Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe
Ion crystal formation in non-equilibrium dusty plasma in a field of an electric probe is investigated in such conditions, at which in equilibrium plasma its formation is impossible. Досліджене формування іонного кристала в нерівноважній пиловій плазмі в полі електричного зонда в таких умовах, при як...
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| Date: | 2003 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Cite this: | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe / N.A. Azarenkov, A.M. Egorov, V.I. Maslov, I.N. Onishchenko, D.Yu. Frolova // Вопросы атомной науки и техники. — 2003. — № 1. — С. 128-129. — Бібліогр.: 3 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859814957732855808 |
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| author | Azarenkov, N.A. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Frolova, D.Yu. |
| author_facet | Azarenkov, N.A. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Frolova, D.Yu. |
| citation_txt | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe / N.A. Azarenkov, A.M. Egorov, V.I. Maslov, I.N. Onishchenko, D.Yu. Frolova // Вопросы атомной науки и техники. — 2003. — № 1. — С. 128-129. — Бібліогр.: 3 назв. — англ. |
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| description | Ion crystal formation in non-equilibrium dusty plasma in a field of an electric probe is investigated in such conditions, at which in equilibrium plasma its formation is impossible.
Досліджене формування іонного кристала в нерівноважній пиловій плазмі в полі електричного зонда в таких умовах, при яких у рівноважній плазмі виникнення кристала неможливо.
Исследовано формирование ионного кристалла в неравновесной пылевой плазме в поле электрического зонда в таких условиях, при которых в равновесной плазме возникновение кристалла невозможно.
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| first_indexed | 2025-12-07T15:21:45Z |
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ION CRYSTAL FORMATION IN NONEQUILIBRIUM DUSTY PLASMAS
NEAR ELECTRODE OR ELECTRIC PROBE
N.A.Azarenkov*, A.M.Egorov, V.I.Maslov, I.N.Onishchenko, D.Yu.Frolova*
NSC Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine,
E-mail: vmaslov@kipt.kharkov.ua;
*Karazin Kharkov National University, Kharkov, 61108, Ukraine
Ion crystal formation in non-equilibrium dusty plasma in a field of an electric probe is investigated in such
conditions, at which in equilibrium plasma its formation is impossible.
PACS: 52.27.Lw
INTRODUCTION
Ion crystal formation in plasmas with heavy negative
ions is investigated now intensively [1-3]. This, so-called
dusty plasma often is realized in the technological plasma
installations. Ion crystals arising in equilibrium plasma
now are well researched. However, in laboratory
experiments the formation of ion (plasma) crystals in non-
equilibrium plasma have been observed in such
conditions, at which their formation in equilibrium plasma
is impossible. In particular, in laboratory experiment [1]
the formation of an ion crystal in dusty plasma in a
neighbourhood of the electric probe was observed. Till
now this phenomenon was not explained and described.
In this paper the formation mechanism of such ion crystal
in dusty plasma in an electric field in a neighbourhood of
an electrode or electrical probe is presented and
described.
The considered plasma represents dusty plasma, that is
plasma, keeping apart from electrons and positive ions the
negative dusty particles. It was observed in [1], that in an
electrical field of the probe there appears a convective
motion of plasma concerning heavy negative ions. In
other words electrical field provides originating a flow of
light positive ions concerning heavy negative ions. The
flow excites perturbations of large amplitudes. The
properties and evolution of these excited perturbations are
considered. The generalized equation is derived for a
spatial distribution of a field of any amplitude for a case
of plasma crystal formation on generalized dust ion-
acoustic mode. At certain conditions velocity of this mode
is close to zero. The evolution equation is also derived. It
is shown, that these perturbations of large amplitude
result in spatial ordering of heavy negatively ions in non-
equilibrium plasma.
ION CRYSTAL FORMATION
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, formed near electric probe, relative to these negative
ions. 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
amplitude 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.
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 of large amplitudes is formed on
generalized 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. The
plasma crystal is motionless, because grains are trapped
by chain of solitary perturbations formed due to
instability development on generalized 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)
128 Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 128-129
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
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 amplitude
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) one
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 localized 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-ϕo/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+(eϕo/T)1/2(no-m+q2
-/no+m+q2
+)1/3 (12)
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. 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 spatial interval, equal to
wavelength, contains the negative ion.
From (2) one can obtain that the crystal is formed,
when amplitude of perturbation ϕo reaches the amplitude
of negative ion trapping
eϕo/T>(n-
2m-q-
4/211n+
2m+q+
4)1/3 (13)
From (16) one can see that the density of negative ions
should be small for crystal formation at final amplitude of
perturbation.
REFERENCES
1. D.A.Law et al. Dust Particle Interaction in RF Plasma
Sheaths // Plasma Phys. 1995, p. 150.
2. H.M.Thomas, G.E.Morfill. // Nature. 1996, v. 379, p.
806.
3. M.Nambu, S.V.Vladimirov, P.K.Shukla. // Phys. Lett.
A. 1995, v. 203, p. 40.
ФОРМУВАННЯ ІОННОГО КРИСТАЛА У НЕРІВНОВАЖНІЙ ПИЛОВІЙ ПЛАЗМІ ПОБЛИЗУ
ЕЛЕКТРОДА АБО ЕЛЕКТРИЧНОГО ЗОНДА
М.О. Азаренков, О.М. Єгоров, В.І. Маслов, І.М. Онищенко, Д.Ю. Фролова
Досліджене формування іонного кристала в нерівноважній пиловій плазмі в полі електричного зонда в
таких умовах, при яких у рівноважній плазмі виникнення кристала неможливо.
ФОРМИРОВАНИЕ ИОННОГО КРИСТАЛЛА В НЕРАВНОВЕСНОЙ ПЫЛЕВОЙ ПЛАЗМЕ ВБЛИЗИ
ЭЛЕКТРОДА ИЛИ ЭЛЕКТРИЧЕСКОГО ЗОНДА
Н.А. Азаренков, А.М. Егоров, В.И. Маслов, И.Н. Онищенко, Д.Ю.Фролова
Исследовано формирование ионного кристалла в неравновесной пылевой плазме в поле электрического зонда в
таких условиях, при которых в равновесной плазме возникновение кристалла невозможно.
129
INTRODUCTION
ION CRYSTAL FORMATION
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| id | nasplib_isofts_kiev_ua-123456789-110537 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:21:45Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Azarenkov, N.A. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Frolova, D.Yu. 2017-01-04T18:38:15Z 2017-01-04T18:38:15Z 2003 Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe / N.A. Azarenkov, A.M. Egorov, V.I. Maslov, I.N. Onishchenko, D.Yu. Frolova // Вопросы атомной науки и техники. — 2003. — № 1. — С. 128-129. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.27.Lw https://nasplib.isofts.kiev.ua/handle/123456789/110537 Ion crystal formation in non-equilibrium dusty plasma in a field of an electric probe is investigated in such conditions, at which in equilibrium plasma its formation is impossible. Досліджене формування іонного кристала в нерівноважній пиловій плазмі в полі електричного зонда в таких умовах, при яких у рівноважній плазмі виникнення кристала неможливо. Исследовано формирование ионного кристалла в неравновесной пылевой плазме в поле электрического зонда в таких условиях, при которых в равновесной плазме возникновение кристалла невозможно. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe Формування іонного кристала у нерівноважній пиловій плазмі поблизу електрода або електричного зонда Формирование ионного кристалла в неравновесной пылевой плазме вблизи электрода или электрического зонда Article published earlier |
| spellingShingle | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe Azarenkov, N.A. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Frolova, D.Yu. Low temperature plasma and plasma technologies |
| title | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe |
| title_alt | Формування іонного кристала у нерівноважній пиловій плазмі поблизу електрода або електричного зонда Формирование ионного кристалла в неравновесной пылевой плазме вблизи электрода или электрического зонда |
| title_full | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe |
| title_fullStr | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe |
| title_full_unstemmed | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe |
| title_short | Ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe |
| title_sort | ion crystal formation in nonequilibrium dusty plasmas near electrode or electric probe |
| topic | Low temperature plasma and plasma technologies |
| topic_facet | Low temperature plasma and plasma technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110537 |
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