Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma
In this paper the chain of correlated solitary perturbations of finite amplitude, accelerating ions in the magnetosphere, is investigated. Досліджено ланцюжок корельованих солітонних збурювань скінченої амплітуди, що прискорюють іони в магнітосфері. Исследована цепочка коррелированных солитонных во...
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| Cite this: | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma / N.A. Azarenkov, A.M. Yegorov, D.Yu. Frolova, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2004. — № 1. — С. 51-53. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859648672117030912 |
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| author | Azarenkov, N.A. Yegorov, A.M. Frolova, D.Yu. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. |
| author_facet | Azarenkov, N.A. Yegorov, A.M. Frolova, D.Yu. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. |
| citation_txt | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma / N.A. Azarenkov, A.M. Yegorov, D.Yu. Frolova, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2004. — № 1. — С. 51-53. — Бібліогр.: 6 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | In this paper the chain of correlated solitary perturbations of finite amplitude, accelerating ions in the magnetosphere, is investigated.
Досліджено ланцюжок корельованих солітонних збурювань скінченої амплітуди, що прискорюють іони в
магнітосфері.
Исследована цепочка коррелированных солитонных возмущений конечной амплитуды, ускоряющих
ионы в магнитосфере.
|
| first_indexed | 2025-12-07T13:31:11Z |
| format | Article |
| fulltext |
EXCITATION OF CORRELATED CHAIN OF NONLINEAR ION-ACOUS-
TIC SOLITARY PERTURBATIONS OF FINITE AMPLITUDE, ACCEL-
ERATING IONS IN CURRENT-CARRYING
MAGNETOSPHERE PLASMA
N.A. Azarenkov*, A.M. Yegorov, D.Yu. Frolova*, V.I. Lapshin, V.I. Maslov, I.N. On-
ishchenko
NSC “Kharkov Institute of Physics & Technology”, 61108, Kharkov, Ukraine;
E-mail: vmaslov@kipt.kharkov.ua
*Karazin Kharkov National University, Kharkov, 61108, Ukraine;
In this paper the chain of correlated solitary perturbations of finite amplitude, accelerating ions in the magneto-
sphere, is investigated.
PACS: 29.27.Bd
1. INTRODUCTION
Plasma with the electron current velocity lower than
the electron thermal velocity is considered. Ion-acoustic
perturbations are excited. The homogeneous ion-acous-
tic turbulence in one-dimensional current-carrying plas-
ma is saturated on the low level. Further this ion-acous-
tic turbulence is modulated into widely spaced short
solitary-type perturbations. The properties of single soli-
tary perturbation have been investigated earlier by the
author. In this paper the chain of correlated solitary per-
turbations of finite amplitude (see Fig.1), accelerating
ions in magnetosphere, are investigated. This perturba-
tion is the nonmonotonous double layer, which is repre-
sented by the electric potential dip with a shock in its
vicinity. The dip reflects electrons with the energy lower
than the dip depth. This leads to the dip depth (ampli-
tude) growth.
The equation describing the shape and evolution of
the chain of correlated nonmonotonous double layers is
derived in this paper. It is obtained that the dip of the
electrostatic potential is excited due to current-carrying
instability. The case of the large amplitude of excited
perturbation is considered. The growth rate of the non-
linear instability development and potential shock in
vicinity of the dip are proportional to the distance be-
tween solitary perturbations.
A growing interest has been given to plasmas with
negative ions (see, for example, [1,2]) due to that nega-
tively charged particles exist frequently in the space
plasmas. It is important to investigate effects of these
negative ions on formation and properties of chain of the
nonmonotonous electric double layers, observed in mag-
netosphere and accelerating ions. This nonmonotonous
electric double layer is the dip of the electric potential
with the potential jump near it. There are many papers
on stationary solitary perturbations of small amplitudes
or nonstationary solitary perturbations in current-carry-
ing plasma or plasma with a hot electron beam (see, for
example, [3−6]). In the present paper the formation and
properties of this chain of monotonous electrical double
layers (electrical potential dip ϕ with a potential shock
in its vicinity) are investigated theoretically. The plasma
consists of electrons, positive and negative ions. The
electrons propagate relative to negative and positive
ions with some velocity. This flow (current) excites non-
monotonous electrical double layer (see Fig.2). The ef-
fect of the electron current on excitation and properties
of this monotonous electrical double layer is investigat-
ed.
Fig.1. The chain of solitary dips in the electrical poten-
tial with potential shocks in their vicinity
The evolution equations describing the shape and
time evolution of the electrical field structure, for the
case of any amplitude, are derived, when there are not
traditional small parameters, permitting to describe
properties and excitation of perturbation. It has been
shown that the nonmonotonous electrical double layer
can be formed on ion-acoustic, on slow ion mode and on
ultra-slow dusty ion mode. The conditions have been
obtained when the double layer is approximately station-
ary and fixed in space.
2. EXCITATION OF THE SOLITARY ELEC-
TRICAL FIELD BY THE ELECTRON CUR-
RENT
We use hydrodynamic equations for negative and
positive ions
∂n±/∂t+∂(n±V±)/∂z=0 ,
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 1.
Series: Nuclear Physics Investigations (42), p.51-53. 51
z
φ
∂V±/∂t+V±∂V±/∂z±(q±/M±)∂ϕ/∂z=0 . (1)
Here q± , n± , V± , M± are charges, densities, velocities
and masses of positive and negative ions.
We use the Vlasov equation. for the electron
distribution function fe
∂fe/∂t+V∂fe/∂z+(e/me)(∂ϕ/∂z)∂fe/∂V=0 (2)
and the Poisson equation.
∂2ϕ/∂z2=4π(ene+q-n --q+n+) . (3)
Fig.2. The solitary dip of the electrical potential with a
potential shock in its vicinity
Electrons propagate relative to negative and positive
ions with some current velocity Vо. The initial electrical
potential perturbation is a dip with the width δz. The dip
reflects the resonant electrons and obtains the energy
from them. The amplitude (depth) -ϕo of the dip grows.
Due to reflection of resonant electrons, with
nonsymmetrical - relative to the dip velocity Vс
-distribution function, the potential jump ∆ϕ is formed
near the dip.
When the dip amplitude increases up to some value
the slowdown of its evolution starts. We use slow
evolution of the dip for its description using a small
parameter α=γδz/Vtr. In zero approximation on α the
electron distribution function depends only on the
energy ε. Taking into account that the resonant electrons
are reflected from the dip one can derive from (2) the
expression for the electron distribution function
fe=foe[-(V2-2e(ϕ±∆ϕ)/me)1/2±Vo] ,
V>
<C(ϕ)sign(z) , C(ϕ)=[2e(ϕo+ϕ)/me]1/2. (4)
We use the normalized values: φ≡eϕ/Te , N-≡no-/no+,
Ne≡noe/no+, Q±=q±/e, Vs±=(Te/M±)1/2. We normalize z on
the Debye radius of electrons rde , Vo on the electron
thermal velocity Vth , time t on the plasma frequency of
positive ions ωp+
-1, ion velocities and Vс on the ion-
acoustic velocity of positive ions (Te/M+)1/2.
Integrating (4) over the velocity, one can derive the
expression for the electron density
ne≈noeexp(φ)[1-(2∆φ/√π)∫o
βdx exp(-x2)-
-2Vo(2/π)1/2∫o
βdx (x2-φ)1/2exp(-x2)] . (5)
Far from the dip the plasma is quasineutral ne(z)z→∞
=ne(z)z→-∞=1. From here one can derive, using (5), the
expression for the potential jump near the dip
∆φ=Vo(2/π)1/2(1-exp(-φo))/[1-(2/√π)∫o
√φo dxexp(-x2)] . (6)
From (1) one can obtain for density perturbations
ni±=n±NL+n±τ , n±NL=no±/[1-(±q±)2ϕ/M±Vc
2]1/2 , (7)
∂n±τ/∂z=±2(∂ϕ/∂t)(no±q±/M±Vc
3)[1-
-(±q±)ϕ/M±Vc
2]/[1-(±q±)2ϕ/M±Vc
2]3/2 .
Substituting (5), (7) in the Poisson equation, one can
derive the nonlinear evolution equation
∂3
zφ+{Q+
2V2
s+(1-2(φ-∆φ)Q+V2
s+/Vc
2)-3/2(1-(φ-∆φ)
Q+V2
s+/Vc
2)+
+Q-
2N-V2
s-(1+2(φ-∆φ)Q-V2
s-/Vc
2)-3/2 (1+(φ-∆φ)Q-V2
s-
/Vc
2)}2∂tφ/Vc
3+
+(∂zφ/Vc
2){Q+
2V2
s+(1-2(φ-∆φ)Q+V2
s+/Vc
2)-3/2+
+Q-
2N-V2
s-(1+2(φ-∆φ)Q-V2
s-/Vc
2)-3/2}-Ne∂zφ{exp(φ)-
sign(z)2Vo(2/π)1/2×
×[(√φo+A)/2(φo+φ)1/2exp(-φo)+exp(φ)∫o
√φo+φ dxexp(-x2)
(( x2-φ)1/2+A)]}=0, (8)
describing the excitation, evolution and properties of the
dip. Here A≡(1-exp(-φo))/(√π-2∫o
√φodxexp(-x2)).
Integrating (8) in quasi-stationary approximation,
one can get
(∂zφ)2/2=(Vc/Vs-)2N-((1+Q-2(φ-∆φ)V2
s-/Vc
2)1/2-1)+
+(Vc/Vs+)2((1-Q+2(φ-∆φ)V2
s+/Vc
2)1/2-1)+Ne{exp(φ)-
-exp(∆φ)+sign(z)2Vo(2/π)1/2×
×{A[exp(φ)∫o
√φo+φ dxexp(-x2)- ∫o
√φo dxexp(-x2)-
-exp(-φo)((φo+φ)1/2-φo
1/2)]+
+exp(-φo)(φo+1)-1+2∫o
√φo+φ dzexp(-z2+φ)z2( z2-φ)1/2}}(9)
From (9) and ∂zφ|φ=-φo=0 one can show that the dip
velocity, Vc, is close to the ion-acoustic velocity of the
positive ions, Vs+, and essentially depends on φo. In the
limiting case N-=0 one can derive
V2
c=V2
s+N2
eB2/2(Q+(φo+∆φ)+NeB), (10)
where B≡exp(φo)-exp(∆φ)+
+sign(z)2Vo(2/π)1/2{A[-∫o
√φodxexp(-x2)+exp(-φo)√φo)]+
+exp(-φo)(φo+1)-1}.
From (8) at φ→-φo one can get the growth rate of the
dip amplitude
γ=Vc
3Neexp(-φo)2Vo(2/π)1/2(√φo+A)(Neexp(-φo)- (11)
Q+(1+2β(φo+∆φ))1/2/2φoQ+
2Vs+
2(1+2β(φo+∆φ))3/2×
×(1+β(φo+∆φ)),
β≡Q+Vs+
2/Vc
2 .
3. EXCITATION OF THE SOLITARY ELEC-
TRICAL FIELD ON THE SLOW ION MODE
Let us consider nonmonotonous double layer, propa-
gating with velocity Vi , approximately equal to thermal
velocity of positive ions, Vthi=(Ti/mi)1/2. The electron
density approximately equals to (5). The expression for
the perturbation of the positive ion density can be ob-
tained from the Vlasov equation
δni≈−θφR(g)+θ2(φ/2)2[R(g)(3−2g2)−1] ,
g≡Vi/Vthi√2 , θ≡Te/Ti , (12)
R(g)=1+(g/√π)∫-∞
∞du exp(-u2)/(u-g).
Substituting (5), (12) into (3), one can derive the
nonlinear equation, describing the potential distribution
of a nonmonotonous double layer in space:
(φ')2=φ2(1+θR(g))+(φ3/6){2+θ2[1+(2g2−3)R(g)]},
52
z
∆φ
-φ
o
φ
∂/∂(z/rd)≡" ' ". (13)
From (13) and φ'|φ=-φo=0 one can derive the expres-
sion for Vi
g=go{1+1/θ−(φo/6)[θ+3−2g2+2/θ]} , go=0.924. (14)
Vi is close to Vthi and decreases with the amplitude
growth.
The width of the nonmonotonous double layer is ap-
proximately determined from (13):
(∆z)−2=(φo/48){2+θ2[1+(2g2−3)R(g)]}. (15)
∆z decreases with the amplitude growth.
In case of large amplitudes, φo>1, we have
ne=noexp(-φo) ,
ni=(no/√π)∫-∞
∞du exp(-u2)/(1-θφ/(g-u)2)1/2 . (16)
From (3) and (16) we obtain
[Φ’(Φ=Φ
o
/2)]
2
=√2-2+2exp(-Φ
o
/2)-√2exp(-Φ
o
), (17)
φo cannot be more than critical one, φa , determined by
the equation:
1-√2+√2exp(-Φ
a
/2)-exp(-Φ
a
)=0, (18)
∆z increases with φo growth. Therefore one needs take
into account trapped ions. We assume their distribution
function ftri=const=foi(Vo). Then their density equals
n
tri
=2(-θΦ)
1/2
(n
o
/√π)exp(-g
o
2
). (19)
From (3), (16), (19) we obtain, that Vi increases with
φo growth.
One can see that for a large φo the dependencies of Vi
and ∆z on φo are inverse in comparison with the case of
a small φo.
4. EXCITATION OF THE SOLITARY ELEC-
TRICAL FIELD ON THE ULTRA-SLOW
DUSTY ION MODE
Let us consider possibility of nonmonotonous double
layer formation on the ultra-slow dusty ion mode, the
velocity Vu of which is low in comparison with Vthi. The
electron density approximately equals to (5). The
potential jump near the dip is formed similar to (6).
We determine the density perturbations of negative
ions δn- from (1) and positive ions δn+ from the Vlasov
equation
3
u
4
c
2
u
o
'22
o
V/NV/3V/
n/n,2//n/n
φ−φ ′φ+φ ′−
≈δθφ+θφ−≈δ
−
−−++
(20)
Here «’»≡∂/∂z, «.»≡∂/∂t.
Substituting (5), (20) in (3) one can derive the non-
linear equation. in partial derivatives for the nonhomo-
geneous and nonstationary potential
0)]})(/()ln[(
)/(]/))/(21(
{[)/2(V
)V/N3/N1(
)V/N/N1(V/N
2/1
o
2/1
o
2/1
2/1
o
2/1
o
2/1
o
2/1
o
2/1
o
4
u
2
2
u
3
u
2
=φ+φ+φφ−+
+φ+φπφπφ++
+φφ ′π+
+φ ′′′++θ−φ ′φ−
−−θ+φ ′−φ
−+
−+−
(21)
From (21) and the condition 0
o
=φ ′ φ−=φ one can
find Vu
( ) ( ) ( ) 2/1
eiioe
2/1
ii
2/1
iiu TnTn1nnMTV +++−−+ +≈
(22)
So, it has been shown that the dip propagates with
very low velocity.
REFERENCES
1. H.M.Thomas, G.E.Morfill// Nature. 1996, v. 379,
p. 806.
2. R.K.Varma, P.K.Shukla//Physica Scripta. 1995,
v. 51, p. 522.
3. C.Chan, M.H.Cho, N.Hershkowitz, T.Intrator//
Phys. Rev. Lett. 1984, v.52, p.1782.
4. A.N.Sekar, Y.C. Saxena // Plasma Phys. and Contr.
Fus. 1985, v. 27, p. 181.
5. T.Sato, H.Okuda // Phys. Rev. Lett. 1980, v. 44,
p. 740.
6. V.I.Maslov // Phys. Lett. A. 1992, v. 165, p. 63.
ВОЗБУЖДЕНИЕ КОРРЕЛИРОВАНОЙ ЦЕПОЧКИ НЕЛИНЕЙНЫХ ИОННО-ЗВУКОВЫХ СО-
ЛИТОННЫХ ВОЗМУЩЕНИЙ КОНЕЧНОЙ АМПЛИТУДЫ, УСКОРЯЮЩИХ ИОНЫ
В ТОКОВОЙ ПЛАЗМЕ МАГНИТОСФЕРЫ
Н.А. Азаренков, А.М. Егоров, Д.Ю. Фролова, В.И. Лапшин, В.И. Маслов, И.Н. Онищенко
Исследована цепочка коррелированных солитонных возмущений конечной амплитуды, ускоряющих
ионы в магнитосфере.
ЗБУДЖЕННЯ КОРЕЛЬОВАНОГО ЛАНЦЮЖКА НЕЛІНІЙНИХ ІОННО-ЗВУКОВИХ
СОЛІТОННИХ ЗБУРЮВАНЬ СКІНЧЕНОЇ АМПЛІТУДИ, ЩО ПРИСКОРЮЮТЬ ІОНИ В
ТОКОВІЙ ПЛАЗМІ МАГНІТОСФЕРИ
Н.А. Азаренков, О.М. Єгоров, Д.Ю. Фролова, В.І. Лапшин, В.І. Маслов, І.Н. Онищенко
Досліджено ланцюжок корельованих солітонних збурювань скінченої амплітуди, що прискорюють іони в
магнітосфері.
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 1.
Series: Nuclear Physics Investigations (42), p.51-53. 53
E-mail: vmaslov@kipt.kharkov.ua
1. INTRODUCTION
REFERENCES
В ТОКОВОЙ ПЛАЗМЕ МАГНИТОСФЕРЫ
|
| id | nasplib_isofts_kiev_ua-123456789-78567 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:31:11Z |
| publishDate | 2004 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Azarenkov, N.A. Yegorov, A.M. Frolova, D.Yu. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. 2015-03-18T19:30:08Z 2015-03-18T19:30:08Z 2004 Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma / N.A. Azarenkov, A.M. Yegorov, D.Yu. Frolova, V.I. Lapshin, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2004. — № 1. — С. 51-53. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 29.27.Bd https://nasplib.isofts.kiev.ua/handle/123456789/78567 In this paper the chain of correlated solitary perturbations of finite amplitude, accelerating ions in the magnetosphere, is investigated. Досліджено ланцюжок корельованих солітонних збурювань скінченої амплітуди, що прискорюють іони в магнітосфері. Исследована цепочка коррелированных солитонных возмущений конечной амплитуды, ускоряющих ионы в магнитосфере. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые и нестандартные ускорительные технологии Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma Збудження корельованого ланцюжка нелінійних іонно-звукових солітонних збурювань скінченої амплітуди, що прискорюють іони в токовій плазмі магнітосфери Возбуждение коррелированой цепочки нелинейных ионно-звуковых со- литонных возмущений конечной амплитуды, ускоряющих ионы в токовой плазме магнитосферы Article published earlier |
| spellingShingle | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma Azarenkov, N.A. Yegorov, A.M. Frolova, D.Yu. Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Новые и нестандартные ускорительные технологии |
| title | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma |
| title_alt | Збудження корельованого ланцюжка нелінійних іонно-звукових солітонних збурювань скінченої амплітуди, що прискорюють іони в токовій плазмі магнітосфери Возбуждение коррелированой цепочки нелинейных ионно-звуковых со- литонных возмущений конечной амплитуды, ускоряющих ионы в токовой плазме магнитосферы |
| title_full | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma |
| title_fullStr | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma |
| title_full_unstemmed | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma |
| title_short | Excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma |
| title_sort | excitation of correlated chain of nonlinear ion-acoustic solitary perturbations of finite amplitude, accelerating ions in current-carrying magnetosphere plasma |
| topic | Новые и нестандартные ускорительные технологии |
| topic_facet | Новые и нестандартные ускорительные технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78567 |
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