Numerical simulations of cathode directed streamer propagation in electronegative gases
The numerical simulations are carried out for the cathode directed streamer propagation at the quasi-stationary stage, far from electrodes, and at the stage of going out to cathode, in the gases with the different combinations of three-body and dissociative attachment. The typical features of the...
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| Zitieren: | Numerical simulations of cathode directed streamer propagation in electronegative gases / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Вопросы атомной науки и техники. — 2018. — № 4. — С. 127-175. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1473532019-02-15T01:23:50Z Numerical simulations of cathode directed streamer propagation in electronegative gases Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Плазменно-пучковый разряд, газовый разряд и плазмохимия The numerical simulations are carried out for the cathode directed streamer propagation at the quasi-stationary stage, far from electrodes, and at the stage of going out to cathode, in the gases with the different combinations of three-body and dissociative attachment. The typical features of the process in presence of intensive attachment are revealed. Виконано числове моделювання поширення катодоспрямованого стримера на квазістаціонарній стадії, далеко від електродів, та на стадії виходу на катод у газах з різним поєднанням трьохтільного та дисоціативного приставання. Виявлено типові риси процесу за наявності інтенсивного приставання. Выполнено численное моделирование распространения катодонаправленного стримера на квазистационарной стадии, вдали от электродов и на стадии выхода на катод в газах с разным сочетанием трехтельного и диссоциативного прилипания. Выявлены типичные черты процесса при наличии интенсивного прилипания. 2018 Article Numerical simulations of cathode directed streamer propagation in electronegative gases / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Вопросы атомной науки и техники. — 2018. — № 4. — С. 127-175. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.80.Hc http://dspace.nbuv.gov.ua/handle/123456789/147353 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Numerical simulations of cathode directed streamer propagation in electronegative gases Вопросы атомной науки и техники |
| description |
The numerical simulations are carried out for the cathode directed streamer propagation at the quasi-stationary
stage, far from electrodes, and at the stage of going out to cathode, in the gases with the different combinations of
three-body and dissociative attachment. The typical features of the process in presence of intensive attachment are
revealed. |
| format |
Article |
| author |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_facet |
Bolotov, O. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_sort |
Bolotov, O. |
| title |
Numerical simulations of cathode directed streamer propagation in electronegative gases |
| title_short |
Numerical simulations of cathode directed streamer propagation in electronegative gases |
| title_full |
Numerical simulations of cathode directed streamer propagation in electronegative gases |
| title_fullStr |
Numerical simulations of cathode directed streamer propagation in electronegative gases |
| title_full_unstemmed |
Numerical simulations of cathode directed streamer propagation in electronegative gases |
| title_sort |
numerical simulations of cathode directed streamer propagation in electronegative gases |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2018 |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147353 |
| citation_txt |
Numerical simulations of cathode directed streamer propagation in electronegative gases / O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada // Вопросы атомной науки и техники. — 2018. — № 4. — С. 127-175. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №4(116) 172
NUMERICAL SIMULATIONS OF CATHODE DIRECTED STREAMER
PROPAGATION IN ELECTRONEGATIVE GASES
O. Bolotov, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran, L. Zavada
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: ostroushko-v@kipt.kharkov.ua
The numerical simulations are carried out for the cathode directed streamer propagation at the quasi-stationary
stage, far from electrodes, and at the stage of going out to cathode, in the gases with the different combinations of
three-body and dissociative attachment. The typical features of the process in presence of intensive attachment are
revealed.
PACS: 52.80.Hc
INTRODUCTION
At the constant applied voltage, the positive corona
at atmospheric pressure usually operates in pulse mode,
through the cathode directed streamers. Streamer is ion-
ization wave, which left behind the ionized channel with
comparatively small transverse dimension. Positive
streamer corona is used for realization of non-
equilibrium plasma-chemistry processes. The energy
expense per ozone molecule forming in positive corona
is usually less than in negative corona. Positive streamer
propagation is widely studied [1] and its study is con-
tinued [2, 3]. In the present work, the numerical simula-
tions of the cathode directed streamer propagation in the
electronegative gases at the constant voltage applied to
the discharge gap are carried out. To reveal clearer the
peculiarities of the propagation caused by attachment,
the numerical simulations of the process are carried out
with the artificially overstated values of attachment re-
action constants.
1. SIMULATION MODEL
The simulations are carried out in assumption of ax-
ial symmetry for the gap between the plane electrodes.
The main details of the simulation model are identical to
ones in [4]. In particular, there are taken into account
drift and diffusion of electrons and ions, positive and
negative, and the processes of impact ionization, at-
tachment, electron-ion and ion-ion recombination. In the
simulations of the quasi-stationary propagation, the av-
erage value of the longitudinal coordinate of electrons in
the simulation domain is kept constant, with aid of mesh
transposition on some its part at each time step, with
corresponding redistribution of particles between cells.
In the atmospheric air the electro-negativity is con-
nected with presence of oxygen, and two different ways
of negative ion forming are essential: dissociative at-
tachment, e + O2 → O + O−, and three-body attachment,
e + O2 + M → O2
− + M, where M is O2 or N2. The simu-
lations are carried out for the case of their ratio corre-
sponding to atmospheric air and for the case of purely
three-body attachment, with the overstated values of the
reaction constants, in both cases. The large attachment
rate leads to the considerable spatial variation of the
charged particle densities on the small length of the
streamer channel, which helps to reveal the attachment
influence in the simulations for the discharge gap of
comparatively small length.
The increase of attachment reaction constant for all
field strength values by multiplication with the same
factor leads to some increase of the strength value cor-
responding to the equilibrium between ionization and
attachment. The dependence of dissociative attachment
intensity on the field strength E is approximately char-
acterized by the factor exp(−E0/E). The same factor, but
with greater value of E0, is characteristic for the intensi-
ty of ionization reaction, e + O2 → e + e + O2
+. Depend-
ence of ionization and attachment constants on the field
strength through the factors exp(−E0/E) with the differ-
ent E0 makes the increase of the equilibrium strength
value comparatively small, approximately logarithmic
with respect to the multiplication factor mentioned
above.
The process of the streamer propagation is based on
avalanche multiplication through the impact ionization.
The seed electrons for the avalanches appear mainly
through ionization by photons radiated from the ioniza-
tion zone in front of the streamer head. The account of
photon transport between the different cells of calcula-
tion mesh requires a considerable calculation time. In
the numerical simulations of streamers, the photo-
ionization is often replaced with the given, very small,
initial electron density. Such replacement usually does
not lead to the considerable change of the streamer
characteristics. But in presence of intensive attachment,
the initial electron density quickly decreases, which
makes unnatural non-stationary contribution to the sim-
ulations. At the present simulations, for the role of seed
electron source, a photo-ionization is chosen, but calcu-
lations of the photon transport between the cells are not
carried out, and the rate of electron appearance is taken
homogeneous and proportional to the total photon radia-
tion rate in the simulation domain.
The streamer propagation is realized through the
ionization wave, which left behind the high conductive
plasma channel. Due to high conductivity of the chan-
nel, the comparatively weak external field (that field,
which is in discharge gap in absence of space charge in
it) through the charge redistribution in the channel caus-
es the field in front of the streamer head, which is suffi-
ciently strong to support intensive ionization there. The
length of the well conducting part of streamer channel is
bounded with the product of the streamer velocity and
the characteristic time of free electron motion before
attachment.
A positive streamer tendency to be transversely lo-
calized is connected with opposition of the directions of
the electron flow and the streamer propagation. Ava-
lanche multiplication begins far from the streamer front,
ISSN 1562-6016. ВАНТ. 2018. №4(116) 173
electron density there is small, and to increase it from
the initial value 105…106 cm−3 given with photo-
ionization to the final value 1014…1015 cm−3 natural for
streamer it is necessary approximately 30 successive
acts of electron number doubling. The difference be-
tween the values of ionization coefficient α for the
points ahead of streamer at the symmetry axis and at the
nonzero distance from it is small, but the proportionality
of the obtained electron density to the quantity
exp(∫αdl) (where integral is taken over the electron drift
path) leads to the considerable preference of one direc-
tion of avalanche development over other, with relevant
consequences for successive ionization results at the
different distance from the symmetry axis.
But for the preference of longitudinal propagation
with respect to radial one, the ratio of the radial and
longitudinal components of the field strength should be
small in all space of intensive ionization. If the attach-
ment frequency is very large then the length of the high
conductive channel part behind the streamer head is not
much more than the transverse streamer dimension. The
charge redistribution in such channel cannot make the
mentioned ratio of the strength components small at the
streamer head side, where ionization is intensive, and
so, it cannot prevent the considerable tendency to the
radial propagation of the ionization wave. At such cir-
cumstances the streamer may be realized in narrow
voltage range. At the lower limit of the range the field in
front of streamer head (even with taking into account of
field enhancement due to polarization of charge on the
channel) is not strong enough to support intensive ioni-
zation, whereas at the upper limit of the range the field
in the considerable part of discharge gap is sufficiently
strong to support intensive ionization even without aid
of the charge in channel, and the ionization wave in
simulations becomes similar to plane one. The range is
narrow because the conductive channel is short and the
field enhancement in front of streamer with aid of
charge polarization in such channel is comparatively
weak. That is, the strong attachment is not favorable for
the transverse localization of ionization wave. On the
other hand, the streamer tendency to be transversely
localized is stronger for more sharp dependence of ioni-
zation coefficient on the electric field strength. It may
be obtained with replacing of the factor exp(−E0/E) on
the factor exp[−(E0/E)p] with p>1. The use of such re-
placing helps to reveal some features of the considered
process in the simulations for the comparatively small
simulation domain. The simulations are carried out for
the simulation domain width 1 mm.
2. SIMULATION RESULTS
In the Fig. 1, for the quasi-stationary streamer prop-
agation the electron density distributions typical for the
cases of strong attachment with the ratio of dissociative
and three-body attachment typical for atmospheric air
(above) and with purely three-body attachment (below)
are shown. The scale (from blue to red, at the top) is
logarithmic, (109…1015) cm−3, the values out of the
range are replaced with limits.
Fig. 1. Electron density distributions typical for the cas-
es of strong attachment with the ratio of dissociative
and three-body attachment typical for atmospheric air
(above) and with purely three-body attachment (below)
Fig. 2. Distributions of electron and positive ion
densities, electric field strength, and potential
in the right half of the simulation domain
at the voltage near the cut-off
The contribution of the dissociative attachment to
the process kinetics is relatively large in the interval of
field strength values, where the dissociative attachment
intensity is large and the ionization intensity is small.
Such strength values are characteristic for the outlying
part of ionization zone and for the side part of streamer
channel beginning. But if the streamer propagates in gas
with intensive purely three-body attachment then the
attachment rate is larger nearer to the symmetry axis of
the streamer channel, whereas in the side part of the
streamer channel beginning, where the field strength is
larger, three-body attachment rate is comparatively
small. So, the decrease of the ratio of dissociative and
three-body attachment constants leads to the decrease of
ISSN 1562-6016. ВАНТ. 2018. №4(116) 174
relative contribution of the near-axis part of streamer
channel to the total channel conductivity.
Both cases in the Fig. 1 illustrate the possibility of
the stationary streamer propagation in the unbounded
space with an attaching gas and uniform external field,
which detailed substantiation is in [5]. In the case of
intensive attachment, the electron density distribution
corresponds to the streamer model described in [6].
Fig. 3. Change of electron density distribution during
streamer approach to cathode in the gas
with the enhanced dissociative and three-body
attachment (time interval 0.6 ns)
The distributions in the Fig. 1 are related to the case
when the applied voltage is not too near to one mini-
mum sufficient for the possibility of streamer propaga-
tion. For the voltage values near the cut-off of streamer
mode, the distributions are somewhat different. In the
Fig. 2, for such voltage in the gas with the attachment
constant enhanced by the factor 100 with respect to one
in atmospheric air, the distributions of electron and
positive ion densities, electric field strength, and poten-
tial in the right half of simulation domain are shown.
The scale is logarithmic for densities, (109…1015) cm−3,
and strength, (104…106) V/cm, and linear for potential
(with the reduced set of colors). The corresponding
form of the streamer head is connected with the consid-
erable decrease of the streamer propagation velocity for
the voltage value approaching to the cut-off, and it is
observed not only for the electronegative gases. This
velocity decrease leads to increase of the time, during
which the relevant portion of gas motionless in the la-
boratory frame of reference is subjected to intensive
impact ionization. At forepart of streamer head near the
axis, the comparatively small space with large positive
charge density is formed. This charge causes the strong
field in the near space, and positive ions in such field
have velocities not much less than the streamer propaga-
tion velocity.
Some variation of positive ion density observed in
the Fig. 2 is connected with the artificial oscillations,
which arise in the simulations of quasi-stationary prop-
agation and dump very slowly for the voltage near cut-
off. They consist of the longitudinal propagation of
comparatively small space with large positive charge
density at forepart of streamer head near the axis and the
propagation of annular ionization wave along the front
of streamer head, by turn. The conditions for the next
cycle are recovered, in particular, due to mesh transposi-
tion with somewhat artificial keeping of the potential
difference on simulation domain length constant, which
is used in the simulations of the quasi-stationary propa-
gation. And if one begins the simulations of the stream-
er approach to cathode in the laboratory frame of refer-
ence (with cancellation of mesh transposition) from the
distributions obtained in the simulations of the quasi-
stationary propagation then the time derivatives of the
different quantities are nonzero at the beginning. In par-
ticular, the propagation of the cathode directed streamer
with the positively charged channel in the bounded gap
is accompanied with the increase of positive charge in
the gap, leading to the field enhancement near the
streamer head and to the enhancement of ionization
there. In the simulations of quasi-stationary propagation
such increase is absent, through the simulation domain
displacement. Relative effect of ionization enhancement
most of all reveals in space, where excess of ionization
over attachment is small, in particular, in the side of
streamer head, where the angle between the perpendicu-
lar to the constant electron density surface and the
symmetry axis direction is near to right angle. And from
the side part of streamer head the annular ionization
wave is developed. The field strength in front of this
wave is determined, mainly, by the charge on the length
approximately equal to transverse streamer dimension.
The next similar wave may be formed due to the charge
accumulation in the neighboring space during the longi-
tudinal streamer propagation. But if this propagation is
accompanied with the sufficiently quick increase of
transverse streamer dimension then the field strength
near the side part of streamer head quickly becomes
insufficient for the next transverse ionization wave de-
velopment. In the simulations, two consecutive annular
ionization waves are obtained.
The streamer going out to cathode in gas without
very large attachment is described in [7] with some de-
tails. When the streamer head approaches to the cath-
ode, the considerable decrease of the streamer propaga-
tion velocity takes place, which is followed by the drift
of positive ions to the cathode and the propagation of
ionization wave in the approximately radial direction.
The going out of the considerable amount of positive
ions to cathode is accompanied with the considerable
potential redistribution in the conductive part of stream-
er channel, stopping of the ionization wave propagation,
and decay of the intensive ionization process. In the
case of large attachment reaction constants, the phe-
nomena based on the electron movement away from the
ISSN 1562-6016. ВАНТ. 2018. №4(116) 175
cathode are suppressed. But in the case of purely three-
body attachment the free electrons obtained in the radial
ionization wave can move far from cathode at such dis-
tance from the axis, which exceeds the channel radius.
In the non-conductive part of streamer channel (if
three-body attachment is strong), the new ionization
waves can propagate already during the propagation of
the main streamer. The main source of seed electrons
for them is photo-ionization. These waves start from the
spaces with the enlarged field strength near the non-
uniformities of charge distribution. Such ionization
wave development is observed in the Fig. 3, where the
electron density distribution with time intervals 0.6 ns
during streamer approach to cathode in gas with the
enhanced dissociative and three-body attachment is
shown.
CONCLUSIONS
The large attachment rate leads to the considerable
spatial variation of the charged particle densities on the
small length of the streamer channel. The length of the
well conducting part of streamer channel is bounded
with the product of the streamer velocity and the charac-
teristic time of free electron motion before attachment.
In presence of intensive attachment, the cathode di-
rected streamer may be realized in narrow voltage
range. The decrease of the ratio of dissociative and
three-body attachment constants leads to the decrease of
relative contribution of the near-axis part of streamer
channel to the total channel conductivity. The form of
streamer head for the voltage values approaching to the
cut-off of streamer mode is connected with the consid-
erable decrease of the streamer propagation velocity.
Already during the propagation of the main streamer,
the new ionization waves can be developed.
REFERENCES
1. Yu.P. Raizer. Gas discharge physics. Springer:
“Verlag”. 1991.
2. O.V. Bolotov, V.I. Golota, B.B. Kadolin, et al. Simi-
larity laws for cathode-directed streamers in gaps
with an inhomogeneous field at elevated air pressure
// Plasma Physics Reports. 2010, v. 36, № 11,
p. 1000-1011.
3. O.V. Manuilenko, V.I. Golota. Computer simulation
of positive streamer dynamics in strongly non-
uniform electric fields in air. Effect of applied volt-
age on a streamer velocity for different needle radii
// Problems of Atomic Science and Technology. Se-
ries “Plasma Physics”. 2014, № 6, p. 187-190.
4. O. Bolotov, B. Kadolin, S. Mankovskyi, et al. Nu-
merical simulations of quasi-stationary streamer
propagation // Problems of Atomic Science and
Technology. Series “Nuclear Physics Investiga-
tions”. 2016, № 5, p. 121-125.
5. M.I. Dyakonov, V.Yu. Kachorovsky. Stationary
propagation of streamers in electronegative gases //
Sov. Phys. JETP. 1990, v. 71, № 3, p. 498-505.
6. G.A. Dawson, W.P. Winn. A model for streamer
propagation // Zeitschrift für Physik. 1965, v. 183,
№ 2, p. 159-171.
7. O. Bolotov, B. Kadolin, S. Mankovskyi, et al. Final
stage of cathode directed streamer propagation //
Problems of Atomic Science and Technology. Series
“Plasma Physics”. 2016, № 6, p. 252-254.
Article received 31.05.2018
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ РАСПРОСТРАНЕНИЯ КАТОДОНАПРАВЛЕННОГО
СТРИМЕРА В ЭЛЕКТРОНЕГАТИВНЫХ ГАЗАХ
О. Болотов, Б. Кадолин, С. Маньковский, В. Остроушко, И. Пащенко, Г. Таран, Л. Завада
Выполнено численное моделирование распространения катодонаправленного стримера на квазистацио-
нарной стадии, вдали от электродов и на стадии выхода на катод в газах с разным сочетанием трехтельного
и диссоциативного прилипания. Выявлены типичные черты процесса при наличии интенсивного прилипа-
ния.
ЧИСЛОВЕ МОДЕЛЮВАННЯ ПОШИРЕННЯ КАТОДОСПРЯМОВАНОГО
СТРИМЕРА В ЕЛЕКТРОНЕГАТИВНИХ ГАЗАХ
О. Болотов, Б. Кадолін, С. Маньковський, В. Остроушко, І. Пащенко, Г. Таран, Л. Завада
Виконано числове моделювання поширення катодоспрямованого стримера на квазістаціонарній стадії,
далеко від електродів, та на стадії виходу на катод у газах з різним поєднанням трьохтільного та дисоціати-
вного приставання. Виявлено типові риси процесу за наявності інтенсивного приставання.
E-mail: ostroushko-v@kipt.kharkov.ua
INTRODUCTION
1. SIMULATION MODEL
2. SIMULATION RESULTS
CONCLUSIONS
REFERENCES
|