Nonliner mechanism of electromagnetic waves generations in space dust plasma
We consider a parametric excitation of electromagnetic waves induced by inertial Alfvén wave (IAW) in space dust plasma. The nonlinear dispersion equations describing decay of upper-hybrid wave (UHW) into the IAW and the ordinary electromagnetic wave as well as decay of UNW into the IAW and the left...
Gespeichert in:
| Veröffentlicht in: | Вопросы атомной науки и техники |
|---|---|
| Datum: | 2007 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/110407 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonliner mechanism of electromagnetic waves generations in space dust plasma / A.D. Voitsekhovskа, A.K. Yukhimuk, O.K. Sirenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 87-89. — Бібліогр.: 7 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-110407 |
|---|---|
| record_format |
dspace |
| spelling |
Voitsekhovskа, A.D. Yukhimuk, A.K. Sirenko, O.K. 2017-01-04T11:53:24Z 2017-01-04T11:53:24Z 2007 Nonliner mechanism of electromagnetic waves generations in space dust plasma / A.D. Voitsekhovskа, A.K. Yukhimuk, O.K. Sirenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 87-89. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.35.-g https://nasplib.isofts.kiev.ua/handle/123456789/110407 We consider a parametric excitation of electromagnetic waves induced by inertial Alfvén wave (IAW) in space dust plasma. The nonlinear dispersion equations describing decay of upper-hybrid wave (UHW) into the IAW and the ordinary electromagnetic wave as well as decay of UNW into the IAW and the left-hand circularly polarized (LHCP) wave are obtained using the three-fluid magnetohydrodynamics. The instability growth rates which depend on dust plasma parameters are found. It is shown that the LPCH wave is preferably excited by the UH pump wave for the parameters of the Saturn's F-ring. Розглянуто параметричне збудження електромагнітних хвиль інерційними альфвенівськими хвилями (ІАХ) в пиловій космічній плазмі. На основі рівнянь трирідинної магнітної гідродинаміки отримано нелінійне дисперсійне рівняння, що описує як розпад верхньогібридної хвилі на ІАХ та звичайну електромагнітну хвилю, так і розпад верхньогібридної хвилі на ІАХ та на лівополяризовану електромагнітну хвилю. Знайдено інкремент розвитку нестійкості, який залежить від параметрів пилової плазми. Показано, що лівополяризована електромагнітна хвиля переважно збуджується верхньогібридною хвилею накачки для параметрів F-кільця Сатурна. Рассмотрено параметрическое возбуждение электромагнитных волн инерциальными альфвеновскими волнами (ИАВ) в пылевой космической плазме. На основе уравнений трехжидкостной магнитной гидродинамики получено нелинейное дисперсионное уравнение, описывающее как распад верхнегибридной волны на ИАВ и обыкновенную электромагнитную волну, так и распад верхнегибридной волны на ИАВ и левополяризованную электромагнитную волну. Найден инкремент развития неустойчивости, зависящий от параметров пылевой плазмы. Показано, что левополяризованная электромагнитная волна преимущественно возбуждается верхнегибридной волной накачки для параметров F-кольца Сатурна. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Space plasma Nonliner mechanism of electromagnetic waves generations in space dust plasma Нелінійний механізм генерації електромагнітних хвиль в пиловій космічній плазмі Нелинейный механизм генерации электромагнитных волн в пылевой космической плазме Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Nonliner mechanism of electromagnetic waves generations in space dust plasma |
| spellingShingle |
Nonliner mechanism of electromagnetic waves generations in space dust plasma Voitsekhovskа, A.D. Yukhimuk, A.K. Sirenko, O.K. Space plasma |
| title_short |
Nonliner mechanism of electromagnetic waves generations in space dust plasma |
| title_full |
Nonliner mechanism of electromagnetic waves generations in space dust plasma |
| title_fullStr |
Nonliner mechanism of electromagnetic waves generations in space dust plasma |
| title_full_unstemmed |
Nonliner mechanism of electromagnetic waves generations in space dust plasma |
| title_sort |
nonliner mechanism of electromagnetic waves generations in space dust plasma |
| author |
Voitsekhovskа, A.D. Yukhimuk, A.K. Sirenko, O.K. |
| author_facet |
Voitsekhovskа, A.D. Yukhimuk, A.K. Sirenko, O.K. |
| topic |
Space plasma |
| topic_facet |
Space plasma |
| publishDate |
2007 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Нелінійний механізм генерації електромагнітних хвиль в пиловій космічній плазмі Нелинейный механизм генерации электромагнитных волн в пылевой космической плазме |
| description |
We consider a parametric excitation of electromagnetic waves induced by inertial Alfvén wave (IAW) in space dust plasma. The nonlinear dispersion equations describing decay of upper-hybrid wave (UHW) into the IAW and the ordinary electromagnetic wave as well as decay of UNW into the IAW and the left-hand circularly polarized (LHCP) wave are obtained using the three-fluid magnetohydrodynamics. The instability growth rates which depend on dust plasma parameters are found. It is shown that the LPCH wave is preferably excited by the UH pump wave for the parameters of the Saturn's F-ring.
Розглянуто параметричне збудження електромагнітних хвиль інерційними альфвенівськими хвилями (ІАХ) в пиловій космічній плазмі. На основі рівнянь трирідинної магнітної гідродинаміки отримано нелінійне дисперсійне рівняння, що описує як розпад верхньогібридної хвилі на ІАХ та звичайну електромагнітну хвилю, так і розпад верхньогібридної хвилі на ІАХ та на лівополяризовану електромагнітну хвилю. Знайдено інкремент розвитку нестійкості, який залежить від параметрів пилової плазми. Показано, що лівополяризована електромагнітна хвиля переважно збуджується верхньогібридною хвилею накачки для параметрів F-кільця Сатурна.
Рассмотрено параметрическое возбуждение электромагнитных волн инерциальными альфвеновскими волнами (ИАВ) в пылевой космической плазме. На основе уравнений трехжидкостной магнитной гидродинамики получено нелинейное дисперсионное уравнение, описывающее как распад верхнегибридной волны на ИАВ и обыкновенную электромагнитную волну, так и распад верхнегибридной волны на ИАВ и левополяризованную электромагнитную волну. Найден инкремент развития неустойчивости, зависящий от параметров пылевой плазмы. Показано, что левополяризованная электромагнитная волна преимущественно возбуждается верхнегибридной волной накачки для параметров F-кольца Сатурна.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110407 |
| citation_txt |
Nonliner mechanism of electromagnetic waves generations in space dust plasma / A.D. Voitsekhovskа, A.K. Yukhimuk, O.K. Sirenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 87-89. — Бібліогр.: 7 назв. — англ. |
| work_keys_str_mv |
AT voitsekhovskaad nonlinermechanismofelectromagneticwavesgenerationsinspacedustplasma AT yukhimukak nonlinermechanismofelectromagneticwavesgenerationsinspacedustplasma AT sirenkook nonlinermechanismofelectromagneticwavesgenerationsinspacedustplasma AT voitsekhovskaad nelíníiniimehanízmgeneracííelektromagnítnihhvilʹvpilovíikosmíčníiplazmí AT yukhimukak nelíníiniimehanízmgeneracííelektromagnítnihhvilʹvpilovíikosmíčníiplazmí AT sirenkook nelíníiniimehanízmgeneracííelektromagnítnihhvilʹvpilovíikosmíčníiplazmí AT voitsekhovskaad nelineinyimehanizmgeneraciiélektromagnitnyhvolnvpylevoikosmičeskoiplazme AT yukhimukak nelineinyimehanizmgeneraciiélektromagnitnyhvolnvpylevoikosmičeskoiplazme AT sirenkook nelineinyimehanizmgeneraciiélektromagnitnyhvolnvpylevoikosmičeskoiplazme |
| first_indexed |
2025-11-26T00:08:21Z |
| last_indexed |
2025-11-26T00:08:21Z |
| _version_ |
1850592056391499776 |
| fulltext |
Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 87-89 87
NONLINEAR MECHANISM OF ELECTROMAGNETIC WAVES
GENERATION IN SPACE DUST PLASMA
A.D. Voitsekhovsk , A.K. Yukhimuk, O.K. Sirenko
Main astronomical Observatory, National Academy of Sciences of Ukraine, Kyiv, Ukraine
We consider a parametric excitation of electromagnetic waves induced by inertial Alfvén wave (IAW) in space dust
plasma. The nonlinear dispersion equations describing decay of upper-hybrid wave (UHW) into the IAW and the
ordinary electromagnetic wave as well as decay of UNW into the IAW and the left-hand circularly polarized (LHCP)
wave are obtained using the three-fluid magnetohydrodynamics. The instability growth rates which depend on dust
plasma parameters are found. It is shown that the LPCH wave is preferably excited by the UH pump wave for the
parameters of the Saturn's F-ring.
PACS: 52.35.-g
1. INTRODUCTION
The physical processes in dust plasmas have been
studied intensively because of their importance for a
number of application in space and laboratory plasmas.
Generally, dust particles in plasma are charged by plasma
current, photoemission, secondary emission, etc. The
interplanetary space, the rings of the giant planets, comet
tails, Earth's magnetosphere and ionosphere are Solar
system objects with significant amount of dust particles.
In recent years there has been much interest in new wave
mode that results from the presence of micron-sized
charged dust particles in plasma. About a decade ago it
was recognized that the dust component may not only
modify the usual plasma waves, such as ion acoustic
waves and Alfvén waves, but leads to the appearance of
new wave type [1,2], e.g., a low frequency mode, in
which the inertia is provided by the massive dust
component. Most of the studies on waves in a magnetized
plasma have dealt with linear theories [3]. However in
dust plasma the set of processes take place, for which
there are important nonlinear effects, in particular
nonlinear wave-wave interaction [4,5].
In the present paper we consider decay of the upper-
hybrid pump wave into the IAW and the o-mode and into
the IAW and the LHCP wave in dust plasma, which
consist from electrons, protons and negatively charged
dust particles.
2. BASIC EQUATIONS
We consider the upper-hybrid pump wave with:
( ) ( )[ ] ..exp 000000 ckzkxktieEeEE zxzzxx +++−+= ω
rrr
,
xz kk 00 << ,
propagating in an homogeneously magnetized
plasma ( )zeBB
rr
00 = . The pump wave decay into IAW with
wave vector k
r
and frequency ω and electromagnetic
waves with wave vectors jk
r
and frequencies jω . It is
assumed that the following wave resonance conditions are
satisfied:
jj kkk
rrr
+=+= 00 ,ωωω ,
where j=1, 2 corresponds of o-mode and left-hand
circularly polarized wave, respectively. Also we assume
that all wave vectors are situated in the xz plane.
For studying parametric interaction, we use the three-
fluid magnetohydrodynamics:
( ) ( ) ,V1
t α
αα
α
ααααα
α
α ω n
nm
TFEeZ
m
V
B ∇−×++=
∂
∂ vvvrr
r
( )αα
α Vn
n rv
∇−=
∂
∂
t
,
t
E
c
j
c
B
∂
∂
+=×∇
r
rrr 14π ,
t
B
c
E
∂
∂
−=×∇
r
rr 1 , (1)
πρ4=⋅∇ E
rr
,
where
( )dddeeii VnZVnVnej
rvvr
−−= , ( )ddei nZnne −−=ρ ,
( ) αααα
αα
α VVmBV
c
eZ
F
rrrrr
∇−
×=
~ . The index =i, e, d
corresponds to the protons, electrons and dust particles,
respectively.
The particles density, velocity, electric and magnetic
fields are written in the forms:
Annnn ~~
00 ++=α , jA VVVV
rrrr
++= 0 ,
jA EEEE
rrrr
++= 0 , jA bbBB
rrrr
++= 0 ,
where 0n and 0B
r
are the average values of the plasma
number density and magnetic field. The subscript A in
these expressions corresponds to the IAW.
3. O-MODE GENERATION
3.1. NONLINEAR DISPERSION RELATION
FOR DUST IAW
Nonlinear dispersion relation for the IAW is (see [6]
for the details):
NLA P=ϕε , (2)
88
where ,
1
22
2
e
Adz
A
Vk
κ
ωε
+
−= 22
exe k δκ = ,
pe
e
c
ωδ = ,
∂
∂
+
∂
∂
+
=
z
F
ez
j
en
mViP ez
NL
ez
e
e
e
Ad
NL
1
1 2
0
2 ω
κ
,
dod
Ad
mn
B
V
π4
0= ,
( )*
100
*
1
~~
zz
NL
ez VnVnej +−= .
Using linear expressions for the electron velocity
components, electron density perturbations and magnetic
field perturbations for the pump wave and o-mode:
( ) ( ) 022
0
0
0022
0
00
0 , ϕ
ωω
ω
ϕ
ωω
ω
Be
xBe
e
y
Be
x
e
x
k
m
eiV
k
m
eV
−
−=
−
−= ,
02
0
2
0
22
0
2
0
000
0
0
0
~, ϕ
ωωω
ϕ
ω
+
−
−=−= z
Be
x
e
e
z
e
z
kkn
m
enk
m
eV ,
z
x
y
z
e
z E
ck
bE
m
eiV 1
1
1
1
1
1
1 ,
ωω
−=−= ,
we get following expression for the nonlinear dispersion
relation for the IAW:
*
10 zAA Eϕµϕε = , (3)
where nonlinear term is
2
0
2
0
1
2
1 ωω
ω
κ
µ x
z
e
Ad
e
A
kkV
m
ei
+
−= .
3.2. NONLINEAR DISPERSION RELATION
FOR O-MODE
The o-mode propagates along the x axis and has an
electric field parallel to the ambient magnetic field.
Excluding the magnetic field from Maxwell’s Eq. (1), we
obtained an equation for the electric field of the ordinary
electromagnetic wave:
( )NLzz
pe
z nVeiF
e
E 11
2
11 4 ωπ
ω
ε +−= ,
where 222
1
2
11 peck ωωε −−= , ( ) zeAzNL VnVnn 0
**
0z
~~V += .
Using linear expressions for the electron velocity
components, electron density perturbations and magnetic
field perturbations for the pump wave and IAW:
ϕ
ω
ϕ
ω
ω
Be
x
e
y
Be
x
e
x
k
m
eiV
k
m
eV == ,2 ,
ϕκϕ
ω
κ
2
2
0
~,
f
Te
e
eeeA
ez
e
z V
V
T
enn
k
m
eV −=−= ,
ϕ
ω
2
Adz
x
y V
c
k
k
ib −=
we find the dispersion relation for the o-mode:
*
0111 ϕϕµε =zE , (4)
where nonlinear term is
22
0
00
2
2
1
Be
x
Adz
x
pe
e
k
Vk
k
m
ei
ωω
ωω
ωµ
−
−= .
3.3. NONLINEAR GROWTH RATE
From Eqs. (3) and (4), we obtained the nonlinear
dispersion relation for the parametric instability:
2
0
*
1
*
1 ϕµµεε AA = . (5)
When we allow for a dissipative part in the wave
frequencies, 1γωω ir += and 111 γωω ir += in Eq.(5),
we can obtaine the expression for the instability growth
rate:
2
1
0
0
01
2
1 2
=
ω
ω
ωω
ω
γ xxTepe kkVW ,
where
ee
x
Tn
E
W
0
2
0
4π
= .
4. LHCP WAVE GENERATION
4.1. NONLINEAR DISPERSION RELATION
FOR LHCP WAVE
Excluding the magnetic field from Maxwell’s Eq. (1),
we obtained an equation for the electric field of the LHCP
wave:
t
j
t
VenE
z
c
t
NL
L
∂
∂
−=
∂
∂
−
∂
∂
−
∂
∂ 22
022
2
2
2
2
44
rr
r
ππ , (6)
where the nonlinear current density is determined by the
beating of the pump wave and the IAW
( )NL
eeeANL VnVnVnej 20
*
00
*
2
~~ rrrr
++−= .
If we use the linear expressions for the electron velocity
components, electron density perturbations and magnetic
field perturbations for the pump wave and IAW in Eq. (6)
we obtained the nonlinear dispersion relation:
*
0222 ϕϕµε =xE , (7)
where
Be
peck
ωω
ω
ωωε
+
−−=
2
2222
2
2
22 ,
nonlinear term is
22
0
0
2
2
02
2
2
Be
xz
epe
e
kk
m
ei
ωωω
ωωκωµ
−
−= .
4.2. NONLINEAR DISPERSION RELATION FOR
DUST IAW
The dispersion relation for the IAW is given by
Eq. (2) in Sec. 3.1, where components of ponderomotive
force Fez and nonlinear current NL
ezj are determined by the
interaction of UHW and LHCP wave. Using linear
expressions for the electron velocity components, electron
density perturbations and magnetic field perturbations for
the pump wave and LHCP wave, we get the following
89
expression for the nonlinear dispersion relation for the
IAW:
*
203 xA Eϕµϕε = , (8)
where nonlinear term is
2
2
0
0
2
3 1 ωωκ
µ zx
ee
Ad kk
m
eV
i
+
−= .
4.3 NONLINEAR GROWTH RATE
From Eqs. (7) and (8), we obtained the nonlinear
dispersion relation for the parametric instability:
2
0
*
32
*
2 ϕµµεε =A . (9)
When we allow for a dissipative part in the wave
frequencies, 2γωω ir += and 222 γωω ir += in (9), we
obtained the following expression for the instability
growth rate:
2
1
22
02
2
2
1
2
−
=
Be
e
Ad
Tepe
V
VW
ωωω
ω
κ
ω
γ .
CONCLUSIONS
We have investigated the nonlinear mechanisms for
the generation of electromagnetic waves in β-low space
dust plasma. We have studied the nonlinear decay process
of the upper-hybrid pump wave into the IAW and the o-
mode as well as decay of pump wave into the IAW and
the LHCP wave. The source of radiation of the left-hand
polarized and ordinary electromagnetic waves is the
nonlinear current produced by the resonant interaction of
the pump wave with the low-frequency inertial Alfvén
wave.
We find the magnitudes of the growth rate of
instabilities, for typical wave and plasma parameters
relevant to the Saturn’s F-ring [4,7]: 410≈dZ ,
3
0 1 −≈ cmn d , 34
0 10 −≈ cmn i , eVTT ie 10≈≈ , GB 02.00 ≈ ,
gmd
1210−≅ , 3
0 10 −≈ cmn e . For decay process
UHWàIAW+O-mode the instability growth rate is
110
1 109.5 −−⋅= sγ . For decay process
UHWàIAW+LHCP the instability growth rate is
17
2 10 −−= sγ . Our calculations show that the generation of
the left-hand polarized electromagnetic wave is faster
than that of the o-mode.
REFERENCES
1. M.P. Hertzberg, N.F. Cramer, S.V. Vladimirov.
Parametric instabilities of Alfven waves in dusty plasma//
Physics of Plasmas. 2003, v.10, N8, p. 3160-3167.
2. A.A. Mamun, P.K.Shukla. Linear and nonlinear dust-
hydromagnetic waves// Physics of Plasmas. 2003, v.10,
N11, p. 4341-4349.
3. P.K. Shukla, I. Kourakis. Low-frequency
electromagnetic waves in a Hall-magnetohydrodynamics
plasma with charged dust macroparticles// Physics of
Plasmas. 2005, v.12, N1, p. 024501-1-014501-4.
4. P.K. Shukla, L. Stenflo. Nonlinearly coupled inertial
Alfven and dust acoustic waves in complex plasmas//
Physics of Plasmas. 2001, v.8, N8, p. 3838-3841.
5. P.K. Shukla, L. Stenflo. Dynamics of nonlinearly
coupled upper-hybrid waves and modified Alfven modes
in a magnetized dusty plasma// Physics of Plasmas. 2003,
v.10, N11, p. 4572-4574.
6. A.D. Voitsekhovska, A.K. Yukhimuk, E.K. Sirenko.
Nonlinear mechanism of inertial Alfvén and
electromagnetic waves generation in space dust plasma//
Kinem. ta Phys. Selec. Bodies. 2005, v.21, N4, p. 278-287
(in Russian).
7. D.A. Mendis, M. Rosenberg. Cosmic dusty plasma//
Annu. Rev. Astron. Astrophys. 1994, v.32, p. 419-463.
. , . , .
( ) .
,
,
. ,
. ,
F- .
. , . , .
( )
.
, ,
.
, . ,
F-
.
|