Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions
The properties of electrostatic potential hollow of solitary kind are investigated theoretically. The potential hollow is excited in current-carrying plasma. The equation, describing the hollow of any amplitude, is derived.
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2000 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/78552 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions / V.I. Maslov, V.L. Stomin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 137-138. — Бібліогр.: 1 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859614401346142208 |
|---|---|
| author | Maslov, V.I. Stomin, V.L. |
| author_facet | Maslov, V.I. Stomin, V.L. |
| citation_txt | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions / V.I. Maslov, V.L. Stomin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 137-138. — Бібліогр.: 1 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The properties of electrostatic potential hollow of solitary kind are investigated theoretically. The potential hollow is excited in current-carrying plasma. The equation, describing the hollow of any amplitude, is derived.
|
| first_indexed | 2025-11-28T17:04:58Z |
| format | Article |
| fulltext |
Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p.137-138 137
UDC 533.9.01
EXCITATION AND PROPERTIES OF SOLITARY PERTURBATION OF
LARGE AMPLITUDES IN NONEQUILIBRIUM PLASMAS WITH
NEGATIVE IONS
V.I.Maslov, V.L.Stomin
NSC Kharkov Institute of Physics & Technology, Kharkov, Ukraine
e-mail: vmaslov@kipt.kharkov.ua, fax: 38 0572 351688, tel: 38 0572
The properties of electrostatic potential hollow of solitary kind are investigated theoretically. The potential hol-
low is excited in current-carrying plasma. The equation, describing the hollow of any amplitude, is derived.
A growing interest has been given to plasmas with
negative ions due to various their applications in tech-
nology and due to that negatively charged particles exist
frequently in laboratory and space plasmas. In experi-
ment [1] the solitary perturbation of large amplitude has
been formed in nonequilibrium plasma with negative
ions. In present paper the plasma with electron current
relative to nonpropagating positive and negative ions is
considered. The case of any densities of negative ions
noi- is considered. This plasma is nonequilibrium. Per-
turbations are excited. At certain conditions the excited
perturbations could be solitary types. Therefore proper-
ties of electrostatic potential hollow of solitary kind are
investigated. Plasma, containing electrons, positive ions,
and also heavy negative ions is considered. The elec-
trons propagate relative to ions with small velocity in
comparison with electron thermal velocity. The electro-
static potential hollow reflects the electrons with energy
smaller than the hollow depth. This leads to hollow
depth growth.
The equation describing the shape and time evolu-
tion of electric field structure is derived. It is obtained
that the ion-acoustic hollow of electrostatic potential is
excited due to current-carrying instability. The case of
large amplitude of excited perturbation is considered,
when there are no traditional small parameters, permit-
ting to describe properties and excitation of perturba-
tion. It is shown that the hollow propagates with velocity
which strongly depends on amplitude of perturbation
and is close to ion-acoustic velocity of positive ions
(Te/Mi+)1/2.
We use hydrodynamic equations for negative and
positive ions
∂n±/∂t+∂(n±V±)/∂z=0, (1)
∂V±/∂t+ V±∂V±/∂z±(q±/M±)∂ϕ /∂z=0
Here q± , n± , V± , M± are charges, densities, veloci-
ties and masses of positive and negative ions. ϕ is the
electrostatic potential.
For description of electron dynamics we use Vlasov
equation for their distribution function fe
∂fe/∂t+V∂fe/∂z+(e/me)(∂ϕ /∂z)∂fe/∂V=0 (2)
and Poisson equation
∂2ϕ /∂z2=4π(ene+q-n—q+n+) (3)
Electrons propagate relative to ions with some cur-
rent velocity Vо. Let us assume that the initial distribu-
tion function is the Maxhollow distribution
foe(0,z,V-Vo)=(me/2πTe)1/2exp[-me(V-Vo)2/2Te]
(4)
The initial potential perturbation is a hollow with
width δz , smaller than the system length L. The poten-
tial hollow with initial conditions (4) is nonequilibrium.
It reflects the resonant particles and obtains energy from
them. The amplitude (depth) of the hollow grows ϕ o .
Due to reflection of resonant electrons with non-
symmetric relative to hollow velocity Vс distribution
function from potential hollow the quasineutrality brakes
near the hollow: before the hollow the electron density
decreases and after the hollow the electron density in-
creases. The quasineutrality is realized due to formation
of potential jump ∆ϕ near the hollow.
At increasing of hollow amplitude up to critical
value, when inverse time
τ-1=Vtr/δz=(2eϕ o/me)1/2/δz(ϕ o) (5)
of resonant electron (with velocities |V - Vс| « Vtr(ϕ o))
interaction with the hollow becomes larger than growth
rate γ(ϕ o)=∂lnϕ o/∂t of hollow amplitude
Vtr(ϕ o)>γ(ϕ o)δz(ϕ o), (6)
the slow evolution of the hollow starts in comparison
with electron dynamics. The resonant electron distribu-
tion function changes. The front with this changed dis-
tribution function propagates from the hollow with rela-
tive velocity equal Vtr .
mailto:vmaslov@kipt.kharkov.ua
138
We use slow evolution of hollow for its description
using small parameter α=γδz/Vtr . In zero approxima-
tion on α phase trajectories of electrons, described by
equations of characteristics of Vlasov equation in rest-
frame of hollow are determined by relation
ε=meV2/2-eϕ (t,z)=const (7)
In this approximation the distribution function before
the hollow z>0 after it z<0 depends only on ε . Here
z=0 corresponds to ϕ (z)=-ϕ o .
Resonant region before the hollow is wider on the
velue of potential jump.
Taking into account that the resonant electrons are
reflected from the hollow one can derive from (2), (4)
the expression for electron distribution function
fe=foe[-(V2-2e(ϕ±∆ϕ )/me)1/2±Vo], V>
<A(ϕ )sign(z) (8)
A(ϕ )=[2e(ϕ o+ϕ )/me]1/2.
We use the normalized values: φ≡eϕ /Te, N-≡no-/no+,
Ne≡noe/no+ , Q±=q±/e, Vs±=(Te/M±)1/2. We normalize x
on Debye radius of electrons rde, Vo on electron thermal
velocity, time t on plasma frequency of positive ions
ωp+
-1 , ion velocities and velocity of solitary perturbation
on ion-acoustic velocity of positive ions (Te/M+)1/2.
Here Te, is the temperature of electrons, no-, no+ are
unperturbed densities of negative and positive ions.
Integrating (8) over velocity, one can derive the ex-
pression for electron density which in first approxima-
tion on Vо is of type
ne≈noeexp(φ)[1-(2∆φ/√π)∫oβdx exp(-x2)-
-2Vo(2/π)1/2∫oβdx (x2-φ)1/2exp(-x2)] (9)
Far from the hollow the plasma is quasineutral
ne(z) z→∞ = ne(z) z→-∞ =1. From here one can derive,
using (9), the expression for potential jump near the
hollow
∆φ=Vo(2/π)1/2(1-exp(-φo))/[1-(2/√π)∫o√φo dxexp(-x2)] (10)
From hydrodynamic equations for ions (1) one can
obtain for perturbations of densities of positive and
negative ions
ni±=n±NL+n±τ ,
n±NL=no±/[1-(±q±)2ϕ /M±Vc
2]1/2, (11)
∂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 (9) , (11) in Poisson equation one can
derive nonlinear evolution equation
∂3
zφ+{Q+
2V2
s+(1-2φQ+V2
s+/Vc
2)-3/2(1-φQ+V2
s+/Vc
2)+
+Q-
2N-V2
s-(1+2φQ-V2
s-/Vc
2)-3/2(1+φQ-V2
s-/Vc
2)}2∂tφ/Vc
3
+(∂zφ/Vc
2){Q+
2V2
s+(1-2φQ+V2
s+/Vc
2)-3/2+
+Q-
2N-V2
s-(1+2φQ-V2
s-/Vc
2)-3/2}- (12)
-{exp(φ)-sign(z)Vo(2/π)1/2{(φo/(φo+φ))1/2exp(-φo)-
-∫√-φ
√φo dy(1-2y2)exp(-y2)/( y2+φ)1/2+
+(1-exp(-φo))[1-(2/√π)∫o√φo dxexp(-x2)]-1×
×[exp(-φo)/(φo+φ)1/2+2(φo+φ)exp(-φo)+
+4∫√-φ
√φo dy y( y2+φ)1/2exp(-y2)]/√π}}∂zφ=0
Integrating (12), one can get
(∂zφ)2/2=(Vc/Vs-)2[N-((1+Q-2φV2
s-/Vc
2)1/2-1)+
+(1-Q+2φV2
s+/Vc
2)1/2-1]+Ne{exp(φ)-1-
-2sign(z)Vo(2/π)1/2[exp(-φo)√φo((φo+φ)3/2-φo
3/2)2/3+
+ exp(-φo)(1+φo+φo
22/3)-exp(φ)(1-φ+φ22/3)+
+(1-exp(-φo))[1-(2/√π)∫o√φo dxexp(-x2)]-1×
×[exp(-φo)((φo+φ)3/2-φo
3/2)2/3+ (13)
+√φoexp(-φo)(1+φo2/3)- √-φexp(φ)(1-φ2/3)-
-∫√-φ
√φo dyexp(-y2)]/√π]}
From (13) and ∂zφ|φ=-φo=0 one can show that the hol-
low velocity is close to the ion-acoustic velocity of the
positive ions and essentially depends on the hollow am-
plitude.
References
1. W.Oohara, S.Ishiguro, R.Hatakeyama, N.Sato. Elec-
trostatic potential modification due to C60
− genera-
tion // Proc. of Symp. on DL-PFNL-96. 1996. p.19.
|
| id | nasplib_isofts_kiev_ua-123456789-78552 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-28T17:04:58Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Maslov, V.I. Stomin, V.L. 2015-03-18T19:04:41Z 2015-03-18T19:04:41Z 2000 Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions / V.I. Maslov, V.L. Stomin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 137-138. — Бібліогр.: 1 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78552 533.9.01 The properties of electrostatic potential hollow of solitary kind are investigated theoretically. The potential hollow is excited in current-carrying plasma. The equation, describing the hollow of any amplitude, is derived. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Вeams and waves in plasma Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions Article published earlier |
| spellingShingle | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions Maslov, V.I. Stomin, V.L. Вeams and waves in plasma |
| title | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions |
| title_full | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions |
| title_fullStr | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions |
| title_full_unstemmed | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions |
| title_short | Excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions |
| title_sort | excitation and properties of solitary perturbation of large amplitudes in nonequilibrium plasmas with negative ions |
| topic | Вeams and waves in plasma |
| topic_facet | Вeams and waves in plasma |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78552 |
| work_keys_str_mv | AT maslovvi excitationandpropertiesofsolitaryperturbationoflargeamplitudesinnonequilibriumplasmaswithnegativeions AT stominvl excitationandpropertiesofsolitaryperturbationoflargeamplitudesinnonequilibriumplasmaswithnegativeions |