the particles correspondingly, 0R is the length
of the inhomogeneity of the radial distribution of the
guiding centers of particles, cTT v is the ther-
mal Larmor radius Tv is the thermal velocity, c is
the cyclotron frequency. Plasma is assumed to slightly
inhomogeneous, so that the inequality
TR 0
holds.
The last condition yield 000 rRR ei .
Measurements have shown that the temperature of
the plasma components in the cavities exceeds their
118 ISSN 1562-6016. ВАНТ. 2018. №6(118)
temperature in the environment which is due to lower
hybrid oscillations; in fact, it means that the tempera-
tures of the electrons and ions inside the plasma cavity
decrease with increasing of radius. Then assuming the
dependence )( 0rT an arbitrary, we are sure that ine-
quality 0T hold.
For the analysis of drift instability in the cavity, we
use the dispersion relation for the linear stage of the
small-scale, 1�0 mrk , low-frequency, ci ,
oscillations in axially-symmetric plasma with arbitrary
dependence of the density and temperature of the plas-
ma components on the radius, which was obtained in
[5]:
22*22
22
1(
1
1,, Ti
i
Ti
fDi
f k
m
k
rk
rk
fDe
fi
rk
r
22
1
1
0
2/1
2
1
*
Tez
fefe
vk
rrm
i
. (3)
Here k , m and zk are the transverse, azimuthal and
longitudinal wave numbers, respectively, zkkk , ,
)(ln/)(ln ff rndrTd , T is the temperature, D
is the Debye length,
frr
Tc
rdr
rnd
ln2
is the drift frequency. For distribution of the plasma
density in the cavity (1), we obtain approximately
2
0
2
2
0
2
2
exp
r
r
r
a
fT
c
with the fulfillment of inequality c . Addi-
tionally in (3) the assumptions ie TT , 1 Tik , are
made.
Equation (3) determines in the short wavelength as-
ymptotic limit 1�0 mrk the dispersion properties of
cylindrical waves analytically expressed by the Bessel
functions ( )mJ k r . The values of the plasma parame-
ters in Eq. (3) are determined at the point kmrf
which is approximately the radial coordinate of the first
maximum of the Bessel function, for which this equa-
tion is written. The solution of the equation (3) yield the
frequency and the growth rate of the drift oscillations in
LHC
22
22
*
1
11
s
iTi
em
k
k
mk
, (4)
22
2
00
1
exp
s
ee
mm
k
zz
kk
, (5)
where ieTis TT /22 , /0 kz me
Tezk v2 . We note
that the increase in the drift oscillations does not depend
on the sign of the density gradient and is due the Che-
renkov interaction of resonant electrons with drift
waves. Considering also that under the conditions of the
cavity the inequalities 0,0 nTi hold we have
0i . Assuming also that the lengths of the inhomo-
geneity of the plasma density and the ion temperature
are approximately equal, we get 1i , so the fre-
quency of the drift oscillations in LHC is
22
*
1 s
e
m
k
m
k
. (6)
Let us estimate the value of the frequency of the
drift oscillations (6) which are excited in the lower hy-
brid cavities. At a height of up to 1000 the main ion
component is the singly ionized oxygen, which here
amounts to 90 %. The ion cyclotron frequency of oxy-
gen ions is approximately 34 Hz, the ratio 3/0 Tir ,
4.0a . In this case, the frequency of the drift oscilla-
tions is of the order of 3…4 Hz. A similar estimate of
the drift frequency at altitudes of 1500…2000 km,
where the main ion component is protons, is of the order
of 8 Hz. we now evaluate the instability development
time instt , which is equal to km
1 . For the given plas-
ma parameters in the cavity we obtain tinst ~0.5…1.5 s.
Nonlinear evolution of the drift instability in the
cavity is determined by the induced scattering of cylin-
drical waves by ions [2-5]. The kinetic equation for the
spectral intensity kIm of small-scale cylindrical waves
in plasma with arbitrary dependences on the radius of
density and temperature is [5]:
kIkk
t
kI
mmm
m
)(
2
1
, (7)
where km is the nonlinear growth rate of drift waves
1
1 1111
1
,,
Re
m
m
m
m mkmkBkIdk
k
k
111 1
,,,Im kmkkmkU mmi . (8)
In (6) the value is given by (3), 11,, mkmkB is
the factor of nonlinear interaction of cylindrical waves
[2-4]
,,
,
,
cos
1
,,
101
2
101
31
1010
32
31
10101
10
11
mmmO
mmmmmO
mmm
k
k
m
mkmkB
where ,110 kmkm 22
10
2 /1cos ff rr , 111 / kmr f ;
iUIm is the matrix element of the induced scattering of
drift waves by ions which is equal to
0
2
2
2*122
12
2
22
cosIm
k
rmm
kk
T
e
k
U
m
fi
Ti
iDi
i
11 kk mm , (9)
where [5]
2
11
ln 22
1
22
2*
frr
iTiTicifi kk
rdr
rnd
r
,
222 / kmrf is the coordinate of the first maximum of
a cylindrical “beat wave” of two cylindrical waves with
wave numbers mk , and 11, mk . The wave num-
bers of the beat wave are determined by [2-4]
ISSN 1562-6016. ВАНТ. 2018. №6(118) 119
12 mmm ,
2
101
2
2 sin2 kkkkk .
In cavity conditions when (1) hold, we have approxi-
mately
2
0
2
2
2
0
2
2*
2
exp
r
r
r
ar
fTi
cifi
.
Apply the equation (7) for the analysis of the nonlin-
ear stage of drift turbulence in the conditions of the
lower hybrid cavities. First by using the condition
11 kk mm we determine the radial wave num-
ber 1k of the cylindrical wave )( 11
rkJm interacting
with the wave ( )mJ k r :
1221122
1 ss k
m
m
m
m
k . (10)
Using (10) we get for 0
2cos
22
122
1
2
1
0
2cos s
s
kmm
km
mm
.
The requirement 0cos 0
2 leads to systems of ine-
qualities
22
1
1 ,
skmm
mm
(11)
or
.
,
22
1
1
skmm
mm
(12)
The system (11) has a solution when 122 sk :
mm
k
m
s
122
. (13)
In this case, only long waves rkJm 11 with azimuthal
wave numbers mm 1 interact with the wave rkJ m .
Then the nonlinear growth rate in equation (7), which is
proportional to the sum
1
1
m
m mmk , is nega-
tive and the wave rkJ m turns out to be nonlinearly
damped. Thus in LHC the part of the drift oscillating
spectrum with 122 sk damped nonlinearly and disap-
pears finally.
The system (12) has a solution for the long wave-
length part of the spectrum when 122 sk :
221
sk
m
mm
. (14)
In this case the wave rkJ m interact only with the
shorter waves rkJm 11 for which mm 1 . Then the non-
linear growth rate
1
1
m
m mmk , is positive and
the wave rkJ m grows nonlinearly. The saturation
analysis of the drift turbulence in LHC at 122 sk re-
quires going beyond the frame of weak turbulence theo-
ry. However, in [3], the saturation level of the drift tur-
bulence is estimated in the case of a homogeneous tem-
perature distribution and the Gaussian dependence of
the plasma density on the radius
2
0
2
0 rTn
W s
i
. (15)
We believe that this level of saturation is also reached
for LHC.
2. ANOMALOUS DIFFUSION OF PLASMA
IN THE LOWER HYBRID CAVITIES
As a result of the drift turbulence, a change in the
averaged distribution function of plasma components
occurs in the cavity plasma. The evolution of the distri-
bution function of electrons is governed by the quasilin-
ear equation [3]
m eece
zzmm
e
e
RR
m
vkkkdkI
m
e
t
F 12
0
z
e
z
e
e
ece
em
z
z
v
F
k
R
F
R
m
RkJ
v
k 002 1
. (16)
Integrating (16) with respect to e and zv , and also
considering that rRe , we obtain the diffusion equa-
tion for resonant electrons
r
n
rD
rrt
n e
e
e 1
, (17)
where
m m
m
meme
k
k
kIRkJ
r
m
dk
B
c
D
2
2
2
2
2
0
2
is the electron diffusion coefficient across the magnetic
field. For the level of turbulence (15) we have
00 r
z
eB
cT
D see
e
. (18)
For the most rapidly growing part of the instability
spectrum, we have 1~ez . The diffusion of ions across
the magnetic field occurs as a result of ion scattering by
random pulsations of the electric field of drift turbu-
lence [3]. The evolution of the ion distribution function
is determined by the equation
r
n
rD
rrt
n i
i
i 1
(19)
with the diffusion coefficient iD which equal to the
electron diffusion coefficient (18) DDD ei , so
that the diffusion is ambipolar. The equations (17) and
(19) give diffusion of plasma in the direction of the cen-
ter of cavity, since the plasma density increases from the
center.
The solution of the diffusion equation (17) or (19)
with initial condition (1) is
tr
r
t
a
ntrn
22
0
2
20
2
exp1,
(20)
where
t
r
D
t
2
0
2 2
1 .
Equation (20) shows that the cavity depth ta decreas-
es with time as
120 ISSN 1562-6016. ВАНТ. 2018. №6(118)
1
2
0
2
1
t
r
D
ata . (21)
In addition to decreasing the depth of the cavity, an in-
crease in the transverse dimension of the cavity occurs,
the mean square root of the cavity is determined by
t
r
D
rtr
2
0
00
2
1 .
Now we evaluate the time of change in the cavity depth
by k times. Equating (21) to ka / we get
D
rk
tk
2
1 2
0 .
Respectively, transverse dimension of the cavity in-
creases by k times. Substitution of the diffusion coef-
ficient (18) yields
se
k
cT
eBrk
t
2
1 0
3
0
. (22)
For the parameters of cavities in the ionosphere
r0 /ρs
3, r0 ~ 50 m, B0 ~ 0.2 Gs, Te ~ 0.3 eV and as-
suming that the depth of the cavity decreases, for ex-
ample, by 10 times, that is 10k , we have t10 ~ 10-
3 s. A comparison of the time of change in the depth of
the cavity and the time of development of the drift
instability, tinst ~0.5…1.5 s, shows that the lifetime ltt
of the cavity is determined basically by the time of
development of the drift instability in the cavit
that is tlt ~0.5…1.5 s.
CONCLUSIONS
Radial inhomogeneity of the plasma density and
temperature in the plasma of LHC leads to the devel-
opment of the drift instability and drift turbulence of
plasma in the cavity. In turn, drift turbulence causes an
anomalous diffusion of the plasma across the magnetic
field, which leads to the disappearance of the cavity.
It was found that the time of anomalous plasma
transport across the magnetic field is much smaller than
the characteristic time of the development of the drift
instability, so that the lifetime of the cavity is deter-
mined by the growth rate of the instability, which is of
the order of or more than 1 s.
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Article received 14.09.2018
АНОМАЛЬНАЯ ДИФФУЗИЯ ПЛАЗМЫ В НИЖНЕГИБРИДНЫХ ПОЛОСТЯХ, НАБЛЮДАЕМЫХ
В ЗЕМНОЙ ИОНОСФЕРЕ
Н.А. Азаренков, Д.В.Чибисов
Рассмотрена проблема исчезновения нижнегибридных полостей, наблюдаемых в земной ионосфере. В каче-
стве возможного механизма, приводящего к исчезновению полостей, рассматривается аномальная диффузия
плазмы, возникающая из-за её дрейфовой турбулентности. Получены частота и характерное время развития
дрейфовой неустойчивости в полости, уровень насыщения неустойчивости и коэффициент аномальной диффузии
плазмы в полости. Также оценивается время жизни полости, которое может составлять больше или порядка 1 с.
АНОМАЛЬНА ДИФУЗІЯ ПЛАЗМИ В НИЖНЬОГІБРИДНИХ ПОРОЖНИНАХ,
ЩО СПОСТЕРІГАЮТЬСЯ В ЗЕМНІЙ ІОНОСФЕРІ
М.О. Азарєнков, Д.В. Чібісов
Розглянуто проблему зникнення нижньогібридних порожнин, які спостерігаються в земній іоносфері. В яко-
сті можливого механізму, який призводить до зникнення порожнин, розглядається аномальна дифузія плазми,
що виникає внаслідок її дрейфової турбулентності. Отримано частоту і характерний час розвитку дрейфової
нестійкості в порожнині, рівень насичення нестійкості і коефіцієнт аномальної дифузії плазми в порожнині.
Також оцінюється час життя порожнини, який може становити більше або порядку 1 с.
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