22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Dissipative dust solitons in reactive plasma of a spherical glow discharge
G. Sukhinin1,2, S. Sakhapov2, A. Fedoseev2 and S. Novopashin2
1
2
Novosibirsk State University, Pirogova St. 2, 630090 Novosibirsk, Russia
Institute of Thermophysics SB RAS, Lavrentyev Ave., 1, 630090 Novosibirsk, Russia
Abstract: The formation of clouds of dust particles in striations of a spherical discharge
due to coagulation of ethanol dissociation products was observed. Periodically, a dust cloud
experienced sudden explosions, split into two clouds, which moved in the directions of the
cathode and anode at “high” velocity. The velocity of the dust cloud was the exponentially
decaying function of time as in the case of dissipative dust solitory waves.
Keywords: spherical glow discharge in ethanol, clouds of nanoparticles, dust solitons.
1. Intoduction
The synthesis of nanoparticles in low temperature
plasma plays a great role in fundamental research as well
as in plasma technology [1]. The formation and growth of
nano- or micrometer sized particles in the processes of
coagulation occur in reactive plasma of RF discharges [25] and DC discharges [6, 7]. Non-stationary periodic
processes of dust clouds formation in RF discharges were
observed in [4, 5]. When the size of particles reached
some critical value, the cloud of dust particles left its
stationary positions and moved to electrodes. Analogous
processes were observed in a DC discharge [7]. The cloud
of particles was formed near the anode and began to move
like localized dust "bullets" along the discharge tube.
In the paper, we present the observation of an intriguing
quasi periodic process of compact dust clouds formation
in strong striations of a spherical DC glow discharge,
which was discovered and investigated in [8-9]. The
cloud of dust nanoparticles experienced sudden
explosions splitting into two clouds. One of these clouds
moved to the chamber walls as a compact solitary wave.
2. Experimental setup.
Experiments were carried out in a steel cylindrical
vacuum chamber (1) with the height of 60 cm and the
diameter of 50 cm (Fig. 1). An isolated electrode with a
non-isolated tungsten end 5 mm in diameter (2) was
placed in the center of the vacuum chamber. The
discharge burnt between the central anode and the
grounded steel chamber wall (cathode). The gas discharge
was supported by a high-voltage current source (3).
Experiments were carried out under continuous pumping.
Pressure was regulated by the speed of pumping and by
ethanol vapor leakage into the vacuum chamber. Under
certain conditions, several spherical striations (4) around
the central electrode were formed [8].
Half-height of the chamber, a quartz window (5) was
placed and a solid-state laser (6) with 35 mW power and
532 nm wave length was installed. A laser sheet was
formed and introduced into the chamber to illuminate
spherical striations and clouds of dust particles in the
region between the anode and the chamber wall. The
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emission of light from the gas discharge was detected by a
video camera with the help of red, green and blue camera
matrices. The readings of the red and blue pixels of
camera matrices were proportional to the intensity of light
emitted from the discharge. The signal recorded by the
green pixels of the camera matrix was connected both
with the light emission from the discharge itself and with
the laser light scattered from the dust particles trapped in
spherical striations (8). The recordings of "red-blue" and
"green" signals from different parts of the discharge
permits us to observe the evolution of the dust clouds.
Fig.1. Spherical glow discharge experimental setup.
1 - vacuum chamber, 2 - central anode, 3 - high-voltage
current source, 4 - striations, 5 - quartz window, 6 - laser,
7 - cylindrical lens, 8 - clouds of dust nanoparticles, 9 hollow cathode.
3. Results and discussions.
Gas discharge conditions were as follows: discharge
current I d = 15 mA, discharge voltage U d = 500 V,
ethanol pressure p = 0.2 Torr. Spherical striations were
formed several seconds after the discharge was switched
on. After several minutes, the green light regions
corresponding to laser light scattered on dust
nanoparticles began to appear on the edge of the
striations. Green light intensity increased (Fig. 2a) due to
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the growth of a dust cloud until a sudden explosion and
expansion of the cloud.
trapped in the potential wells of spherical striations.
However, the discharge chamber wall is somewhat nonuniform. The non-covered flange ((9) in Fig.1) forms a
Fig. 2: Photos of the striations and the clouds of dust
nanoparticles at five consequent moments: a) t = 0 s, b)
0.04 s, c) 0.08 s, d) 0.12 s, e) 0.40 s. Ethanol pressure p =
0.2 Torr, discharge current I d =15 mA, voltage U d =500
V.
Fig. 3. Radial dependencies of green light (solid lines)
and half the sum of red and blue light (dashed lines)
intensities for moments corresponding to Figs. 2a-2b.
In a glow discharge burning in a high molecular gas, the
molecule dissociation, ionization, formation of radicals
and positive ions due to electron-molecule collisions take
place. These active species lead to complicated plasmachemistry reactions and formation of molecular clusters in
the processes of coagulation. In a low-temperature plasma
of gas discharges, large-scale clusters (dust particles)
acquire large negative charges, Z d >> 1. The charged
particles are acted upon by plasma electrostatic forces.
The radial component of the electric field E r (r) has a nonhomogeneous radial distribution corresponding to a
stratified positive column of the gas discharge [10, 11]. In
strong spherical striations, regions with inverse electric
fields can be formed [10]. These regions are placed near
the strata glow regions and present potential wells for
negatively charged dust particles. Dust particles are
current channel to the anode. Dust nanoparticles are
collected and dust clouds are formed primarily in the
region of the intersection of potential wells of spherical
striations and the current channel. At the same time, the
electric field non-homogeneity produced by the current
channel is rather weak and does not disturb substantially
the positions and the form of spherical striations.
In Figs.2a-2e, the photos of the central anode lighting
and three striations with the clouds of dust nanoparticles
are presented for five successive times. Fig. 2a
corresponds to a stable regime with three dust clouds,
which levitated on the cathode side edge of each striation.
The number density N d and the charge number Z d , of dust
nanoparticle increase with time. The large value of charge
number density N d ·Z d begins to disturb the distribution of
the electric field in spherical striations, the potential well
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for dust particles becomes shallower, and when some
critical value of N d ·Z d is reached, the potential well
disappears. The cloud cannot be trapped in the striation
anymore. The dust cloud explodes and splits into two
approximately equal parts (figs 2b, 3b), which fly away in
opposite directions at "high" velocities. The internal part
moves toward the anode side (from the third striation to
the second one), reflects from the second striation, and
returns to its initial position in the third striation. The
external part of the cloud moves toward the cathode side.
Fig. 4. Time dependence of the dust cloud position R d for
several runs.
(at the edge of external striation). Fig.4 presents the radial
positions R d (t) of clouds peaks after the cloud explosion.
It is seen that R d (t) is a rather smooth curve unique for all
individual clouds, which can be approximated by the
function R d (t) = (R 0 + V 0 /γ) - V 0 exp(-γ t)/γ , where R 0 ≈
6.82 ± 0.02 cm, V 0 ≈ 16.12 ± 0.2 cm/s, and γ ≈ 3.2312 ±
0.2 s-1 is the value of velocity damping rate. The value R 0
≈ 6.82 cm corresponds to the position of the cloud
formation in the external striation. With the help of
numerical differentiation of radial positions with respect
to time we obtained the velocity of dust clouds (points in
Fig.5). Differentiating the fitting curve R d (t) with respect
to time we can obtain a smoothed time dependence of the
velocity of clouds V d (t) ≈ V 0 exp((-γ t)), and the value V 0
≈ 16.12 cm/s is very close to the maximum velocity value
V max . (See Fig.5: the time dependence of velocity for all
seven dust clouds is shown by a solid line).
There is one interesting peculiarity. After each
explosion, the external clouds began to move to the
cathode side and immediately (in 0.04 s) gained the
velocity with the same maximum value V max , which can
be estimated in the following way. The dust nanoparticles
are captured in a potential well of strong spherical
striations. The number of dust particles in cloud N and
their charge number Z d increase with time. The cloud is
compressed; the mean inter-particle distance Δ decreases
with the increase of the number N of dust nanoparticles
captured in a potential well. The total potential energy E t
of inter-particle interaction in a cloud accumulates in the
dust cloud. When the value Z d N d acquires some critical
value, the potential well in the striation confining the
cloud disappears, and the cloud explodes. Just before the
moment of explosion, the potential energy of the cloud
can be estimated as
(
)
Et = Nq e02 Z d2 / ∆ exp(−∆ / λi ) ,
Fig. 5. Time dependence of the dust cloud velocity V d for
several runs.
Figs. 3a-3e present the radial distribution of green light
intensity at five time moments, which correspond to the
regimes presented in figs 2a-2e. It is seen that while the
external cloud of nanoparticles fly away, a new portion of
dust nanoparticles begins to collect in the striation in the
same position. It means that the formation of clouds of
dust nanoparticles in our conditions is a recurrent process.
The process repeated quasi periodically with the time τ ~
20-40 s.
We have analyzed the dynamics of the clouds
movement toward the cathode side for seven consecutive
series of cloud explosions. Each explosion occurred at a
different time onset but in the same radial position R d (0)
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(1)
where λ i is ion Debye screening length. We take into
account the interaction of the dust particle only with the
nearest q neighbors in the dust cloud. In dusty liquids q =
6 – 12. The critical value of Δ has the order of the ion
Debye screening length λ i (dust particles in the cloud
cannot be compressed more due to the rapid increase of
repulsive inter-particle forces for Δ ≤ λ i ). After the
explosion, the cloud of nanoparticles splits into two
moving clouds, and the accumulated potential energy is
released into the kinetic energy E k of all N dust
nanoparticles moving with equal velocities: E k = N
M d V2/2. Here M d = (4/3)πR d 3 ρ d is a dust particle mass,
R d is the dust particle radius, ρ d ~ 1 g/cm3 is the dust
particle mass density. The velocities of the internal and
external clouds are assumed to be approximately equal to
each other. Thus, we can estimate the initial velocity
V max :
[(
)
Vmax = 3qe02 Z d2 / 4pRd3 ρ d ∆ exp(−∆ / λi )
]
1/ 2
. (2)
For estimation, we take the following values for plasma
parameters: electron temperature in ethanol plasma Te ≈ 1
eV, particle radius R d ≈ 0.1 μm, ion Debye screening
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length λi ≈ 100 μm, the mean inter-particle distance Δ ≈
100 μm. We also take into account the fact that a
dimensionless nanoparticle charge z = e 0 2 Zd/(R d T e ) has
the value of about z ≈ 1 for regimes when the ratio of the
mean ion free path to the Debye length has the order li/λ i
≈ 5 [12]. Thus, we see that the value of initial velocity can
be equal to the measured value Vmax ≈ 15 cm/s only for
dust particles with rather small radii, R d ≤ 100 nm, and the
mean particle charge in the cloud has the value of around
Z d ≈ 100. This conclusion confirms the fact that in the
experiments we could not distinguish particular particles
illuminating them by laser light with λ = 532 nm but
observed the whole cloud of particles.
The time dependence of dust cloud velocity Vd(t) after
the explosion is determined by the forces acting on dust
nanoparticles in the moving cloud: the gravity force Fg,
the electric force Fel, the neutral drag force Fnd, and the
ion drag force Fid:
(3)
M d dV / dt = Feff = Fg + Fel + Fnd + Fid .
The gravity force Fg = M d ·g acts in the perpendicular
direction to the cloud movement. For nanoparticles with
R d ≤ 0.1 μm, it is two orders less than the typical values of
other forces. Moreover, for such small particles neither
the electrostatic force Fel = e 0 Z d E r (r) nor the ion drag
force Fnd = - αFel, which is proportional to the electric
field but has the direction opposite to Fel [13], can explain
the exponential decrease of dust cloud velocity. E r (r) is
the electric field of a spherical stratified discharge. The
exponentially time decaying velocity can be obtained for
an effective force proportional to the dust cloud velocity,
F eff ~ - M d γV. The only force proportional to the particle
velocity is the Epstein’s neutral drag force [14]:
Fnd = −(8π / 3)dRd2 N n mnVTnVd ,
(4)
where δ ≈ 1.4, Nn ≈ 0.7·1016 cm-3 is the neutral gas density
for the present condition, the mn and V Tn (≈ 3·105 cm/s)
are the mass and the thermal velocity of neutral
molecules. As follows from the motion equation (3), if a
cloud moves only under the action of the neutral drag
force, the cloud velocity has exponential time
dependence: Vd(t) ≈ V max ·exp(-γ epsh ·t) with the value of
Epstein’s damping rate equal to γ epsh ≈ 150 s-1 , which is
much greater than the value obtained in the experiment, γ
≈ 3.23 s-1. This discrepancy can be explained by the
action of an effective force, Feff(r), in which the
electrostatic force Fel = e 0 Z d E r and the ion drag force F id
inside the moving dust cloud are determined by an
effective electric field E eff .
The effective electric field E eff formed inside the dust
cloud confines negatively charged dust particles and
trapped ions. This should be a collective phenomenon: the
moving dust cloud can be regarded as a solitory wave
(soliton) propagating in a low-pressure low-temperature
inhomogeneous plasma. Solitons are known to be able to
retain their shapes due to a concurrence between a
dispersion-induced broadening and a nonlinear wave
steepening. This concurrence leads to the formation of
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some effective electric field inside the moving narrow
dust cloud that confines dust particles, prevents them
from dispersing, and decreases the damping of the cloud
velocity. It should be mentioned that there have been
several experimental studies on the propagation of
nonlinear dust acoustic solitary waves [15, 16], which
showed an unexpectedly low damping rate of soliton
velocity.
4. Conclusion.
An intriguing phenomenon was observed in a stratified
positive column of a spherical glow discharge in ethanol.
The dust nanoparticles grew in the plasma itself in the
processes of coagulation of ethanol dissociation products.
The negatively charged particles were captured in certain
regions of electric potential wells. Periodically, the cloud
of dust nanoparticles, which formed on the external
striation, exploded. The dust cloud splits into two moving
clouds. The cloud moved through the gas in the direction
from the discharge center decelerating surprisingly
slowly. Its velocity was an exponentially decaying
function of time, with the damping rate much smaller than
the Epstein's damping rate as it was observed in the case
of dissipative solitory waves.
5. Acknowledgements
This research was funded by Russian Scientific Foundation, Project No 14-19-01379.
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