Negative ion crystal formation in nonequilibrium plasmas
The crystal formation of heavy negative ions is considered in following system. The plasma flow with positive ions and electrons propagates vertically up and extends in radial direction. The flow propagates relative to heavy negative ions, subjected to gravity. The flow excites the perturbations of...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2000 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Цитувати: | Negative ion crystal formation in nonequilibrium plasmas / V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, V.L. Stomin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 139-140. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859827768362008576 |
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| author | Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Stomin, V.L. |
| author_facet | Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Stomin, V.L. |
| citation_txt | Negative ion crystal formation in nonequilibrium plasmas / V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, V.L. Stomin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 139-140. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The crystal formation of heavy negative ions is considered in following system. The plasma flow with positive ions and electrons propagates vertically up and extends in radial direction. The flow propagates relative to heavy negative ions, subjected to gravity. The flow excites the perturbations of large amplitudes. The properties and evolution of these excited perturbations are considered. The evolution equation is derived for the case of any amplitudes. It is shown that these perturbations of large amplitude lead to spatial ordering of heavy negative ions in nonequilibrium plasma.
|
| first_indexed | 2025-12-07T15:30:00Z |
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UDC 533.9.01
Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p. 139-140 139
NEGATIVE ION CRYSTAL FORMATION IN NONEQUILIBRIUM
PLASMAS
V.I.Lapshin, V.I.Maslov, I.N.Onishchenko, V.L.Stomin
NSC Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine
The crystal formation of heavy negative ions is considered in following system. The plasma flow with positive
ions and electrons propagates vertically up and extends in radial direction. The flow propagates relative to heavy
negative ions, subjected to gravity. The flow excites the perturbations of large amplitudes. The properties and
evolution of these excited perturbations are considered. The evolution equation is derived for the case of any
amplitudes. It is shown that these perturbations of large amplitude lead to spatial ordering of heavy negative ions in
nonequilibrium plasma.
Plasma with heavy negative ions, strongly coupled
dusty plasmas (or so called colloidal plasmas), plasma
crystal formation (or so called ion crystal formation)
and wave propagation through a plasma crystal are
investigated now intensively (see, for example, [1, 2]).
In particular, the formation of the plasma crystals has
been observed in experiments at providing of
nonequilibrium state. If in equilibrium plasma there was
no plasma crystal but at propagation of laser radiation
through plasma or at providing of small nonequilibrium
state by electric probe in plasma in experiment an ion
crystal has been formed. The ion crystals have been
formed also in plasma flow relative to heavy negative
ions.
In this paper the formation of crystals of heavy
negative ions is considered in plasma flow relative to
these negative ions. Namely, the plasma flow with
positive ions and electrons propagates vertically up and
extends in radial direction. The flow propagates relative
to heavy negative ions, subjected to gravity. The flow
excites the perturbations of large amplitudes. The
properties and evolution of these excited perturbations
are considered. The generalised equation is derived for
the spatial distribution of field of any amplitudes for the
case of the plasma crystal formation on generalised dust
ion-acoustic mode. Also the evolution equation is
derived. It is shown that these perturbations of large
amplitude lead to spatial ordering of heavy negative ions
in nonequilibrium plasma. Considered state of plasma
constitutes a special form of colloidal plasmas, i.e.
plasmas containing micron-sized particles (dust grains).
We investigate theoretically of a plasma crystal
formation in colloidal nonequilibrium plasmas. The
considered plasma crystal is the lattice of heavy negative
ions of grains.
Investigations of a plasma crystal formation are
performed for the case of strong magnetic field with
field strength so that the gyro radii of ions comparable
with distance between the grains in the lattice.
We show theoretically that the plasma crystal is
formed at providing of nonequilibrium state. If in
equilibrium plasma there is no plasma crystal but at
providing of small nonequilibrium state by propagation
of plasma flow through cloud of colloidal particles a
plasma crystal is formed.
The formation of a plasma crystal is considered in
dusty colloidal plasma with relative propagation of
grains and plasma with light ions with small flow
velocity.
It is shown that the longitudinal chain of solitary
perturbations (similar to [3]) of large amplitudes is
formed on generalised ion-acoustic mode in plasma
flow; the velocity of this mode in system, propagating
with light ions, is faster than the ion-acoustic velocity,
but in laboratory system the velocity of this mode is near
zero; these perturbations of large amplitude lead to
trapping of heavy negative ions of grains and to spatial
ordering of them in nonequilibrium dusty colloidal
plasmas. Though gravity provide relative propagation of
heavy grains downwards relative to light positive ions,
the plasma crystal is motionless, because grains are
trapped by chain of solitary perturbations formed due to
instability development on generalised dust ion-acoustic
mode with velocity equal zero.
The excitation by a plasma flow, propagating
relative to negative heavy ions, linear perturbations is
described by a following ratio
1+1/(krde)2-ω2
p+/(ω-kVo+)2-ω2
p-/ω2=0 (1)
Here ω, k are frequency and wave vector of the
perturbations; ωp± , ωp- are the plasma frequencies of the
positive and negative ions; rde is the electron Debye’s
radius; Vo+ is the flow velocity of the positive ions.
From (1) one can obtain, that one can select the
plasma flow velocity such, that
Vph=ω/k≈(Vo+/24/3)(n-m+q-
2/ n+m-q+
2)1/3<<Vs+,
λ=2π/k=2πrde/(Vs+
2n+q+
2/Vo+
2nee2-1)1/2>>rde (2)
the periodic in space field is motionless, that is
Vph<<Vs+. Vs+=(T/m+)1/2 is the ion-acoustic velocity of
the positive ions.
From (1) one can obtain, that the growth rate of the
perturbation equals
γ= (3)
=(1.5)1/2(Vo+/rde)(n-m+q-
2/n+m-q+
2)1/3(Vs+
2q+/Vo+
2e-1)1/2
At non-linear stage of instability development an
electrical potential ϕ of the perturbation represents the
chain of the solitary narrow humps of finite amplitudes
ϕ o. Let us consider properties of the separate solitary
perturbation. Because the negative ions are heavy and
their density is small, we suppose, that the shape of a
quasistationary perturbation is determined by dynamics
and distribution in space of electrons and positive ions.
The interaction of this perturbation with heavy negative
140
ions results in excitation of a perturbation, that is to
growth its amplitude.
With growth of the amplitude of the perturbation the
adiabatic stage of the evolution starts early for electrons
ϕ o >(me/e)(γ/k)2 . Then the velocity distribution function
of electrons, located outside of a separatrix, has the
following kind
fe(v)=[noe/Vte(2π)1/2]exp(eϕ /Te- mev2/2Te) (4)
For the trapped electrons, i.e. for electrons, located
inside a separatrix, the distribution function does not
depend on velocity due to adiabatic evolution.
Integrating the velocity distribution function of
electrons one can derive the expression for electron
density
ne= (no/(2π)1/2)(2/T)3/2∫∞odε(ε+eϕ )1/2exp(-ε/T) (5)
The expression for density of the positive ions one
can get from hydrodynamic equations
n+=no+/[1-2q+ϕ /m+(Vo+-Vh)2]1/2 (6)
Here q+, m+, Vo+ are charge, mass and velocity of the
positive ions; Vh is the velocity of the solitary
perturbation.
Substituting (5), (6) in Poisson’s equation, one can
derive the equation for spatial distribution of an
electrical potential of the perturbation of any amplitudes
φ’’=(2/√π)∫∞odae-a(a+φ)1/2-1/(1-2Qφ/voh
2)1/2 (7)
Q =q+/e, φ=eϕ /T, “’”=∂/∂x, x=z/rde, voh=(Vo+-Vh)/Vs+.
The equation (7) can be transformed to following
kind
(φ’)2=(8/3√π)∫∞odae-a(a+φ)3/2-4+(2v2
oh/Q)[(1-
-2Qφ/voh
2)1/2-1] (8)
From a condition φ’|φ=φo=0 and (8) the nonlinear
dispersion relation follows
voh
2/Q=(A-2)2/2(A-2-φo),
A=(8/3√π)∫∞odae-a(a+φ)3/2 (9)
In approximation of small amplitudes from (8), (9) on
can get for voh and width of the solitary perturbation L
voh
2≈ Q, L≈[(15√π/4(1-1/√2)]1/2φo
-1/4 (10)
Therefore, if to select the velocity of the plasma
motion, equal (q+/e)1/2Vs+, then the perturbation is
approximately fixed in a laboratory system. Then also
we have from (2) λ>>L. That is the perturbations
represent the chain of the narrow potential humps with a
large distance between them. Because the potential
humps trap the negative heavy ions, then last are
localised in space.
Until now we considered a quasistationary
longitudinal structure of a field, determined by dynamics
of electrons and light positive ions. Now we consider
the growth in time of the amplitude of separate solitary
perturbation due to its interaction with negative heavy
ions. For that we take into account in hydrodynamic
equations for positive and negative ions the next terms
of expansion on small parameter γ/kVtr-, Vtr- = (q-ϕ o/m-
)1/2. Substituting them in Poisson’s equation, we obtain
the evolution equation
2ω2
p+ ∂3ϕ /∂t3/(Vo+-Vh)3=-ω2
p-∂3ϕ /∂z3 (11)
From (11) one can get that the growth rate in time of the
nonlinear perturbation amplitude equals
γNL≈ωp+(eϕ o/T)1/2(no-m+q2
-/no+m+q2
+)1/3 (12)
Let us show that the plasma flow also excites the
transversal oscillations with growth rate closed to the
growth rate of longitudinal oscillations. From [4] one
can obtain that in the case cosθ<<ωp-/ωpe , when the
term ω2
p-/ω2 in the dispersion law, determining the
instability development and oscillation excitation, is
essential, then the dispersion law has following kind
1+ω2
pe/ω2
ce-ω2
p+/((ω-kVo+)2 -ω2
c+)-ω2
p-/ω2≈0 (13)
Here θ is the angle between direction of transversal
perturbation propagation and vertical direction.
At first, neglecting the last term, in the first
approximation on ω/ωp+ from (13) one can find the
wave vector of the most unstable wave
k≈ωp+/Vo+(1+ω2
pe/ω2
ce)1/2 (14)
In the next approximation on ω/ωp+, taking into
account the last term, from (13) one can find, that the
growth rate of the excitation of the transversal spatially
periodic field
γ=(1.5)1/2ωp+(n-m+q-
2/n+m-q+
2)1/3/2(1+ω2
pe/ω2
ce)1/2 (15)
is closed to the growth rate of longitudinal periodic field
excitation. In the same approximation from (13) one can
obtain, that the transversal perturbation propagates with
velocity, approximately equal to the phase velocity of
the longitudinal perturbation. The last promotes for
trapping of negative ions by transversal field as well as
by longitudinal field.
From (2), (14) one can see that the transversal period
of the lattice approximately equals to the longitudinal
spatial period. Therefore, if density of negative ions is
such one no-, that a single negative ion appears in area,
which radius is equal to the wavelength λ, and volume
is equal (4π/3)λ3 , i.e. no-(4π/3)λ3 =1, then the trapped
heavy negative ions form crystal with the same
dimensions in a longitudinal direction and in a
transversal direction. If the density of the negative ions
is small, no-(4π/3)λ3 <1, then nonideal crystal is formed.
Nonideal crystal is due to that not each longitudinal and
transversal spatial interval, equal to wavelength,
contains the negative ion.
From (2) one can obtain that the crystal is formed,
when amplitude of perturbation ϕ o reaches the
amplitude of negative ion trapping
eϕ o/T>(n-
2m-q-
4/211n+
2m+q+
4)1/3 (16)
From (16) one can see that the density of negative ions
should be small for crystal formation at final amplitude
of perturbation.
References
1. H.M.Thomas, G.E. Morfill // Nature. (379). 1996, p.806.
2. R.K.Varma, P.K.Shukla // Physica Scripta. (51). 1995,
p.522.
3. W.Oohara, S.Ishiguro, R.Hatakeyama, N.Sato.
Electrostatic potential modification due to C60
- generation
// Proc. of Symp. on DL-PFNL-96. 1996. p. 19.
4. A.I.Akhiezer, I.A. Akhiezer, R.V.Polovin, A.G.Sitenko,
K.N.Stepanov. Plasma Electrodynamics. Moscow, 1995.
|
| id | nasplib_isofts_kiev_ua-123456789-78554 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:30:00Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Stomin, V.L. 2015-03-18T19:10:39Z 2015-03-18T19:10:39Z 2000 Negative ion crystal formation in nonequilibrium plasmas / V.I. Lapshin, V.I. Maslov, I.N. Onishchenko, V.L. Stomin // Вопросы атомной науки и техники. — 2000. — № 6. — С. 139-140. — Бібліогр.: 4 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78554 533.9.01 The crystal formation of heavy negative ions is considered in following system. The plasma flow with positive ions and electrons propagates vertically up and extends in radial direction. The flow propagates relative to heavy negative ions, subjected to gravity. The flow excites the perturbations of large amplitudes. The properties and evolution of these excited perturbations are considered. The evolution equation is derived for the case of any amplitudes. It is shown that these perturbations of large amplitude lead to spatial ordering of heavy negative ions in nonequilibrium plasma. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Вeams and waves in plasma Negative ion crystal formation in nonequilibrium plasmas Article published earlier |
| spellingShingle | Negative ion crystal formation in nonequilibrium plasmas Lapshin, V.I. Maslov, V.I. Onishchenko, I.N. Stomin, V.L. Вeams and waves in plasma |
| title | Negative ion crystal formation in nonequilibrium plasmas |
| title_full | Negative ion crystal formation in nonequilibrium plasmas |
| title_fullStr | Negative ion crystal formation in nonequilibrium plasmas |
| title_full_unstemmed | Negative ion crystal formation in nonequilibrium plasmas |
| title_short | Negative ion crystal formation in nonequilibrium plasmas |
| title_sort | negative ion crystal formation in nonequilibrium plasmas |
| topic | Вeams and waves in plasma |
| topic_facet | Вeams and waves in plasma |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78554 |
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