High-frequency oscillations in plasma of lower hybrid cavities
The problem of the presence of high-frequency oscillations in lower hybrid cavities in the plasma of the earth's ionosphere is considered. It is assumed that the oscillations in the cavity are excited due to the ring ion current across the magnetic field, in addition to the mechanism of the Hal...
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irk-123456789-1951602023-12-03T16:34:52Z High-frequency oscillations in plasma of lower hybrid cavities Azarenkov, N.A. Chibisov, D.V. Non-relativistic and relativistic electronics The problem of the presence of high-frequency oscillations in lower hybrid cavities in the plasma of the earth's ionosphere is considered. It is assumed that the oscillations in the cavity are excited due to the ring ion current across the magnetic field, in addition to the mechanism of the Hall current arising from the radial inhomogeneity of the plasma density. The radial dependence of the density of the ring ion beam is also taken into account. Розглядається проблема присутності високочастотних коливань у нижньогібридних порожнинах у плазмі іоносфери Землі. Передбачається, що коливання в порожнині збуджуються за рахунок струму кільцевого іонного пучка поперек магнітного поля на додаток до механізму струму Холла, що виникає через радіальну неоднорідність щільності плазми. Враховується також радіальна залежність щільності кільцевого іонного пучка. Рассматривается проблема присутствия высокочастотных колебаний в нижнегибридных полостях в плазме ионосферы Земли. Предполагается, что колебания в полости возбуждаются за счет тока кольцевого ионного пучка поперек магнитного поля в дополнение к механизму тока Холла, возникающего из-за радиальной неоднородности плотности плазмы. Учитывается также радиальная зависимость плотности кольцевого ионного пучка. 2019 Article High-frequency oscillations in plasma of lower hybrid cavities / N.A. Azarenkov, D.V. Chibisov // Problems of atomic science and technology. — 2019. — № 4. — С. 24-26. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.35.Qz, 52.35.Ra, 94.20.wf http://dspace.nbuv.gov.ua/handle/123456789/195160 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Non-relativistic and relativistic electronics Non-relativistic and relativistic electronics Azarenkov, N.A. Chibisov, D.V. High-frequency oscillations in plasma of lower hybrid cavities Вопросы атомной науки и техники |
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The problem of the presence of high-frequency oscillations in lower hybrid cavities in the plasma of the earth's ionosphere is considered. It is assumed that the oscillations in the cavity are excited due to the ring ion current across the magnetic field, in addition to the mechanism of the Hall current arising from the radial inhomogeneity of the plasma density. The radial dependence of the density of the ring ion beam is also taken into account. |
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Article |
| author |
Azarenkov, N.A. Chibisov, D.V. |
| author_facet |
Azarenkov, N.A. Chibisov, D.V. |
| author_sort |
Azarenkov, N.A. |
| title |
High-frequency oscillations in plasma of lower hybrid cavities |
| title_short |
High-frequency oscillations in plasma of lower hybrid cavities |
| title_full |
High-frequency oscillations in plasma of lower hybrid cavities |
| title_fullStr |
High-frequency oscillations in plasma of lower hybrid cavities |
| title_full_unstemmed |
High-frequency oscillations in plasma of lower hybrid cavities |
| title_sort |
high-frequency oscillations in plasma of lower hybrid cavities |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2019 |
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Non-relativistic and relativistic electronics |
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http://dspace.nbuv.gov.ua/handle/123456789/195160 |
| citation_txt |
High-frequency oscillations in plasma of lower hybrid cavities / N.A. Azarenkov, D.V. Chibisov // Problems of atomic science and technology. — 2019. — № 4. — С. 24-26. — Бібліогр.: 10 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT azarenkovna highfrequencyoscillationsinplasmaoflowerhybridcavities AT chibisovdv highfrequencyoscillationsinplasmaoflowerhybridcavities |
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2025-07-16T23:00:00Z |
| last_indexed |
2025-07-16T23:00:00Z |
| _version_ |
1837846287739781120 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2019. №4(122) 24
HIGH-FREQUENCY OSCILLATIONS IN PLASMA
OF LOWER HYBRID CAVITIES
N.A. Azarenkov, D.V. Chibisov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: dmitriychibisov@karazin.ua
The problem of the presence of high-frequency oscillations in lower hybrid cavities in the plasma of the earth's
ionosphere is considered. It is assumed that the oscillations in the cavity are excited due to the ring ion current
across the magnetic field, in addition to the mechanism of the Hall current arising from the radial inhomogeneity of
the plasma density. The radial dependence of the density of the ring ion beam is also taken into account.
PACS: 52.35.Qz, 52.35.Ra, 94.20.wf
INTRODUCTION
The lower hybrid cavities (LHC) are axisymmetric
spatially localized solitary structures in the ionosphere,
elongated along the geomagnetic field. They are charac-
terized by localized oscillations of the electric field at
frequencies near the lower hybrid resonance as well as a
decrease in density to several tens of percent [1]. Cur-
rently, there are two class of theories applied to LHC.
The first class [2 - 4] includes the theory of strong tur-
bulence of the lower hybrid collapse, which suggests
that the depletion of density and oscillations of the elec-
tric field are directly related to the ponderomotive force.
However, it was stated in [5] that the theoretical conclu-
sions of the theory of strong turbulence do not corre-
spond to the statistical properties of most of the ob-
served cavities. Second class [6, 7] includes linear theo-
ries which suggest that density depletions already exist,
and use the spatial properties of density depletions to
determine the characteristics of low-hybrid waves. It is
assumed that the excitation mechanism of the lower
hybrid waves is the Hall current created by electron drift
across the gradient of a density profile. This current is
not canceled by ions, which, for these oscillation fre-
quencies, can be considered unmagnetized in the cavity.
As for the mechanism of wave excitation due to the cur-
rent across the density gradient, this assumption of line-
ar theories is generally true, but there is every reason to
believe that ions moving in the cavity also participate in
the initiation of lower-hybrid waves. Observations by
spacecraft showed that ions in a cavity have an in-
creased energy across the magnetic field compared to
ions of the surrounding plasma. Thus, a group of ions
may appear in the cavity, which encircles the axis of
depletion. These ions produce an azimuth current,
which will be another factor besides the Hall current to
amplify the lower hybrid waves.
In [8] the excitation of electrostatic lower hybrid
waves in a cylindrically symmetric magnetized plasma
by ions encircles the plasma axis was investigated. The
Gaussian plasma density distribution over the radius
was considered. It was shown that the instability is ex-
cited as a result of the Cherenkov interaction of resonant
ionsrotating around the plasma axis with lower hybrid
waves. In [9] the excitation of lower hybrid waves in a
plasma with an ion-ring distribution with a radially in-
homogeneous density in a homogeneous plasma was
studied. The effect of inhomogeneity of the ring ion
beam on the conditions for the excitation of waves was
established. In the present paper the excitation of lower
hybrid waves by ion beam encircling of axis of sym-
metry, taking into account its in homogeneity, is consid-
ered as applied to the plasma conditions of lower hybrid
cavities.
INSTABILITY OF LOWER HYBRID WAVES
IN PLASMA OF LHC
The radial density profile in plasma of LHC has the
form of an inverted Gaussian distribution [1]
( )
2
0 2
0
1 exp
2
= − −
rn r n a
r
, (1)
where 0r is the length of the inhomogeneity of plasma
density, a is the positive constant, equal to the depth of
the cavity. Suppose that a part of plasma ions in the cav-
ity encircle the axis of depletion and thereby form an
ion ring beam. The presence of such ions in the cavity
can be explained by their energization, which is con-
firmed by observations. Assume, that density profile of
ion ring beam in the cavity is
( )
2 2
0 2 2
0
1 exp
2 2
= − − −
b b
b
r rn r n a
r r
, (2)
which takes into account the distribution of plasma den-
sity in the cavity, as well as the inhomogeneity of the
profile of the beam itself, whose density outside the
cavity tends to zero. The characteristic length of the
inhomogeneity of the ion beam br actually characterizes
the level of its heating and is equal to the thermal gyro
radius of heated ions in the cavity. It is assumed that
0<br r . The part of ions encircling the cavity axis are
considered small in comparison with the bulk of plasma
ionsso it is assumed that 0 0<<bn n . Distribution (2) has
a minimum at 0=r , and a maximum at
2
1/2
0 2
0
2 ln 1
= +
b
m
r
r r a
r
, (3)
when the condition
2
2
0
1 1
+ >
bra
r
(4)
is satisfied. Otherwise, the distribution has only a max-
imum at 0=r . In other words, the ion flux, encircling
the axis of depletion has a density maximum at a radius
(3) different from zero if the depth of the cavity is suffi-
ciently large so that the condition (4) is true. Otherwise,
when the depth of the cavity is small and the condition
(4) is not fulfilled, the density of ions encircling the axis
ISSN 1562-6016. ВАНТ. 2019. №4(122) 25
of depletion is decreasing for all radius values. Figure
shows examples of two cases of density distribution of
ion beam, where curve 1 corresponds to the case when
condition (4) is satisfied, and curve 2, when (4) is not
satisfied
Dependence of the ion beam density in the cavity
on the radiuswhen condition (4) is satisfied, 1,
and not satisfied, 2
Let us now consider the conditions for the excitation
of lower hybrid waves in the plasma of the cavity by a
ring ion beam having a radial density profile as (2).
Dispersion equation for lower hybrid waves in a cylin-
drically symmetric plasma has the form [9]
( )
2 2
2 2
2 2, , 1 sin cos
ω ω
ε ω θ θ
ω ω
= + − +pe pe
ce
K m
( )( ), ,2 2
, ,
1 1 0π
λ
+ + =∑ i b i b
i b Di b
i z W z
k
, (5)
where m and ( ),⊥ zK k k are azimuthal, transverse and
longitudinal wavenumbers, αλD is the Debye length,
( )arctan /θ ⊥= zk k is the angle of wave propagation
relative to the magnetic field, ωpe is the plasma fre-
quency
/ 2i Tiz k vω ⊥= , ( )* /ω ω ω= + −b cb bz m m 2 ⊥ Tbk v ,
*ω =b ( )( )2 ln /ω ρ− cb Tb b s s sd n r r dr
is the drift frequency of beam ions and ( )sbn r is the
density of beam ions (2), where radial coordinate r is
replaced by variable | | / ⊥=sr m k . Equation (5) in the
short wavelength limit | | 1m >> determines the disper-
sion properties of cylindrical waves ( )mJ k r⊥ which are
Bessel functions. The value of radius | | / ⊥=sr m k sepa-
rates the aperiodic and oscillatory parts of Bessel func-
tion, which approximately is equal the radial coordinate
of its first maximum.
The dielectric permittivities for beam and plasma
ions in (5) correspond to the approximation of null
magnetic field, assuming that the ions move in straight
orbits. However, the cyclotron motion of beam ions in
expressions for bz is taken into account by the term
cbmω which is the Doppler shift causedby theirrotation
around the axis of depletion. We now suppose that ine-
quality | | 1iz >> is met. However we assume that Che-
renkov interaction of resonant ions rotating around axis
for the beam ions is significant, i.e. equality | | 1bz
hold. This equality is possible when the resonant condi-
tion *| | 2cb b Tbm m k vω ω ω ⊥+ − ≈ is satisfied. In this
case the dispersion relation takes the form [9]
( )
2 2 2
2 2 2
2 2 2, , 1 sin cos sinpe pe pi
ce
K m
ω ω ω
ε ω θ θ θ
ω ω ω
= + − −
( )2
2 2 2 2
1 1 exp 0b b
Db Db
i z z
k k
π
λ λ
+ + − = . (6)
Suggesting that / /z e ik k m m< , as well as 2 2 1Dbk λ >
we get the real frequency ( )mRe Kω and growth rate
( )m Kγ for lower hybrid waves
( )
2 21 /
pi
m LH
pe ce
Re k
ω
ω ω
ω ω
⊥ = =
+
, (7)
( ) ( )2 2
0
2 2 22
pb LH
m LH
pi Tb
r
k
k v
ω ω
γ πω
ω⊥
⊥
≈ −
( ) ( )* 2exp
2
LH cb b
b
Tb
m m
z
k v
ω ω ω
⊥
+ −
× − . (8)
From eq. (8) it follows that the growth rate is posi-
tive, and therefore the lower hybrid waves are unstable
when the azimuthal wave number satisfies the condi-
tions 0m < and
( ) 1||
*
>
−
>
bcb
LHm
ωω
ω . (9)
Condition (9) indicates that for the radial coordinates
of ion ring beam where ( ) 0∇ >bn r unstable waves
have a greater absolute value of azimuthal wave num-
bers, than where ( ) 0∇ <bn r . However, Figure shows
that the region along radius with a negative density gra-
dient of the ion beam prevails; therefore, lower hybrid
waves with lower azimuthal wave numbers occupy a
larger region. In addition, if the depth of the cavity is
insignificant, so that condition (4) is not fulfilled, a part
of radius with a positive density gradient of the ion
beam is completely absent. Thus, taking into account
the inhomogeneity of the ion beam along the radius cor-
rects the azimuthal wave numbers down.
Now we estimate the electric field strength in the
lower hybrid wave in the cavity and for this we use the
saturation level of lower hybrid instability due to a ring-
ion beam in a cylindrically symmetric plasma which
was obtained in [9]. It was assumed that the instability
is saturated due to effect of scattering of beam ions by
the random fluctuations of the electrostatic turbulence
[10]. It is established, that the level of saturation of in-
stability is
( ) ( )
~
γ ω
ω ω
⊥Φb m cb
b LH LH
e r k
T
, (10)
where ( )rΦ is a root-mean-square amplitude of the
perturbed electrostatic potential, bT is the temperature
of ion beam, ωcb is the ion cyclotron frequency. Since
for the ionosphere the condition ω ω<<cb LH , is satis-
fied, then the oscillation energy is much lower than ion
ISSN 1562-6016. ВАНТ. 2019. №4(122) 26
temperature. To estimate the strength of the electric
field created by lower-hybrid oscillations we assume
that the temperature of ions is about 0.5 eV, wavelength
is 2 /λ π= r m , where r is the oscillation localization
radius, which in order of magnitude is equal to the
thermal Larmor radius of the ions of the ring beam,
ρ= Tbr , and m is the azimuthal wavenumber, which
determined by (9). Electric field strength in density de-
pletion we estimate as
( ) ( )
~
/ 2λ πρ
=
Φ Φ
Tb
m
E
r r
. (11)
Considering (9) and (10), we get
~
πρ
b
Tb
T
E
e
. (12)
Assuming 5ρ =Tb m for cavity conditions, we obtain
~ 0.03E V/m, which is generally consistent with the
measurement data.
CONCLUSIONS
Energization of ions in the cavity leads to the ap-
pearance of a group of ions that encircle the axis of den-
sity depletion and thereby create an azimuth current.
The radial density profile of a ring ion beam is deter-
mined by the relation (2). This density profile can have
a local maximum or on the axis of the cavity or on a
radius not equal to zero (3), depending on the depth of
the cavity, which is determined by the condition (4).
Ions encircling the cavity axis lead to the growth of
lower hybrid waves, due to the Cherenkov interaction of
resonant ions with waves. These waves are unstable when
the azimuthal wave number satisfies the condition (7).
Taking into account the radial inhomogeneity of the
density distribution of the ring ion beam decrease the
values of azimuthal wave numbers. The presented insta-
bility mechanism is an addition to the mechanism of the
Hall current, created by electron drift due to the density
profile gradient [1].
The saturation of the lower hybrid instability in the
cavity occurs due to the effect of beam ion scattering by
random fluctuations of electrostatic turbulence. An es-
timate of the electric field strength in the lower hybrid
wave is ~ 0.03E V/m, which is generally consistent
with the measurement data.
REFERENCES
1. P.W. Schuck, J.W. Bonnell, P.M. Kintner. A review
of lower hybrid solitary structures // IEEE Trans.
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Wave collapse at the lower-hybrid resonance //
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3. P.A. Robinson. Scalings, spectra, and statistics of
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4. V.D. Shapiro. Modulational interaction of the lower-
hybrid waves with a kinetic-Alfven mode // Phys.
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5. P.W. Schuck and G.I. Ganguli. The role of lower-
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Phys. Rev. Lett. 2002, v. 89, № 6, p. 065002-1-
065002-4.
6. C.E. Seyler. Lower hybrid wave phenomena associ-
ated with densitydepletions // J. Geophys. Res. 1994,
v. 99, № A10, p. 19 513-19 525.
7. P.W. Schuck, C.E. Seyler, et al. Theory simulation
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8. V.S. Mikhailenko, D.V. Chibisov, et al. Electrostatic
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Plasma Phys. Reps. 1997, v. 23, № 1, p. 44-52.
9. D.V. Chibisov, V.S. Mikhailenko. The lower hybrid
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// Problems of Atomic Science and Technology. Se-
ries “Plasma Physics”. 2012, № 6, p. 99-101.
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Article received 31.05.2019
ВЫСОКОЧАСТОТНЫЕ КОЛЕБАНИЯ ПЛАЗМЫ НИЖНЕГИБРИДНЫХ ПОЛОСТЕЙ
Н.А. Азаренков, Д.В.Чибисов
Рассматривается проблема присутствия высокочастотных колебаний в нижнегибридных полостях в
плазме ионосферы Земли. Предполагается, что колебания в полости возбуждаются за счет тока кольцевого
ионного пучка поперек магнитного поля в дополнение к механизму тока Холла, возникающего из-за ради-
альной неоднородности плотности плазмы. Учитывается также радиальная зависимость плотности кольце-
вого ионного пучка.
ВИСОКОЧАСТОТНІ КОЛИВАННЯ ПЛАЗМИ НИЖНЬОГІБРИДНИХ ПОРОЖНИН
М.О. Азарєнков, Д.В.Чібісов
Розглядається проблема присутності високочастотних коливань у нижньогібридних порожнинах у плазмі
іоносфери Землі. Передбачається, що коливання в порожнині збуджуються за рахунок струму кільцевого
іонного пучка поперек магнітного поля на додаток до механізму струму Холла, що виникає через радіальну
неоднорідність щільності плазми. Враховується також радіальна залежність щільності кільцевого іонного
пучка.
N.A. Azarenkov, D.V. Chibisov
Suggesting that , as well as we get the real frequency and growth rate for lower hybrid waves
, (7)
. (8)
|