Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere
The linear and nonlinear stages of the ion cyclotron instability in plasma of lower hybrid cavities in the Earth's ionosphere are investigated. Because these structures are cylindrically symmetric, the analysis uses the model, which considers as elementary perturbations the small-scale cylindri...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Цитувати: | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere / D.V. Chibisov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 148-151. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859730698765598720 |
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| author | Chibisov, D.V. |
| author_facet | Chibisov, D.V. |
| citation_txt | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere / D.V. Chibisov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 148-151. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The linear and nonlinear stages of the ion cyclotron instability in plasma of lower hybrid cavities in the Earth's ionosphere are investigated. Because these structures are cylindrically symmetric, the analysis uses the model, which considers as elementary perturbations the small-scale cylindrical waves. It is shown that at the nonlinear stage of instability the suppression of high cyclotron harmonics, as well as short-wavelength part of the spectrum of the azimuthal wave numbers occurs. The estimate of the rate of ion heating is carried out.
Досліджуються лінійна та нелінійна стадії іонної циклотронної нестійкості в плазмі нижньогібридних порожнин земної іоносфери. Оскільки такі структури мають циліндричну симетрію, аналіз проводиться на основі моделі, що розглядає в якості елементарних збурень дрібномасштабні циліндричні хвилі. Показано, що на нелінійній стадії нестійкості відбуваються пригнічення високих циклотронних гармонік, а також короткохвильової частини спектра азимутальних хвильових чисел. Виконано оцінку швидкості нагріву іонів.
Исследуются линейная и нелинейная стадии ионной циклотронной неустойчивости в плазме нижнегибридных полостей земной ионосферы. Поскольку такие структуры имеют цилиндрическую симметрию, анализ проводится на основе модели, рассматривающей в качестве элементарных возмущений мелкомасштабные цилиндрические волны. Показано, что на нелинейной стадии неустойчивости происходят подавления высоких циклотронных гармоник, а также коротковолновой части спектра азимутальных волновых чисел. Выполнена оценка скорости нагрева ионов.
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| first_indexed | 2025-12-01T13:16:49Z |
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 148
ION CYCLOTRON TURBULENCE IN PLASMA OF LOWER HYBRID
CAVITIES IN THE EARTH’S IONOSPHERE
D.V. Chibisov
V.N. Karazin Kharkiv National University, Department of Physics, Kharkov, Ukraine
E-mail: dmtchibisov@gmail.com
The linear and nonlinear stages of the ion cyclotron instability in plasma of lower hybrid cavities in the Earth's
ionosphere are investigated. Because these structures are cylindrically symmetric, the analysis uses the model,
which considers as elementary perturbations the small-scale cylindrical waves. It is shown that at the nonlinear stage
of instability the suppression of high cyclotron harmonics, as well as short-wavelength part of the spectrum of the
azimuthal wave numbers occurs. The estimate of the rate of ion heating is carried out.
PACS: 52.35.Ra, 94.20.wf
INTRODUCTION
Lower hybrid cavities (LHC) are the common phe-
nomenon in plasma of the topside ionosphere and mag-
netosphere of the Earth, which were observed in the
auroral zone using sounding rockets at altitudes up to
1000 km [1 - 3], as well as satellites from 1000 to
35000 km [4 - 6]. LHC are the spatially localized cylin-
drically symmetric structures in plasma, whose axis
coincides with the direction of the geomagnetic field
lines. They are characterized by significantly increased
level of electrostatic lower hybrid oscillations, as well
as depletion of the plasma density in comparison with
the environment. LHC have dimensions across the mag-
netic field from a few meters to several hundred meters
(a few ion Larmor radius) and the dimensions along the
magnetic field, considerably exceeding their transverse
ones. Apart from the increased level of the lower hybrid
oscillations in LHC where also detected the broadband
fluctuations in the low frequency range, including the
ion cyclotron frequency rang, and which in the back-
ground plasma are absent. Here we consider the prob-
lem of the occurrence of these oscillations in LHC. We
assume that the cause of the ion cyclotron oscillations in
the LHC is the inhomogeneity of plasma density in the
cavity across the magnetic field and arising as a result of
this the drift-cyclotron instability of plasma. Because
these structures are cylindrically symmetric, the analysis
of both linear and non-linear stages of instability is
based on the theory using as elementary perturbations
the small-scale cylindrical waves. This theory was de-
veloped earlier in papers [7 - 9] for cylindrically sym-
metric laboratory plasma. We also estimated the rate of
heating of the plasma ions in LHC due to ion cyclotron
turbulence.
1. LINEAR THEORY
In homogeneous magnetized plasma we consider a
cylindrically symmetric cavity whose axis coincides
with the direction of the magnetic field. Assume, that
the plasma density in the cavity determined by the "in-
verted" Gaussian distribution
( )
−−= 2
0
2
0 2
exp1
r
ranrn , (1)
where 0n is the plasma density outside of the cavity; a
is a constant determines the depth of the cavity; 0r is
the characteristic length of plasma density inhomogenei-
ty. This dependence of plasma density in the cavity is
confirmed by satellite measurements [10]. It was found
that a = 0.1…0.4 at altitudes of 600…1000 km,
a = 0.1…0.2, at altitudes of 1500…13000 km, and
a = 0.02…0.05 at altitudes of 20000…35000 km. Dis-
tribution of the components of the plasma velocity as-
sumed Maxwellian, which is also confirmed by observa-
tions. The equilibrium distribution function for the
components of plasma in this case has the form
( )
−−
−−= 2
2
2
2
2
0
2
32/3
0
0 2v
v
2
exp
2
exp1
v2 αα
α
α
α
α
α
ρ
ρ
π T
z
TT R
R
a
n
F , (2)
where the superscript α denotes ions (i) or electrons
(e); Rα , αρ and vz , are the radial coordinate of the
guiding center; Larmor radius and velocity along the
magnetic field of the particles correspondingly; 0R α is
the characteristic size of the inhomogeneity of the radial
distribution of the guiding centers of particles;
vT T cα α αρ ω= is the thermal Larmor radius; vTα is the
thermal velocity; cαω is the cyclotron frequency. Plas-
ma is assumed to slightly inhomogeneous, with
0 TR α αρ which also gives 000 rRR ei ≈≈ . Observa-
tions have shown that the temperature of ions and elec-
trons in the cavities exceeds the background plasma
temperature due to lower hybrid oscillations; it means
that the temperatures of the components within the
plasma cavity are inhomogeneous and decrease with
increasing of radius. Therefore, supposing dependence
0( )T Rα αρ an arbitrary, we can assume that inequality
0Tαρ∇ < is met.
For the analysis of ion cyclotron instability in the
cavity, we use the dispersion relation describing the
linear stage of the small-scale ion cyclotron plasma in-
stability in cylindrically symmetric plasma with arbi-
trary dependence on the radius of the density and tem-
perature of the plasma components which was obtained
in Ref. [9]:
( ) ( )
( )
( )
++= ⊥
22
0
0
22 v2
111,, Te
sTez
e
e
De
s kI
rk
zWli
k
rK ρωπ
λ
ωε
( )] ( )
( )
++−× ∑
∞
−∞=
⊥
n sTiz
ni
i
Di
Te rk
zWli
k
k
v2
11exp 22
22 ωπ
λ
ρ
( ) ( )] 0exp 2222 =−× ⊥⊥ TiTin kkI ρρ , (3)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 149
where ( ) ααα ωω Tzcn knz v2−= , ⊥= kmrs , m is
the azimuthal wave number, k⊥ and zk are the wave
numbers across and along the magnetic field, Dαλ is the
Debye length, ( )xI n is the modified Bessel function,
( )
+= ∫−
z
z deiezW
0
22 21 ξ
π
ξ , the operator lα
is equal
to
srr
Tc
dT
d
rdr
dT
rdr
rndnml
=
+
+
−=
α
ααα
α ω
ρω )(ln)(1 0
2
. (4)
Equation (3) determines in the small-scale asymptot-
ic limit 10 >⊥ mRk α the dispersion properties of the
spatially inhomogeneous waves structures – cylindrical
waves which analytically expressed by Bessel functions
( )mJ k r⊥ . The dependence of the plasma density (1) as
well as temperature on the radial coordinate r in equa-
tion (3) is transformed in the depending on the value
⊥= kmrs that corresponds to the radial coordinate of
the first maximum of the Bessel function for which eq.
(3) is written, i.e. the coordinate of the point where the
oscillating and non-oscillating parts of this function are
separated. Assume that the waves propagate almost
across the magnetic field, so that 1inz > and Landau
damping by ions can be neglected, however for elec-
trons 0 1ez < . Using the corresponding asymptotic
forms for the )(zW function, and assuming that the
wave numbers k⊥ satisfy the condition 1Tik ρ⊥ > , we
write the equation (3) for one of the cyclotron harmonic
( )ci mn kω ω δω= + :
( ) *
0 2 2
(1 2)1, , 1 1
2 v
e e
De z Te
m
K R i
k k
ω ω η
ε ω π
λ
− −
= + +
( ) ( )*
2 2
1 21 1 0,
2
i i
Di Ti
m n
k k
ω ω η
λ π ρ δω⊥
− + −
+ − =
(5)
where
( )
α
α
αααα ωρωρωω c
r
r
T
c
ss
s
Tc
s
ae
rdrr
rnd
<<≈=
− 2
0
2
* 2
0
2
02 ln
is the drift frequency, )(ln)(ln rndrTd αααη = with
0αη < . In the dispersion relation (5) as in eq. (3) tem-
perature and density of plasma components are deter-
mined at the radius ⊥= kmrs corresponding to the
first maximum of the cylindrical wave ( )mJ k r⊥ .
The dispersion ( )m kδω and growth rate obtained
from eq. (5) are
( )
−
+−=
⊥ 2
111
2
* i
ci
i
Ti
ci
m n
m
k
nk η
ω
ω
ρπ
ωδω , (6)
( )*( ) 1 1
22 v
i ci e e
m m
e ciz Te
T n m
k k
T nk
ω ω η
γ π δω
ω
≈ − − ⋅
. (7)
The instability occurs due to inverse Landau damp-
ing by electrons because of their thermal motion along
the magnetic field. We now determine from (6), (7) the
range of azimuthal wave numbers for unstable oscilla-
tions. Because in the cavity 0 ( ) 0n r∇ > , then the drift
frequencies satisfy the inequalities * 0eω < and
* 0iω > . In this case, the growth rate is positive and
instability occurs when the azimuthal wave number sat-
isfies the inequality
0
)2/1(*
01 <
−
−=−<
ee
cinmm
ηω
ω . (8)
Obviously, for weakly inhomogeneous plasma the
inequality
1
)2/1(
2
0
2
2
2
0
01 >>
−
≈ r
r
eTie
i
s
e
a
r
T
Tnm
ηρ
(9)
holds and the applicability of small-scale approximation
is provided. In addition, we verify the validity for the
assumption 1Tik ρ⊥ > :
1
)2/1(
2
0
2
0
0
01
0
0 >
−
≈≈= ⊥⊥
r
r
eTie
iTiTi
Ti
s
e
a
r
T
T
r
m
r
rkk
ηρ
ρρ
ρ .(10)
The last inequality for the parameters of LHC holds.
Note that the scale of oscillations depends not only on
the ratio Tir ρ/0 but on the depth of the cavity a .
Wavelengths are smaller, the smaller the depth of the
cavity.
2. NONLINEAR THEORY
Nonlinear evolution of ion cyclotron instability at
the first stage is determined by the induced scattering of
cylindrical waves by ions. The equation for the spectral
intensity )(kIm of cylindrical waves describes this pro-
cess for the ion cyclotron instability has the form [9]:
( ) ( )( ) ( )kIkk
t
kI
mmm
m Γ+=
∂
∂ γ)(
2
1 , (11)
where ( )kmΓ is the nonlinear decrement:
( ) ( ) ( ) ( )∑∫ ⊥⊥
−
∂
∂
=Γ
1
1 1111
1
,,Re
m
m
m
m mkmkBkIdk
k
k
ω
ε
( ) ( )( )111 1
,,,Im kmkkmkU mmi ωω× . (12)
Here ε is given by eq. (5), ( )11,, mkmkB ⊥⊥ is the
coefficient of nonlinear interaction of cylindrical waves
[7, 8]:
( ) ( )
( )
>
<<−
−<
=
−
−
⊥
⊥
⊥⊥
,,
,
,
cos
1
,,
101
2
101
31
1010
32
31
10101
10
11
mmmO
mmmmmO
mmm
k
k
m
mkmkB
απ
(13)
where 10 1 ,m mk k⊥ ⊥= 22
10
2 /1cos ss rr−=α , ⊥= 111 / kmr s ;
iUIm is the matrix element of induced scattering of
waves by ions equals
( )( )1lncos1Im 0
22
12
2
22 Okkk
T
e
k
U TiTi
iDi
i +−≈ ⊥⊥⊥ ραρ
λ
ISSN 1562-6016. ВАНТ. 2015. №4(98) 150
( ) ( )∑
−−−−×
1
2
1
)(
*
2
112
3
n
i
ci
ici mmnn η
ω
ω
δω
ω
( )1δωδωδ −× , (14)
where
srrTicii rdrrnd
2
)/)(ln( 0
2*
2 =−= ρωω , 222 / ⊥= kmr s .
Value sr2 is equal to the radial coordinate of the first
maximum of the cylindrical beat wave for the waves
( )mJ k r⊥ and
1 1( )mJ k r⊥ . The beat wave has the wave
numbers determined by
−−+=−= ⊥⊥⊥⊥⊥ 01
2
1
22
212 2
cos2, απkkkkkmmm ;
m
mkkk 122
1
2 2 ⊥⊥⊥ −+= . (15)
Induced scattering of cylindrical waves has charac-
teristic distinction from a similar process of plane
waves. In the case of plane waves to obtain the equation
describing the nonlinear evolution of the spectral inten-
sity ( )I 1k of the wave-interaction partners, it is suffi-
cient to replace
( ) ( )1 1, ω ω1k k k k (16)
and take into account the basic properties of the sym-
metry of the matrix elements. In this case the appear-
ance of non-linear increment in the equation for the
spectral intensity ( )I k is accompanied by the appear-
ance of symmetric nonlinear decrement in the equation
for ( )I 1k and vice versa. In the case of cylindrical
short-waves in the derivation of equation for ( )11mI k in
addition to replacements (16) should also take into ac-
count the relation (13) as well as inequality 1cos 0
2 <α
or ss rr <1 . Their accounting leads to an asymmetric
response influence of wave ( )mJ k r⊥ to wave
1 1( )mJ k r⊥ , which reduce the nonlinear decrement in the
equation for ( )
1 1mI k in 1>>m times. Thus, the pro-
cess of induced scattering of short cylindrical waves is
asymmetric. This asymmetry of the nonlinear interac-
tion of cylindrical waves leads to the appearance of for-
bidden and permitted intervals of azimuthal wave num-
bers 1m affecting on the wave with azimuthal wave
number m , that significantly affects on the evolution of
instability.
Now we consider the effect of induced scattering of
cylindrical waves on the ion cyclotron instability with
the parameters of LHC, when conditions 00 >∇n ,
0<eη , 0<iη are met. Proportionality of the matrix
element (14) to δ -function determines the transverse
wave numbers of the interacting cylindrical waves:
⊥⊥ ≈ 11 // knkn . In its turn the requirement ss rr <1 de-
termines the limit on the azimuthal wave numbers 1m :
nmnm // 11 < . Taking into account the inequality (8)
we obtain permitted interval for these wave numbers:
0011
1 <−<< mm
n
mn . (17)
For azimuthal wave numbers determined by (9) and
(17) the first term in the square brackets of eq. (14) is
greater than the second one in ie TT times and at the
first phase of the nonlinear evolution of the oscillation
spectrum the main process is the interaction of different
cyclotron harmonics with cici nn ωω 1≠ . As a result at
the energy density fluctuations
4
0 ))(/( −
⊥≈ Tieii kTTTnW ρ the high-frequency part of
the spectrum of the drift-cyclotron instability is sup-
pressed; so that only main cyclotron harmonic with
1=n remains (see also [11]).
At the second phase of the nonlinear evolution of
spectrum, when the first term in the square brackets
vanishes, a nonlinear interaction of waves with different
values of the azimuthal wave numbers becomes the
main. Taking into account inequality 01 << mm we
obtain for nonlinear decrement ( ) ( )∑
<
<−∝Γ
mm
m mmk
1
01 .
This leads to damping of shorter wave ( )mJ k r⊥ com-
pared with
1 1( )mJ k r⊥ wave, and ultimately to the sup-
pression of the short-wavelength part of the azimuthal
wave numbers spectrum. As a result the narrow part of
the spectrum near the boundary value 01mm −= (9)
remains. Simultaneously the evolution of the spectrum
of the transverse wave numbers ⊥k does not occur so
that the frequency spectrum near the fundamental har-
monic of the ion cyclotron frequency, which is deter-
mined by the dispersion (6), does not change.
The second stage of the evolution of the drift-
cyclotron instability is determined by the scattering of
particles in the random fluctuations of the electric field
drift-cyclotron turbulence (broadening of the resonance)
[12, 13]. At this phase the saturation of growing fluctua-
tions at the level [8]:
4
0
4
0 )(
1
≈≈
⊥ r
a
T
T
kTn
W Ti
i
e
Tii
ρ
ρ
. (18)
The ion cyclotron turbulence in the LHC leads to
additional turbulent heating of the plasma ions. To de-
termine the rate of heating we use the results of [14],
where was estimated the rate of quasi-linear change of
the thermal Larmor radius, resulting from collisions
with turbulent fluctuations of the electrostatic fields:
( )
5
0
5 v1v~
∼
∂
∂
⊥ r
a
T
T
T
T
kT
T
t
Ti
i
e
e
i
Ti
Tie
i
Ti
i ρ
ρ
ρ . (19)
Characteristic time of variation of the thermal Lar-
mor radius due to ion cyclotron turbulence is of the or-
der of
5
0
1~
R
a
T
T
T
T Ti
i
e
e
i
ci
ρ
ω
τ ρ . (20)
The rate of heating of the ions due to ion cyclotron
turbulence is much less than the ion cyclotron frequen-
cy, and therefore the contribution of the ion cyclotron
heating compared with the lower-hybrid heating is in-
significant.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 151
CONCLUSIONS
In plasma of the lower hybrid cavities which exist in
the Earth's topside ionosphere and magnetosphere, the
ion cyclotron instability may occurs due to the radial
inhomogeneity of plasma. For weakly inhomogeneous
plasma in cavities as well as for cavities with small
depth, the cylindrical waves are short across the mag-
netic field; the azimuthal and transverse wave numbers
are given by the expressions (9) and (10).
At the nonlinear stage of development of instability
the higher cyclotron harmonics in the frequency spec-
trum as well as the short-wavelength part of the spec-
trum of the azimuthal wave numbers are suppressed due
to induced scattering of waves by ions. As a result only
first harmonic of the ion cyclotron oscillations and a
narrow part of the spectrum near the long-wavelength
stability boundary (9) remain in the spectrum. The in-
stability saturates at energy density fluctuations (18) due
to the effect of scattering of ions by the random fluctua-
tions of the electric fields of drift-cyclotron turbulence.
The development of the instability is accompanied by
turbulent heating of the ions; however, the contribution
of this effect compared with the lower hybrid heating is
insignificant.
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Article received 05.05.2015
ИОННАЯ ЦИКЛОТРОННАЯ ТУРБУЛЕНТНОСТЬ ПЛАЗМЫ НИЖНЕГИБРИДНЫХ ПОЛОСТЕЙ
ЗЕМНОЙ ИОНОСФЕРЫ
Д.В. Чибисов
Исследуются линейная и нелинейная стадии ионной циклотронной неустойчивости в плазме нижнеги-
бридных полостей земной ионосферы. Поскольку такие структуры имеют цилиндрическую симметрию,
анализ проводится на основе модели, рассматривающей в качестве элементарных возмущений мелкомас-
штабные цилиндрические волны. Показано, что на нелинейной стадии неустойчивости происходят подавле-
ния высоких циклотронных гармоник, а также коротковолновой части спектра азимутальных волновых чи-
сел. Выполнена оценка скорости нагрева ионов.
ІОННА ЦИКЛОТРОННА ТУРБУЛЕНТНІСТЬ ПЛАЗМИ НИЖНЬОГІБРИДНИХ ПОРОЖНИН
ЗЕМНОЇ ІОНОСФЕРИ
Д.В. Чібісов
Досліджуються лінійна та нелінійна стадії іонної циклотронної нестійкості в плазмі нижньогібридних
порожнин земної іоносфери. Оскільки такі структури мають циліндричну симетрію, аналіз проводиться на
основі моделі, що розглядає в якості елементарних збурень дрібномасштабні циліндричні хвилі. Показано,
що на нелінійній стадії нестійкості відбуваються пригнічення високих циклотронних гармонік, а також ко-
роткохвильової частини спектра азимутальних хвильових чисел. Виконано оцінку швидкості нагріву іонів.
D.V. Chibisov
The linear and nonlinear stages of the ion cyclotron instability in plasma of lower hybrid cavities in the Earth's ionosphere are investigated. Because these structures are cylindrically symmetric, the analysis uses the model, which considers as eleme...
1. LINEAR THEORY
In homogeneous magnetized plasma we consider a cylindrically symmetric cavity whose axis coincides with the direction of the magnetic field. Assume, that the plasma density in the cavity determined by the "inverted" Gaussian distribution
2. NONLINEAR THEORY
where , ; is the matrix element of induced scattering of waves by ions equals
where , . Value is equal to the radial coordinate of the first maximum of the cylindrical beat wave for the waves and . The beat wave has the wave numbers determined by
;
Induced scattering of cylindrical waves has characteristic distinction from a similar process of plane waves. In the case of plane waves to obtain the equation describing the nonlinear evolution of the spectral intensity of the wave-interaction partn...
and take into account the basic properties of the symmetry of the matrix elements. In this case the appearance of non-linear increment in the equation for the spectral intensity is accompanied by the appearance of symmetric nonlinear decrement in the...
The second stage of the evolution of the drift-cyclotron instability is determined by the scattering of particles in the random fluctuations of the electric field drift-cyclotron turbulence (broadening of the resonance) [12, 13]. At this phase the sat...
The ion cyclotron turbulence in the LHC leads to additional turbulent heating of the plasma ions. To determine the rate of heating we use the results of [14], where was estimated the rate of quasi-linear change of the thermal Larmor radius, resulting ...
Characteristic time of variation of the thermal Larmor radius due to ion cyclotron turbulence is of the order of
CONCLUSIONS
In plasma of the lower hybrid cavities which exist in the Earth's topside ionosphere and magnetosphere, the ion cyclotron instability may occurs due to the radial inhomogeneity of plasma. For weakly inhomogeneous plasma in cavities as well as for cavi...
At the nonlinear stage of development of instability the higher cyclotron harmonics in the frequency spectrum as well as the short-wavelength part of the spectrum of the azimuthal wave numbers are suppressed due to induced scattering of waves by ions....
ИОННАЯ ЦИКЛОТРОННАЯ ТУРБУЛЕНТНОСТЬ ПЛАЗМЫ НИЖНЕГИБРИДНЫХ ПОЛОСТЕЙ ЗЕМНОЙ ИОНОСФЕРЫ
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| id | nasplib_isofts_kiev_ua-123456789-112140 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T13:16:49Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Chibisov, D.V. 2017-01-17T18:08:21Z 2017-01-17T18:08:21Z 2015 Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere / D.V. Chibisov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 148-151. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.35.Ra, 94.20.wf https://nasplib.isofts.kiev.ua/handle/123456789/112140 The linear and nonlinear stages of the ion cyclotron instability in plasma of lower hybrid cavities in the Earth's ionosphere are investigated. Because these structures are cylindrically symmetric, the analysis uses the model, which considers as elementary perturbations the small-scale cylindrical waves. It is shown that at the nonlinear stage of instability the suppression of high cyclotron harmonics, as well as short-wavelength part of the spectrum of the azimuthal wave numbers occurs. The estimate of the rate of ion heating is carried out. Досліджуються лінійна та нелінійна стадії іонної циклотронної нестійкості в плазмі нижньогібридних порожнин земної іоносфери. Оскільки такі структури мають циліндричну симетрію, аналіз проводиться на основі моделі, що розглядає в якості елементарних збурень дрібномасштабні циліндричні хвилі. Показано, що на нелінійній стадії нестійкості відбуваються пригнічення високих циклотронних гармонік, а також короткохвильової частини спектра азимутальних хвильових чисел. Виконано оцінку швидкості нагріву іонів. Исследуются линейная и нелинейная стадии ионной циклотронной неустойчивости в плазме нижнегибридных полостей земной ионосферы. Поскольку такие структуры имеют цилиндрическую симметрию, анализ проводится на основе модели, рассматривающей в качестве элементарных возмущений мелкомасштабные цилиндрические волны. Показано, что на нелинейной стадии неустойчивости происходят подавления высоких циклотронных гармоник, а также коротковолновой части спектра азимутальных волновых чисел. Выполнена оценка скорости нагрева ионов. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Коллективные процессы в космической плазме Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere Іонна циклотронна турбулентність плазми нижньогібридних порожнин земної іоносфери Ионная циклотронная турбулентность плазмы нижнегибридных полостей земной ионосферы Article published earlier |
| spellingShingle | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere Chibisov, D.V. Коллективные процессы в космической плазме |
| title | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere |
| title_alt | Іонна циклотронна турбулентність плазми нижньогібридних порожнин земної іоносфери Ионная циклотронная турбулентность плазмы нижнегибридных полостей земной ионосферы |
| title_full | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere |
| title_fullStr | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere |
| title_full_unstemmed | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere |
| title_short | Ion cyclotron turbulence in plasma of lower hybrid cavities in the Earth’s ionosphere |
| title_sort | ion cyclotron turbulence in plasma of lower hybrid cavities in the earth’s ionosphere |
| topic | Коллективные процессы в космической плазме |
| topic_facet | Коллективные процессы в космической плазме |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112140 |
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