Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas
A review on dust ion-acoustic nonlinear wave structures in dusty plasmas is presented. The basic experiments on the nonlinear wave structures in dusty plasmas are considered and the corresponding theoretical descriptions are given. A possibility of the existence of the dust ion-acoustic nonlinear st...
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irk-123456789-1091062016-11-21T03:02:37Z Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas Popel, S.I. Фундаментальная физика плазмы A review on dust ion-acoustic nonlinear wave structures in dusty plasmas is presented. The basic experiments on the nonlinear wave structures in dusty plasmas are considered and the corresponding theoretical descriptions are given. A possibility of the existence of the dust ion-acoustic nonlinear structures under near-Earth and space conditions is discussed. Представлен обзор по пылевым ионно-звуковым нелинейным волновым структурам в пылевой плазме. Рассмотрены основные эксперименты по нелинейным волновым структурам в пылевой плазме и приведено соответствующее теоретическое описание. Обсуждаются возможности существования пылевых ионно- звуковых нелинейных структур в условиях околоземной и космической плазмы. Представлено огляд по пиловим іонно-звуковим нелінійним хвильовим структурам у пиловій плазмі. Розглянуто основні експерименти з нелінійних хвильових структур в пиловій плазмі та наведено відповідний теоретичний опис. Обговорюються можливості існування пилових іонно-звукових нелінійних структур в умовах навколоземної і космічної плазми. 2012 Article Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas / S.I. Popel // Вопросы атомной науки и техники. — 2012. — № 6. — С. 72-76. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.27.Lw, 52.27.Gr, 52.35.-g http://dspace.nbuv.gov.ua/handle/123456789/109106 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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A review on dust ion-acoustic nonlinear wave structures in dusty plasmas is presented. The basic experiments on the nonlinear wave structures in dusty plasmas are considered and the corresponding theoretical descriptions are given. A possibility of the existence of the dust ion-acoustic nonlinear structures under near-Earth and space conditions is discussed. |
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Popel, S.I. |
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Popel, S.I. |
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Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas |
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Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas |
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Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas |
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Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas |
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Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas |
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dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Фундаментальная физика плазмы |
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Dust ion-acoustic nonlinear wave structures under conditions of near-earth and laboratory plasmas / S.I. Popel // Вопросы атомной науки и техники. — 2012. — № 6. — С. 72-76. — Бібліогр.: 14 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-07T22:34:37Z |
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2025-07-07T22:34:37Z |
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1837029317535596544 |
| fulltext |
72 ISSN 1562-6016. ВАНТ. 2012. №6(82)
DUST ION-ACOUSTIC NONLINEAR WAVE STRUCTURES UNDER
CONDITIONS OF NEAR-EARTH AND LABORATORY PLASMAS
S.I. Popel
Institute for Dynamics of Geospheres RAS, Moscow, Russia
A review on dust ion-acoustic nonlinear wave structures in dusty plasmas is presented. The basic experiments on
the nonlinear wave structures in dusty plasmas are considered and the corresponding theoretical descriptions are
given. A possibility of the existence of the dust ion-acoustic nonlinear structures under near-Earth and space
conditions is discussed.
PACS: 52.27.Lw, 52.27.Gr, 52.35.-g
INTRODUCTION
A dusty plasma is the plasma containing electrons,
ions, neutrals, and dust microscopic particles which are
composed of either solid or liquid material. It is always
an open system because the currents of electrons and
ions flowing onto the dust grains (as well as the energy
flows) should be maintained by external sources of the
plasma particles and the energy. The dissipation rate is
high. Therefore, there is a tendency to self-organization
and to formation of long-living nonlinear dissipative
and coherent structures in a plasma such as shock
waves, solitons, cavitons, collapsing cavities, etc. One
can expect wider manifestations of nonlinear structures
in dusty plasmas than in the case of usual plasmas. The
significant property of dusty plasmas is the dust particle
charging process. As a rule, under conditions of
laboratory experiments the microparticles are negatively
charged, their charges being determined by the fluxes of
electrons and ions, which are absorbed by
microparticles. Any changes of plasma parameters vary
these fluxes that results in variable charge of the latter.
At present, the problem of the excitation and
propagation of nonlinear waves occupies an important
place in the physics of dusty plasma. Interest in this
kind of research is often associated with the fact that the
processes of dust grain charging are far from
equilibrium, so that the anomalous dissipation, which,
by its very nature, originates from the charging process,
can play a decisive role. It is this anomalous dissipation
mechanism that is responsible for the existence of a new
kind of shocks [1, 2], namely dust ion-acoustic shocks,
that are “collisionless” in the sense that they are almost
completely insensitive to electron-ion collisions.
However, in contrast to classical collisionless shock
waves, the dissipation due to dust charging involves
interaction of electrons and ions with dust grains
through microscopic electron and ion currents to the
grain surfaces. The anomalous dissipation plays a very
important role in the propagation of other dust ion-
acoustic nonlinear structures, e.g., in the case of the so-
called “weakly dissipative” dust ion-acoustic solitons,
whose shape is described by soliton solutions in a
certain range of values of the Mach number [3-6].
Because of the anomalous dissipation, these solitons are
slowed down and damped. Dust ion--acoustic shock
waves were observed in a double plasma device at the
Institute of Space and Astronautical Science (Japan) [7]
and in a Q machine device at the University of Iowa
(USA) [8] almost simultaneously. Observation of dust
ion-acoustic solitons was reported in [9].
There are plans to carry out experiments on dust ion-
acoustic nonlinear wave structures during the mission of
the International Space Station. The purpose of this
brief review is to present the most important results on
dust ion-acoustic nonlinear wave structures in dusty
plasmas.
1. SHOCKS IN LABORATORY PLASMA
Let us formulate the main experimental results on
dust ion-acoustic shocks in dusty plasmas. In
experiments [7], Nakamura et al. revealed that the most
important feature of dust ion-acoustic shocks in dusty
plasmas is the following.
(i) In the absence of dust, the effect of the electron
and ion charge separation gives rise to oscillations in the
shock wave profile in the vicinity of the shock front,
while the presence of dust suppresses these oscillations.
The experiments [8] showed that:
(ii) Dust ion-acoustic shocks are generated at
sufficiently high dust densities (under the experimental
conditions of [8], at dust densities such that
0.75/nZnεZ i0d0d0d0 ≥≡ , where ed0-
d
Zq = is the
dust grain charge, e- is the electron charge, d(i)n is the
dust (ion) density, and the subscript “0” stands for the
unperturbed plasma parameters). In Ref. [8], the
conclusion about the formation of a shock wave was
drawn from the fact that the perturbation front steepens
as time elapses. At sufficiently low dust densities, the
perturbation front does not steepen but instead widens.
(iii) When the shock wave structure has formed, the
shock front width ξΔ is described by the theoretical
estimate, which is based on the model developed in Ref. [1]
qs
Mc νξ /∝Δ , (1)
where
s
Mc is the shock wave speed, M is the Mach
number,
s
c is the ion-acoustic speed,
q
ν is the grain
charging rate.
(iv) The velocity of the dust ion-acoustic shocks
increases considerably with increasing d0εZ .
ISSN 1562-6016. ВАНТ. 2012. №6(82) 73
In this context, the requirement to the theoretical
model is the adequate description of the relevant
experiments. We use the so-called ionization source
model developed in Refs. [10, 11] and based on the
hydrodynamical approach. We note that under the
experimental conditions of Refs. [7, 8], the ionization
source term in the evolutionary equation for the ion
density should be independent on the electron density.
Fig. 1. Time evolutions of the ion density at different
distances from the grid for the data of the experiments
[7] in the absence (a) and in the presence (b) of dust
Now, we test our theoretical model against the
experimental result (i), which was obtained in Ref. [7].
The experiments described in that paper were carried
out with a double plasma device, which was modified so
that the dust component was present in the plasma. The
calculations were carried out for different dust densities
and for the parameter values which correspond to the
values of the experiments [7]. The width of the
perturbation and its shape were determined self-
consistently, in accordance with the method for exciting
a shock wave. In Fig. 1 (which is analogous to Fig. 3
from Ref. [7]), we illustrate the time evolution of the ion
density at different distances from the grid. We can see
that the electron and ion charge separation gives rise to
oscillations in the shock wave profile and that the dust
suppresses these oscillations, as is the case in the
experiments [7]. The theoretically calculated rise time
of the shock front is about 5 μs, which corresponds to
the experimental data.
Theory modeling of the experiments [8] performed
with a Q-machine has been carried out for the cesium
vapor plasma parameters, which correspond to the
experimental those. The calculations were carried out
for different values of the parameter d0εZ . In Fig. 2
(which is analogous to Fig. 2 from Ref. [8]), we
illustrate the time evolution of the ion density at
different distances from the grid. The time evolutions
(heavy curves) were calculated for 0εZd0 = (a) and
0.75εZd0 = (b). The light curves show the widening of
the wave front (at 0εZd0 = ) and its steepening (at
0.75εZd0 = ). This agrees with the experimental data
from Ref. [8].
Fig. 2. Time evolutions of the ion density (heavy curves)
at different distances from the grid for the data of the
experiments [8] and 0εZd0 = (a) and 0.75 (b). The
light lines show the widening of the wave front (at
0εZd0 = ) and its steepening (at 0.75εZd0 = )
74 ISSN 1562-6016. ВАНТ. 2012. №6(82)
The extent to which the shock front widens was
calculated to be 3.0/ ∝Δ
s
Mcξ ms (see Fig. 2,b),
which corresponds to that observed experimentally (see
Fig. 2,b) in Ref. [8]) and also to the estimate obtained
using the theoretical model of Ref. [1].
In the data shown in Fig. 2,b in Ref. [8], we notice
that in the case where dust is present, the amplitude of
the shock decreases as we move away from the grid.
Such a decrease in the shock amplitude is due to
momentum loss by ions as a result of their absorption on
the grain surfaces and their Coulomb collisions with the
grains and is associated, in particular, with an
attenuation of the ion flux as the ions pass through the
region of the dust. Numerical analysis shows that the
decrease in the shock amplitude and the attenuation of
the ion flux manifest themselves stronger with increase
in the dust size and the ion density.
Fig. 3. Dependence of the perturbation front velocity
(normalized to its value in the absence of dust) on
d0εZ for the data of the experiments[8.
The initial perturbation evolves in such a way that its
front velocity
p
V becomes nearly constant about 1 ms
after it starts propagating through the background
plasma. Fig. 3 shows the dependence of the perturbation
front velocity (normalized to its value in the absence of
dust, 0ε = ) on the parameter d0εZ . For comparison,
we also plot the experimental points (crosses) taken
from Fig. 3 in Ref. [8]. The calculated results are
represented by closed circles. The agreement between
theory and experiment is quite good.
Thus, the ionization source model [10, 11] makes it
possible to describe all the main experimental results on
dust ion-acoustic shock waves.
2. SOLITONS
Here, we describe briefly the main results of the
investigation of the dust ion-acoustic solitons in dusty
plasmas [3-6]. The anomalous dissipation caused by the
charging processes means that the existence of
completely steady-state nonlinear structures is
impossible. In reality, this note is truth for any real
system. However, in dusty plasmas it leads to
qualitatively new results which are related, in particular,
to the necessity to take into account the effect of
adiabatically trapped electrons for the case when the
plasma potential in the soliton is positive. In this case,
the electron density is described by Gurevich
distribution [3]. The main results of the investigations
[3-6] are the following:
(1) The properties of the compressive solitons with
the trapped electrons are very different from those with
not trapped those (Boltzmann electrons). In particular,
the maximum possible amplitude of the soliton with the
trapped electrons is much larger than that of the
“Boltzmann” soliton, while the region of allowable
Mach numbers for the former is much wider than for the
latter. This shows the principal possibility to study
experimentally the role of trapped electrons in the
soliton formation.
(2) A specific feature of ion-acoustic solitons in the
presence of dust is the possibility of existence of
rarefaction solitons, or so-called hybrid solitons [4]. In
this case, the plasma potential in the soliton is negative
and the electron density is described by Boltzmann
distribution.
(3) The evolution of the initial perturbation in the
form of the steady-state soliton in dusty plasmas occurs
in the following manner. The soliton is damped due to
the dissipation originating from the dust particle
charging processes. The speed of the perturbation
decreases. However, at any time the form of the
evolving perturbation is similar to that of the steady-
state soliton corresponding to the Mach number at this
moment of time.
(4) In contrast to conventional solitons, the total
energy and total momentum of a weakly dissipative
soliton decrease in time.
(5) After the interaction of two damped solitons,
each perturbation has the form, which is close to that of
the same soliton perturbation propagating individually
from the beginning (not subjected to the interaction).
This property is the property inherent in solitons. Thus
there is a possibility of the existence of the dust ion
acoustic solitons which are damped and slowed down,
but their form corresponds to the soliton one for the
running value of their speed. They can be called as
“weakly-dissipative solitons”.
Fig. 4 presents the results of simulation [6] of
interaction between a compression and rarefaction
solitons. The dashed lines in Fig. 4 show the envelopes
of the amplitudes of the corresponding perturbations in
the absence of interaction. After the interaction, each of
the solitons restores the shape of the corresponding
soliton propagating without interaction. The grey
vertical lines show the positions of the soliton peaks
after the interaction, while the black vertical lines show
the positions of the corresponding peaks in the absence
of interaction. The perturbations arising between the
solitons after their interaction are residual electrostatic
oscillations, the amplitude of which decreases with
distance between the solitons.
The above five properties are inherent in dusty
plasmas with negatively charged dust. In the case of
positively charged dust grains [5], perturbations are
attenuated more slowly and propagate over longer
distances than in the case of negatively charged grains.
ISSN 1562-6016. ВАНТ. 2012. №6(82) 75
An important point is that, in the case of positively
charged dust grains (in contrast to the case of negatively
charged grains), no rarefaction dust ion-acoustic
solitons can exist.
Fig. 4. Profiles of the dimensionless electrostatic
potential φ at different instants of time t during the
interaction between a weakly dissipative compression
dust ion-acoustic soliton and a counter-propagating
weakly dissipative rarefaction dust ion-acoustic soliton
Dust ion-acoustic solitons can be studied
experimentally by using a double plasma device and Q-
machine [7, 8]. Observations of solitons in ionospheric
and space plasmas can also be used to determine the
sign of the dust grain charge and diagnose the dust grain
substance.
3. NEAR-EARTH AND SPACE PLASMAS,
APPLICATIONS
Here, we present some possibilities of observation of
the dust ion-acoustic shocks and some applications
where their physics can be important.
(1) The idea of the formation of shocks related to
dust charging in active rocket experiments, which use
the scheme of the experiments Fluxus-1 and -2 and
involve the release of some gaseous substance in near-
Earth space, was forwarded in [12]. The source for the
charged particle release in the ionosphere in these
experiments is the generator of high-speed plasma jets.
The shock wave front is associated with the fore
(border)-part of the jet propagating in the plasma of the
ionosphere. Macro (dust) particles appear as a result of
condensation. Drops are charged due to their interaction
with the ambient plasma and the photoelectric effect.
The optimum speeds of the jet are 10 km/s. The
optimum altitudes for such experiments are
500…600 km. The active experiments, where the
shocks in charge-varying dusty plasmas can be
observed, can be helpful to model different physical
phenomena occurring in nature, e.g., in the process of a
large meteoroid impact with the Moon surface [13]. The
evolution of the impact plume can lead to the formation
of shock wave structure associated with an appearance
of charged microparticles which are created in the
process of condensation of the substance of vapor plume
as well as are thrown from the crater and surrounding it
regolith layer.
(2) The presence of dust in cometary coma can
modify shock wave formed as a result of the solar wind
interaction with a comet [14]. The outer shock wave
(bow shock) can be considered as the dust ion-acoustic
shock wave, because it is formed as a result of the
interaction of cometary ions with the solar wind
protons. For dust densities 6
d
10n > cm-3 near the
comet nucleus, charged dust particles influence
drastically the structure of the bow shock front. Its
width is in accordance with the theory of shocks related
to dust particle charging.
(3) The dust ion-acoustic shocks also may find
significant technological applications in, e.g., the so-
called hypersonic aerodynamics. The main difficulties
of hypersonic flight in the atmosphere are associated
with the generation of shock waves, which leads to
heavy mechanical and thermal loads on the structural
components of an aircraft, considerably increases the
resisting forces, and lowers the engine efficiency.
Usually, these negative effects are reduced through an
optimum streamlining of the aircraft. However, a more
promising possibility seems to be changing the
properties of the air surrounding the aircraft. In this
way, the negative effects may be lessened by modifying
the mechanisms for the formation and propagation of
shock waves by plasma methods (such as local heating
of air around the aircraft). However, the dust (aerosol)
that is produced due to condensation from the
surrounding air can, in turn, modify the behavior of the
shock-wave structures. That is why an understanding of
the dissipation mechanisms in shock-wave structures is
of key importance in such situations.
SUMMARY
Thus, an anomalous dissipation originating from the
charging processes results in a possibility of the
existence of a new kind of shocks. The theoretical
ionization source model allows us to describe all the
main results on the dust ion-acoustic shocks obtained in
the laboratory experiments. There is a possibility of the
existence of the dissipative dust ion-acoustic solitons.
The dust ion acoustic nonlinear structures are important
in different real and artificial objects of near-Earth and
space plasmas. Observations of dust ion-acoustic
nonlinear wave structures in ionospheric and space
plasmas can, in particular, be used to determine the sign
of the dust grain charge and diagnose the dust grain
substance.
This work was supported by the Presidium of the
Russian Academy of Sciences (basic research program
76 ISSN 1562-6016. ВАНТ. 2012. №6(82)
№. 22 “Fundamental Problems of Research and
Exploration of the Solar System”), by the Division of Earth
Sciences of the Russian Academy of Sciences (the basic
research program № 5 “Nanoscale particles: conditions of
formation, methods of analysis and recovery from mineral
raw”), and by the Russian Foundation for Basic Research
(project № 12-02-00270-a).
REFERENCES
1. S.I. Popel, M.Y. Yu, V.N. Tsytovich. Shock waves in
plasmas containing variable-charge impurities // Physics
of Plasmas. 1996, v. 3, № 12, p. 4313-4315.
2. S.I. Popel, A.A. Gisko, et al. Shock waves in charge-
varying dusty plasmas and the effect of electromagnetic
radiation // Physics of Plasmas. 2000, v. 7, № 6,
p. 2410-2416.
3. S.I. Popel, A.P. Golub', et al. Weakly-dissipative
dust-ion-acoustic solitons // Physical Review E. 2003,
v. 67, № 5, p. 056402.
4. T.V. osseva, S.I. Popel, et al. Evolution of weakly-
dissipative hybrid dust ion-acoustic solitons in complex
plasmas // Physics of Plasmas. 2009, v. 16, № 9,
p. 093704.
5. T.V. Losseva, S.I. Popel, et al. Weakly dissipative
dust-ion-acoustic solitons in complex plasmas and the
effect of electromagnetic radiation // Physics of
Plasmas. 2012, v. 19, № 1, p. 013703.
6. T.V. Losseva, S.I. Popel, A.P. Golub'. Ion-acoustic
solitons in dusty plasma // Plasma Physics Reports.
2012, v.38, №. 9, p. 729-742.
7. Y. Nakamura, H. Bailung, P.K. Shukla. Observation
of Ion-Acoustic Shocks in a Dusty Plasma // Physical
Review Letters. 1999, v. 83, № 8, p. 1602-1605.
8. Q.-Z. Luo, N. D'Angelo, R.L. Merlino, Experimental
study of shock formation in a dusty plasma // Physics of
Plasmas. 1999, v. 6, p. 3455-3458.
9. Y. Nakamura, A. Sarma. Observation of ion acoustics
solitary waves in a dusty plasma system // Physics of
Plasmas. 2001, v. 8, p. 3921-3926.
10. S.I. Popel, A.P. Golub', et al. Formation of shocks
related to dust particle charging in complex plasmas //
JETP Letters. 2001, v. 73, № 5, p. 223-227.
11. S.I. Popel, A.P. Golub', et al. Evolution of
perturbation in charge-varying dusty plasmas // Physics
of Plasmas. 2001, v. 8, №. 5, p. 1497-1504.
12 S.I. Popel, V.N. Tsytovich. Shocks in space dusty
plasmas // Astrophysics and Space Science. 1999,
v. 264, № 1-4, p. 219-226.
13. I.V. Nemtchinov, V.V. Shuvalov, et al. Transient
atmosphere generated by large meteoroid impacts onto
an atmosphereless cosmic body: gasdynamic and
physical processes // International Journal of Impact
Engineering. 2002, v. 27, № 5, p. 521-534.
14. S.I. Popel, A.A. Gisko. Charged dust and shock
phenomena in the Solar System // Nonlinear Processes
in Geophysics. 2006, v. 13, p. 223-229.
Article received 19.09.12
ПЫЛЕВЫЕ ИОННО-ЗВУКОВЫЕ НЕЛИНЕЙНЫЕ ВОЛНОВЫЕ СТРУКТУРЫ
В УСЛОВИЯХ ОКОЛОЗЕМНОЙ И ЛАБОРАТОРНОЙ ПЛАЗМЫ
С.И. Попель
Представлен обзор по пылевым ионно-звуковым нелинейным волновым структурам в пылевой плазме.
Рассмотрены основные эксперименты по нелинейным волновым структурам в пылевой плазме и приведено
соответствующее теоретическое описание. Обсуждаются возможности существования пылевых ионно-
звуковых нелинейных структур в условиях околоземной и космической плазмы.
ПИЛОВІ ІОННО-ЗВУКОВІ НЕЛІНІЙНІ ХВИЛЬОВІ СТРУКТУРИ
В УМОВАХ НАВКОЛОЗЕМНОЇ І ЛАБОРАТОРНОЇ ПЛАЗМИ
С.І. Попель
Представлено огляд по пиловим іонно-звуковим нелінійним хвильовим структурам у пиловій плазмі.
Розглянуто основні експерименти з нелінійних хвильових структур в пиловій плазмі та наведено
відповідний теоретичний опис. Обговорюються можливості існування пилових іонно-звукових нелінійних
структур в умовах навколоземної і космічної плазми.
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