Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow
The ion cyclotron instability of magnetic field aligned sheared plasma flow with two H+ and ion species is investigated. The oxygen ions are assumed to be the active species while hydrogen ions are a background one, so that the frequency of oscillation approximately equals O+O+ cyclotron frequency....
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nasplib_isofts_kiev_ua-123456789-906182025-02-09T09:40:55Z Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow Збуджувана широм потокової швидкості іонна циклотронна нестійкість потоку багатокомпонентної плазми вздовж магнітного поля Возбуждаемая широм потоковой скорости ионная циклотронная неустойчивость потока многокомпонентной плазмы вдоль магнитного поля Chibisov, D.V. Mikhailenko, V.S. Stepanov, K.N. Фундаментальная физика плазмы The ion cyclotron instability of magnetic field aligned sheared plasma flow with two H+ and ion species is investigated. The oxygen ions are assumed to be the active species while hydrogen ions are a background one, so that the frequency of oscillation approximately equals O+O+ cyclotron frequency. The threshold and growth rate of instability versus the flow velocity shear and relative concentration of oxygen ions are analyzed. Досліджено іонна циклотронна нестійкість зсуненого потоку плазми вздовж магнітного поля з двома видами, H+ і , іонів. Іони кисню вважаються основним видом, тоді як іони водню є фоном, так що частота коливань приблизно дорівнює циклотронній частоті іонів O+O+. Аналізується залежність порога та інкремента нестійкості від градієнта швидкості потоку і відносної концентрації іонів кисню. Исследована ионная циклотронная неустойчивость сдвигового течения плазмы вдоль магнитного поля с двумя сортами, H+ и , ионов. Ионы кислорода считаются основным видом, тогда как ионы водорода являются фоном, так что частота колебаний приблизительно равна циклотронной частоте ионов O+O+. Анализируется зависимость порога и инкремента неустойчивости от градиента скорости течения и относительной концентрации ионов кислорода. 2011 Article Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow / D.V. Chibisov, V.S. Mikhailenko, K.N. Stepanov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 44-46. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 94.05.Lk, 94.20.wf https://nasplib.isofts.kiev.ua/handle/123456789/90618 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Фундаментальная физика плазмы Фундаментальная физика плазмы |
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Фундаментальная физика плазмы Фундаментальная физика плазмы Chibisov, D.V. Mikhailenko, V.S. Stepanov, K.N. Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow Вопросы атомной науки и техники |
| description |
The ion cyclotron instability of magnetic field aligned sheared plasma flow with two H+ and ion species is investigated. The oxygen ions are assumed to be the active species while hydrogen ions are a background one, so that the frequency of oscillation approximately equals O+O+ cyclotron frequency. The threshold and growth rate of instability versus the flow velocity shear and relative concentration of oxygen ions are analyzed. |
| format |
Article |
| author |
Chibisov, D.V. Mikhailenko, V.S. Stepanov, K.N. |
| author_facet |
Chibisov, D.V. Mikhailenko, V.S. Stepanov, K.N. |
| author_sort |
Chibisov, D.V. |
| title |
Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow |
| title_short |
Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow |
| title_full |
Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow |
| title_fullStr |
Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow |
| title_full_unstemmed |
Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow |
| title_sort |
shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2011 |
| topic_facet |
Фундаментальная физика плазмы |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/90618 |
| citation_txt |
Shear-flow-driven ion cyclotron instability of multicomponent magnetic field-aligned plasma flow / D.V. Chibisov, V.S. Mikhailenko, K.N. Stepanov // Вопросы атомной науки и техники. — 2011. — № 1. — С. 44-46. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
SHEAR-FLOW-DRIVEN ION CYCLOTRON INSTABILITY
OF MULTICOMPONENT MAGNETIC FIELD-ALIGNED PLASMA FLOW
D.V. Chibisov, V.S. Mikhailenko, K.N. Stepanov
V.N. Karazin Kharkov National University, Kharkov, Ukraine
E-mail: chibisovdm@mail.ru
The ion cyclotron instability of magnetic field aligned sheared plasma flow with two H + and ion species is
investigated. The oxygen ions are assumed to be the active species while hydrogen ions are a background one, so that
the frequency of oscillation approximately equals
O +
O + cyclotron frequency. The threshold and growth rate of instability
versus the flow velocity shear and relative concentration of oxygen ions are analyzed.
PACS: 94.05.Lk, 94.20.wf
1. INTRODUCTION
44 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. № 1.
Series: Plasma Physics (17), p. 44-46.
The investigations of the auroral region of the Earth’s
ionosphere have discovered the inhomogeneous structures
of electrostatic potentials which are correlated with
regions of the formation and acceleration of the magnetic
field-aligned upward ion beams [1]. One of the main
signatures of these beams is the gradient of the flow
velocity across the magnetic field (flow velocity shear)
which can reach specifically for ions the values
of
0iV ′ O +
6 ciω [2]. The upflowing ion beams are mainly
composed of H + and O ions the composition of
which varies significantly from beam to beam [3]. These
auroral ion beams are often correlated with electrostatic
ion cyclotron (EIC) oscillations having the cyclotron
frequencies of hydrogen and oxygen ions [4,5]. It was
shown that the flow velocity shear along with the other
mechanisms may be responsible for the excitation of EIC
waves in the auroral ionosphere due to development of
the shear-flow-driven EIC instability [6,7].
+
The shear-flow-driven EIC instability was studied in
plasma with single ion species. However, the application
of these results in ionosphere investigations requires
taking into account the presence of several ion
components, the relative concentrations of which are
changed significantly with the altitude in ionospheric
plasma. We have carried out the study of the shear-flow-
driven EIC instability in the sheared magnetic field-
aligned plasma flow with two, H + and , ion species.
The oxygen ions are assumed to be the main species,
while hydrogen ions are a background one, so that the
frequency of oscillation approximately equals the
O +
O +
cyclotron frequency. We have analyzed the dispersion
equation for ion-hydrodynamic mode of the shear-flow-
driven EIC instability assuming that the waves propagate
nearly perpendicularly to the magnetic field but under the
assumption that electrons are adiabatic.
2. THE INSTABILITY OF THE FIRST
CYCLOTRON HARMONIC
The kinetic dispersion relation for homogeneous
multi-ion component plasma with a flow velocity shear is
given by [8]
( ) 2 2 2 2
1 1, 1 1 y
zDe D
k
K S
kk k
α
αα
iε ω π
λ λ
⎛
= + + − +⎜⎜
⎝
∑ × (1)
( ) ( ) 0 0
2
yz
n n n
zz Tn
kk V
W z b S z
kk V
α
α α α α
α
ω∞
=−∞
⎞⎛ ⎞− ⎟× Γ −⎜ ⎟⎜ ⎟⎟⎝ ⎠⎠
∑ = ,
where Dαλ is the Debye length, ( ) ( )b
n nA b e I b−= , ( )nI b is
the modified Bessel function, b k , ( )2Tα αρ⊥= Tαρ =
T cV α αω is the thermal Larmor radius, Sα =
( )0 cV Xα αω′ is the normalized flow velocity shear,
( )0 2n c z zz n k V k TVα α αω ω= − − α , ( )
2zW z e−= ×
( ) 2
0
1 2
z
i e dξπ ξ
⎛ ⎞
+⎜⎜
⎝ ⎠
∫ ⎟⎟ . We study the heavy-ion cyclotron
mode having the frequency ( ) ( )0ch z hk n k V kω ω δω= + +
with ( ) chKδω ω
0lV=
0lV
. Assume, that both ion species have
the equal flow velocities V and equal magnitudes
of velocity shear V
0h
0h′ ′= , where indexes h and mean
the heavy
l
O + and light H + ions.
We first analyze the instability of the main 1n =
cyclotron harmonic. For the oscillations propagating
almost across the magnetic field so that inequality
1 1iz > holds the asymptotic form of W - function for
large argument ( )iW z ( )( )21 1 2ii z zπ + i can be
used. In this case the ion cyclotron damping can be
neglected for both light and heavy ions. The dielectric
permittivity of heavy ions can be written as
( )
( )
1 12 2
2 2
12
1 1
,
ch
h h h
Dh
y z Th
h h
z
G A b
k
k k V
S A b
k
ω
δε
δωλ
δω
⎛≈ − −⎜
⎝
⎞
+ ⎟⎟
⎠
(2)
where ( ) ( )( )1 1 01h h hG A b A b b= + − h . In the sum over
cyclotron harmonics of light ions we retain only null
summand because of significant difference in the masses
of heavy and light ions. Then the dielectric permittivity of
light ions becomes
( ) ( )0
02 2 2
0
1 1
2
y l l
l l
zDl l
k S A b
A b
kk z
δε
λ
⎛ ⎞
≈ − +⎜ ⎟⎜ ⎟
⎝ ⎠
, (3)
where 0 2l ch z Tlz k Vω= , l hS S= μ and h lm mμ = .
The dispersion equation (1) ultimately takes the form
( ) ( )2 0K p K qδω δω− +
45
= , (4)
where
( )( )
12 2
1 11h h h Dh lp G k kδω τ α λ δε ω, ,k
−
⎡= + − +⎣
⎤
⎦
( )( )
12 2 2
11 , ,h h h Dh lq G k k kσ τ α λ δε ω
−
⎡ ⎤= + − +⎣ ⎦
( )1 1h ch hA bδω ω= , , ( )2 2
1h y z Th h hk k V S A bσ = h h en nα =
is the relative concentration of heavy ions, i eT Tτ = with
. The solution of Eq. (4) has the form h lT T T= = i
( )1 1 12h h hδω δω β= ±Ω , (5)
where ( )1 22 2
1 1 14h h h hδω σ βΩ = − , 1 11h hG hβ τ α= − + +
( ) ( ) ( )( )2
01l h l y z Th h l0A b k k S A bα α ρ+ − + . The solution
(5) gives the shear-flow-driven EIC instability if
inequality 2
14 h h h
2
1σ β δω> is met. For the wave numbers
such as 1y Thk ρ and respectively 1z Tlk ρ this
condition can be written as 1λ λ< , where 1 z Thkλ ρ= is
the normalized wavelength parallel to the magnetic field,
( )1 1 1y Th h h hk S A bλ ρ β is the threshold wavelength of
instability for harmonic and 1n = 1 11h hG hβ τ α− + .
Then let us estimate the effect of the relative
concentration of heavy ions on the condition 1 1hz > .
From the definition of we have 1hz
( )1 12 2h z Th y h hz k V k S A b k 1z hδω β= = . (6)
Taking into account that 1 1h hβ α∝ and ( )1 0.2hA b ≈
we obtain from Eq. (6) that the inequality 1 1hz > holds
when 10h z hk S kyα τ .
Now we investigate the effect of hα and on the
growth rate of the shear-flow-driven EIC instability. The
growth rate of instability obtained from Eq. (5) is
approximately
hS
( ) 1 2
1 11 2 h .γ λ λ β−⎡ ⎤⎣ ⎦ (7)
With a decrease of hα the growth rate away from
threshold decreases approximately as hα , however, the
magnitude of threshold wavelength increases as hα , so
that the longer waves become unstable. The dependence
of the growth rate on the normalized shear is
expressed by the similar relation, i.e.
hS
hSγ ∝ and
1 hSλ ∝ . Thus the effects of relative concentration of
oxygen ions on the growth rate and long-wavelength
threshold is identical with the flow velocity shear.
We also numerically solved the dispersion equation
(1) for the different values of relative concentration of
oxygen ions and obtained the dependence of the growth
rate versus the normalized wavelength along the magnetic
field. The results of calculations for , 3hS = 1y Thk ρ =
and 1τ = are shown in Figure. The maximum of the
growth rate occurs at 1 1hz what is a boundary of ion-
hydrodynamic mode which is located to the right of the
point of maximum. The Figure shows a decrease of the
growth rate as well as an increase of the long-wavelength
threshold with the decrease of hα that is in a good
agreement with analytical results.
The growth rate of instability vs the normalized
wavelength along the magnetic field for different
magnitudes of relative concentration of O + ions
2. THE INSTABILITY OF THE HIGH
CYCLOTRON HARMONICS
Now we investigate the instability of the high, 1n ,
cyclotron harmonics. Using the same assumptions as for
the first harmonic we sum over cyclotron harmonics at
1y Thk nρ and obtain approximately the dielectric
permittivity of heavy ions as
( )
( )
2 2
2 2
2
1 1
,
ch
h hn n h
Dh
y z Th
h n h
z
n
G A b
k
k k V
S A b
k
ω
δε
δωλ
δω
⎛≈ − −⎜
⎝
⎞
+ ⎟⎟
⎠
(8)
where
( )
2 2
0
2
h
h
z
z t
hn h n hG z e e dt A b
⊥
⊥−
⊥= +∫
and ( ) 2 2h Thz k k V n k Thω ρ⊥ ⊥= ≈ ⊥ . In the
dielectric permittivity of light ions (3) we take into
account that inequality 1y Thk ρ holds, so that
1y Tlk ρ > and then 2 21l k Dlδε ≈ λ . In this case the
dispersion equation (1) takes the similar form as for the
first harmonic (4). Its solution is
( ) 2nh nh nhδω ω β= ±Ω , (9)
where ( )nh ch n hn A bδω ω= , ( )1 22 24nh nh h nhδω σ βΩ = − ,
1nh nh h l hGβ τ α α α≈ − + + . The solution (9) gives the
shear-flow-driven EIC instability if inequality
24 h nh nh
2σ β δω> is met. This condition can be also written
as nλ λ< , where ( )2
n y Th h nh n hk S n A bλ ρ β is the
threshold wavelength of instability for harmonics. 1n
Note that the function ( )n hA b at 1y Thk nρ has the
asymptotic form ( ) ( ) ( 2 2 21 2 exp 2n h Th TiA b k n k )π ρ⊥ − ρ⊥
n
and for y Thk ρ = we have ( ) 0.2n hA b n≈ that gives
1nλ λ≈ . Thus the long-wavelength threshold is the same
as for the first and high cyclotron harmonics.
2. W.E. Amatucci. Inhomogeneous plasma flows: A
review of in situ observations and laboratory
experiments// J. Geophys. Res. (104). 1999, N A7,
p. 14481-14503.
46
Evaluating the effect of the relative concentration on
the condition 1hnz > , we conclude that for y Thk nρ =
the condition on the hα coincides with that of the main
harmonic. Now we estimate the effect of hα and on
the growth rate of high cyclotron harmonic of the shear-
flow-driven EIC instability. The growth rate of instability
obtained from Eq. (9) approximately equals
hS
3. E. Moebius, L. Tang, L.M. Kistler, M. Popecki,
E.J. Lund, D. Klumpar, W. Peterson, E. Shelley,
B. Kle-cker, D. Hovestadt, C.W. Carlson, R.E. Ergun,
J.P. McFadden, F.S. Mozer, M. Temerin, C. Cattell,
R. Elphic, R. Strangeway, R. Pfaff. Species dependent
energies in upward directed ion beams over auroral arcs
as observed with FAST TEAMS // Geophys. Res. Lett.
(25). 1998, N 12, p. 2029-2032.
4. C.A. Cattell, F.S. Mozer, I. Roth, R.R. Anderson,
R.C. Elphic, W. Lennartsson, and E. Ungstrup. ISEE 1
observations of electrostatic ion cyclotron waves in
association with ion beams on auroral field lines from
2.5 to 4.5 RE // J. Geophys. Res. (96). 1991, N A7,
p. 11421-11439.
( ) 1 21 2n nγ λ λ β−⎡ ⎤⎣ ⎦ .h (10)
Since the thresholds 1λ and nλ are equal we obtain that
the dependence of growth rate on the concentration and
the shear is the same as for the main cyclotron harmonic.
The numerical calculations confirm these results.
5. C. Cattell, R. Bergmann, K. Sigsbee, C. Carlson,
C. Chaston, R. Ergun, J. McFadden, F.S. Mozer,
M. Temerin, R. Strangeway, R. Elphic, L. Kistler,
E. Moebius, L. Tang, D. Klumpar, and R. Pfaff. The
association of electrostatic ion cyclotron waves, ion and
electron beams and field-aligned currents: FAST
observations of an auroral zone crossing near midnight
// Geophys. Res. Lett. (25). 1998, N 12, p. 2053-2056.
3. CONCLUSIONS
The presence of the light H + ion species in the
sheared plasma flow with O ions leads to a decrease of
the growth rate of the shear-flow-driven EIC instability
with ion cyclotron frequency, whereas the long-
wavelength threshold of instability is shifted toward
longer wavelengths both for the main and high
cyclotron harmonics. In so doing the effects of relative
concentration of oxygen ions on the growth rate and long-
wavelength threshold is identical to the flow velocity
shear.
+
O +
1n =
6. V.S. Mikhailenko, D.V. Chibisov, and
V.V. Mikhailenko. Shear-flow-driven ion cyclotron
instabilities of magnetic field-aligned flow of
inhomogeneous plasma // Phys. Plasmas (13). 2006,
N 10, p. 102105 (6 p.).
7. E.V. Belova, Ya. Blenski, M. Denis, L.М. Zelenyj,
S.P. Savin. Excitation of ion-cyclotron waves at the
boundary of the magnetosphere // Fizika Plasmy. 1991,
v. 17, N 8, p. 952-961 (in Russian).
REFERENCES 8. D.V. Chibisov, V.S. Mikhailenko, and K.N. Stepanov.
Current-driven ion cyclotron instability of
multicomponent field-aligned sheared flow // Phys.
Plasmas (17). 2010, N 8, p. 082903 (6p.).
1. R.E. Ergun, L. Andersson, D.S. Main, Y.-J. Su,
C.W. Carlson, J.P. McFadden, and F.S. Mozer. Parallel
electric fields in the upward current region of the
aurora: Indirect and direct observations// Phys. Plasmas
(9). 2002, N 9, p. 3685-3694.
Article received 27.10.10
ВОЗБУЖДАЕМАЯ ШИРОМ ПОТОКОВОЙ СКОРОСТИ ИОННАЯ ЦИКЛОТРОННАЯ
НЕУСТОЙЧИВОСТЬ ПОТОКА МНОГОКОМПОНЕНТНОЙ ПЛАЗМЫ ВДОЛЬ МАГНИТНОГО ПОЛЯ
Д.В. Чибисов, В.С. Михайленко, К.Н. Степанов
Исследована ионная циклотронная неустойчивость сдвигового течения плазмы вдоль магнитного поля с
двумя сортами, H + и , ионов. Ионы кислорода считаются основным видом, тогда как ионы водорода
являются фоном, так что частота колебаний приблизительно равна циклотронной частоте ионов
O +
O + .
Анализируется зависимость порога и инкремента неустойчивости от градиента скорости течения и
относительной концентрации ионов кислорода.
ЗБУДЖУВАНА ШИРОМ ПОТОКОВОЇ ШВИДКОСТІ ІОННА ЦИКЛОТРОННА НЕСТІЙКІСТЬ
ПОТОКУ БАГАТОКОМПОНЕНТНОЇ ПЛАЗМИ ВЗДОВЖ МАГНІТНОГО ПОЛЯ
Д.В. Чібісов, В.С. Михайленко, К.М. Степанов
Досліджено іонна циклотронна нестійкість зсуненого потоку плазми вздовж магнітного поля з двома
видами, H + і , іонів. Іони кисню вважаються основним видом, тоді як іони водню є фоном, так що частота
коливань приблизно дорівнює циклотронній частоті іонів
O +
O + . Аналізується залежність порога та інкремента
нестійкості від градієнта швидкості потоку і відносної концентрації іонів кисню.
D.V. Chibisov, V.S. Mikhailenko, K.N. Stepanov
Article received 27.10.10
ВОЗБУЖДАЕМАЯ ШИРОМ ПОТОКОВОЙ СКОРОСТИ ИОННАЯ ЦИКЛОТРОННАЯ НЕУСТОЙЧИВОСТЬ ПОТОКА МНОГОКОМПОНЕНТНОЙ ПЛАЗМЫ ВДОЛЬ МАГНИТНОГО ПОЛЯ
Д.В. Чибисов , В.С. Михайленко, К.Н. Степанов
Д.В. Чібісов , В.С. Михайленко, К.М. Степанов
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