Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace
The numerical simulations of positive corona at the constant voltage less than streamer mode threshold are carried out. The pulse mode based on photon generation and photo-ionization is obtained, and its simple analytical model is proposed. In addition to axially symmetrical process, it is studied t...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2014
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| Cite this: | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace / O. Bolotov, V. Golota, B. Kadolin, V. Ostroushko, I. Pashchenko, L. Zavada // Вопросы атомной науки и техники. — 2014. — № 6. — С. 195-197. — Бібліогр.: 3 назв. — англ. |
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| author | Bolotov, O. Golota, V. Kadolin, B. Ostroushko, V. Pashchenko, I. Zavada, L. |
| author_facet | Bolotov, O. Golota, V. Kadolin, B. Ostroushko, V. Pashchenko, I. Zavada, L. |
| citation_txt | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace / O. Bolotov, V. Golota, B. Kadolin, V. Ostroushko, I. Pashchenko, L. Zavada // Вопросы атомной науки и техники. — 2014. — № 6. — С. 195-197. — Бібліогр.: 3 назв. — англ. |
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| description | The numerical simulations of positive corona at the constant voltage less than streamer mode threshold are carried out. The pulse mode based on photon generation and photo-ionization is obtained, and its simple analytical model is proposed. In addition to axially symmetrical process, it is studied the instability of the azimuthal harmonic, in the linear approximation, on the same two-dimensional mesh. It is noted the possible connection of the first harmonic instability with the sinuous streamer trace obtained in photo.
Выполнено численное моделирование положительной короны при постоянном напряжении, меньшем, чем порог для стримерного режима. Получен импульсный режим, основанный на генерации фотонов и фотоионизации, и предложена его простая аналитическая модель. Кроме аксиально-симметричного процесса, исследуется неустойчивость азимутальных гармоник в линейном приближении на той же двумерной сетке. Указано на возможную связь неустойчивости первой гармоники с извилистым следом стримера, полученным на фото.
Виконано числове моделювання позитивної корони при постійній напрузі, меншій від порогу для стримерного режиму. Отримано імпульсний режим, який ґрунтується на генерації фотонів та фотоіонізації, і запропоновано його просту аналітичну модель. Крім аксіально-симетричного процесу, досліджується нестійкість азимутальних гармонік у лінійному наближенні на тій же двовимірній мережі. Вказано на можливий зв’язок нестійкості першої гармоніки зі звивистим слідом стримера, отриманим на фото.
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| first_indexed | 2025-12-01T14:12:11Z |
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ISSN 1562-6016. ВАНТ. 2014. №6(94)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, №6. Series: Plasma Physics (20), p. 195-197. 195
AZIMUTHAL INSTABILITY OF THE PULSED POSITIVE GLOW
CORONA AND SINUOUS STREAMER TRACE
O. Bolotov, V. Golota, B. Kadolin, V. Ostroushko, I. Pashchenko, L. Zavada
NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: ostroushko-v@kipt.kharkov.ua
The numerical simulations of positive corona at the constant voltage less than streamer mode threshold are carried
out. The pulse mode based on photon generation and photo-ionization is obtained, and its simple analytical model is
proposed. In addition to axially symmetrical process, it is studied the instability of the azimuthal harmonic, in the linear
approximation, on the same two-dimensional mesh. It is noted the possible connection of the first harmonic instability
with the sinuous streamer trace obtained in photo.
PACS: 52.80.Hc
INTRODUCTION
Even if electrode system and gas properties are axially
symmetric the process development may break an axial-
symmetry. For example, there may take place the flashes
by turn in two near areas of the needle anode surface in
positive corona [1].
The numerical simulations of axially symmetric
processes may be carried out on two-dimension mesh.
Three dimension simulations demand much greater
computer power, and it is possible to simulate only
comparatively simple systems now. But to reveal the
instability of an axially symmetric process with respect to
development of the azimuthally non-uniformity, it is not
necessary to carry out three-dimension simulations.
Assuming the non-uniformity small, one can make
linearization of the nonlinear equations for change of the
charged particle densities with respect to the non-
uniformity. And using the independence of the different
azimuthal harmonics in the linear problem, one can
integrate with time the nonlinear equations for the axially
symmetric process and the linear equations for one or
several azimuthal harmonics, on the same two-dimension
mesh.
Such approach was applied to ‘positive glow corona’
mode, which arises at voltage, greater than one sufficient
for the self-consistent discharge operation, but less than
one necessary for streamer formation. Azimuthal
instability of such mode may lead to the sinuous streamer
trace observed on the photo described below.
1. POSITIVE GLOW CORONA
The processes connected with the positive glow corona
develop mainly near the needle anode. Positive glow
corona accompanies with the pulses of total current and
light intensity. In the paper [2], it is well explained the
physical mechanism of the pulses and of the oscillations,
from which the pulses develop. It is worthy to supplement
the explanation with the simple model. Its analysis helps
to find out the influence of the different factors on the
development of oscillations.
For self-consistency, discharge needs in a source of
electrons and in a mechanism of the source feeding with
aid of the available electrons. In air discharge, the source
may be ionization of oxygen molecules, and the photons
necessary for it may be radiated from the exited states of
nitrogen molecules. In the one-component gas, there are
no states, which energy exceeds the ionization energy, but
it is possible the associative ionization, which lies in the
joining of the exited molecule with another one (not
necessary exited) and the following formation of ion and
free electron. The ionization energy of the joined
molecule is usually less than the ionization energy of the
single simple molecule. In the frames of classical ideas,
this corresponds to the fact that a neutral molecule is or
becomes dipole and attracts to ion. Although the
mentioned three phenomena (excitation of molecules by
electrons, photon radiation, and release of electrons
through photo-ionization) suffice for the discharge self-
consistency, the availability of impact ionization leads to
considerable intensification of electron multiplication and
to decrease of voltage necessary for such discharge.
If voltage value is greater than the self-consistent
discharge threshold then occasional intensification of
ionization leads to increase of positive ion density.
Positive charge weakens the field near anode, and
ionization weakens. Through such degenerative feedback
the discharge can operate in stationary mode, although the
lag of ion charge accumulation from intensive ionization
and the lag of intensive ionization from field
strengthening may promote oscillations with the
characteristic time determined by electron drift to anode.
However, the oscillations may be dumped with relaxation
[3]. Excitation of oscillations may be promoted with the
effect of field strengthening in the space slightly distant
from anode by the positive charge disposed nearer to
anode. The process may be described with the equations
t tpa pa pa a ea ea ea ea ec ecN N f N N N N ,
t tpc pc pc pa pa c ec ec ec ecN N N f N N N .
In them
t is time derivative, the indexes e and p
indicate electrons and positive ions, the indexes a and c
refer to the space nearer to anode and the space slightly
distant from anode,
ea ,
ec ,
pa , and
pc are the
quantities reciprocal to the characteristic time of
removing of relevant particles from relevant spaces,
af
and
cf are ionization frequencies.,
eaN ,
ecN ,
paN , and
pcN are densities. The frequencies
af and
cf are
assumed to be dependent on the charge densities,
( , )a a pa ea pc ecf f N N N N ,
( , )c c pa ea pc ecf f N N N N .
196 ISSN 1562-6016. ВАНТ. 2014. №6(94)
Let us introduce the designations (0)
af and (0)
cf for the
stationary values of the functions ( , )a a cf N N and
( , )c a cf N N , and the designations (1)
aaf , (1)
acf , (1)
caf , and
(1)
ccf for the values of the derivatives with respect to
charge densities at the stationary values of the densities
(the second index at the bottom indicates the space, with
respect to the density in which the derivative is taken). It
may be sought that inequalities (1) 0aaf , (1) 0acf ,
(1) 0caf , and (1) 0ccf are held. They mean that positive
charge weakens the field in the space of its disposition
and in the space nearer to anode and it strengthens the
field father from anode, with relevant consequences for
ionization frequency. A non-stationary solution is
searched in the linear approximation,
0 1 exp( )N N N t , where the indexes 0 and 1
indicate a stationary value and a small perturbation,
respectively, and other indexes are not written. With usual
method, one can get the equations for the stationary
values, the linear equations for the perturbations, and the
conditions of their nonzero solution existence. In
particular, there are held the equalities (0)
c ecf and
0 0 0ea ec ecC N N , where (0)
0 ea aC f . Taking into
account that ion velocity is much less than electron one,
for the perturbation increment one gets
4 3 2
0 1 2 3C C C C ,
where
(1) (1) (1)
1 0 0[ ( ) ]ea ca cc ea aaC N C f f f ,
(1) (1) (0)
2 0 0 0( )ea cc ca aC N C f C f f ,
2 (1) (1) (1) (1)
3 0 0 ( )ea ea aa cc ca acC N C f f f f .
Supposing that ionization coefficient in the space a
achieves the saturation, so that (1)
aaf and (1)
acf are very
small, in comparing with (1)
caf and (1)
ccf , one can obtain
the relationship
3 2/C C (for one very small
increment) and the relationship
3 2 (1) (1)
0 0
(1) (1) (0)
0 0
[ ( )
( )]
ea ca cc
ea cc ca a
C N f f
N f C f f
(for three other increments). If ionization takes place
mainly in the space a , so that (0)
0 ea aC f , then for
the mentioned three increments one gets
3 (1)
0 0ea ca eaC N f . One of them is positive. It
corresponds to monotonous instability. Two other
increments are complex conjugated. They have negative
real part, which means the dumped oscillations. In the
case of small
0C , the very small increment mentioned
above is also positive. It corresponds to the monotonous
instability with very slow development.
2. RESULTS OF NUMERICAL SIMULATIONS
If one is interesting in common features of corona
discharge then it is expedient to consider the space
bounded by prolate ellipsoid of revolution and by
electrodes, hyperboloids of revolution with the same
focuses, and to use hyperboloidal coordinates. Potential in
such space may be obtained with the expansion in terms
of eigenfunctions of relevant problem for the coordinate,
which is constant at hyperboloids. In the linear
approximation, potential and densities of harmonic with
the number m depend on polar coordinates ( , ) near
axis through the factor cos( )m m . It is expedient to
remove relevant factor in hyperboloidal coordinates and
to write the equations for the coefficients at it.
Fig. 1. Positive ion density and field strength with time
step 50 ns; the quantities are logarithmically
distinguished by color (range at the bottom) in intervals
10
…10
cm
and 10
…10
V/cm; relevant time
dependence of total current (within 200 ns) is in right plot
at the top; left plot includes 2 s; anode and cathode are
right and left hyperboloids
The simulations were carried out for the electrode
spacing near 1 mm and constant voltage. The obtained
pulse mode is approaching to the periodic one. In result of
every pulse the perturbation amplitudes for the first
( 1m ) azimuthal harmonics get some factor greater than
unit, which means instability development. A typical look
of the formed positive ion bunches is shown in the Fig. 1.
Also, at successive pulses, the azimuthal harmonic of the
charge in the half-space cos 0 obtains the different
signs by turn, which means divergence of positive ion
bunches in opposite directions.
ISSN 1562-6016. ВАНТ. 2014. №6(94) 197
Fig. 2. Photo of streamers trace near anode with
exposition 2 minutes; anode (oval) and a probable
disposition of positive bunches just before streamer start
(circles) are sketched
Formerly, it was obtained the photo (Fig. 2) of positive
corona in the streamer mode with exposition, during
which the streamers were formed hundreds of thousands
times. According to the photo, every streamer has left
approximately the same trace; its form near anode is
sinuous. So, the streamer, as by inertia, continues to
change the direction of its movement and tends to move
not by the shortest way to cathode, but somewhat
sideway, whereas at atmospheric pressure the usual
mechanical inertia is dumped through collisions. To
explain such streamer behavior, it may be supposed that
before the start of every streamer, at the end of
destruction of previous streamer channel, the field
strength near anode increases up to the value sufficient for
the pulsed positive glow corona mode. In connection with
its azimuthal instability, there is the appointed succession
of the positive bunches situated by turn near anode just
before every streamer start. Namely, the nearest bunch
and the streamer are opposite with respect to symmetry
axis, and the next bunch is opposite to the previous one
(as it is sketched in the Fig. 2). The field in the space
between the formed cathode-directed positively charged
streamer and any positive ion bunch is weakened through
the opposite directions of their field strength. So, the
streamer almost does not develop in the bunch direction
and goes round bunch. Also, there is great probability of
every streamer start from the determined space near
anode, which is distinguished by local field enhancement.
These three things (appointed disposition of bunches,
trying of a streamer to go round bunch, and appointed
space of streamer start) certainly determine the sinuous
streamer trace.
CONCLUSIONS
In the work, the axially symmetric simulations of
positive corona at the constant voltage less than the
streamer mode threshold are carried out, and the linear
stage of the azimuthal harmonic instability development
is studied. The pulsed mode based on photon generation
and photo-ionization is obtained, and the simple analytical
model clarified its mechanism is proposed. It is pointed
out the possible connection of the first harmonic
instability with the sinuous streamers trace observed on
photo.
REFERENCES
1. R. Morrow. The theory of positive glow corona //
Journal of Physics D: Applied Physics. 1997, v. 30,
p. 3099-3114.
2. R.S. Sigmond. The oscillations of the positive glow
corona // Journal de Physique IV France. 1997, v. 7,
p. C4-383–C4-395.
3. O. Bolotov, V. Golota, B. Kadolin, V. Karas,
V. Ostroushko, I. Pashchenko, L. Zavada. Development
of azimuthally not uniform processes in corona discharge
in axially symmetric gap // Problems of Atomic Science
and Technology. Series” Plasma Electronics and New
Methods of Acceleration” (8). 2013, № 4, p. 161-165.
Article received 28.10.2014
АЗИМУТАЛЬНАЯ НЕУСТОЙЧИВОСТЬ ИМПУЛЬСНОЙ ПОЛОЖИТЕЛЬНОЙ КОРОНЫ
И ИЗВИЛИСТЫЙ СЛЕД СТРИМЕРА
О. Болотов, В. Голота, Б. Кадолин, В. Остроушко, И. Пащенко, Л. Завада
Выполнено численное моделирование положительной короны при постоянном напряжении, меньшем, чем
порог для стримерного режима. Получен импульсный режим, основанный на генерации фотонов и
фотоионизации, и предложена его простая аналитическая модель. Кроме аксиально-симметричного процесса,
исследуется неустойчивость азимутальных гармоник в линейном приближении на той же двумерной сетке.
Указано на возможную связь неустойчивости первой гармоники с извилистым следом стримера, полученным
на фото.
АЗИМУТАЛЬНА НЕСТІЙКІСТЬ ІМПУЛЬСНОЇ ПОЗИТИВНОЇ КОРОНИ ТА ЗВИВИСТИЙ СЛІД
СТРИМЕРА
О. Болотов, В. Голота, Б. Кадолін, В. Остроушко, І. Пащенко, Л. Завада
Виконано числове моделювання позитивної корони при постійній напрузі, меншій від порогу для
стримерного режиму. Отримано імпульсний режим, який ґрунтується на генерації фотонів та фотоіонізації, і
запропоновано його просту аналітичну модель. Крім аксіально-симетричного процесу, досліджується
нестійкість азимутальних гармонік у лінійному наближенні на тій же двовимірній мережі. Вказано на
можливий зв’язок нестійкості першої гармоніки зі звивистим слідом стримера, отриманим на фото.
|
| id | nasplib_isofts_kiev_ua-123456789-81939 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T14:12:11Z |
| publishDate | 2014 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bolotov, O. Golota, V. Kadolin, B. Ostroushko, V. Pashchenko, I. Zavada, L. 2015-05-22T17:36:57Z 2015-05-22T17:36:57Z 2014 Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace / O. Bolotov, V. Golota, B. Kadolin, V. Ostroushko, I. Pashchenko, L. Zavada // Вопросы атомной науки и техники. — 2014. — № 6. — С. 195-197. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.80.Hc https://nasplib.isofts.kiev.ua/handle/123456789/81939 The numerical simulations of positive corona at the constant voltage less than streamer mode threshold are carried out. The pulse mode based on photon generation and photo-ionization is obtained, and its simple analytical model is proposed. In addition to axially symmetrical process, it is studied the instability of the azimuthal harmonic, in the linear approximation, on the same two-dimensional mesh. It is noted the possible connection of the first harmonic instability with the sinuous streamer trace obtained in photo. Выполнено численное моделирование положительной короны при постоянном напряжении, меньшем, чем порог для стримерного режима. Получен импульсный режим, основанный на генерации фотонов и фотоионизации, и предложена его простая аналитическая модель. Кроме аксиально-симметричного процесса, исследуется неустойчивость азимутальных гармоник в линейном приближении на той же двумерной сетке. Указано на возможную связь неустойчивости первой гармоники с извилистым следом стримера, полученным на фото. Виконано числове моделювання позитивної корони при постійній напрузі, меншій від порогу для стримерного режиму. Отримано імпульсний режим, який ґрунтується на генерації фотонів та фотоіонізації, і запропоновано його просту аналітичну модель. Крім аксіально-симетричного процесу, досліджується нестійкість азимутальних гармонік у лінійному наближенні на тій же двовимірній мережі. Вказано на можливий зв’язок нестійкості першої гармоніки зі звивистим слідом стримера, отриманим на фото. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Низкотемпературная плазма и плазменные технологии Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace Азимутальная неустойчивость импульсной положительной короны и извилистый след стримера Азимутальна нестійкість імпульсної позитивної корони та звивистий слід стримера Article published earlier |
| spellingShingle | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace Bolotov, O. Golota, V. Kadolin, B. Ostroushko, V. Pashchenko, I. Zavada, L. Низкотемпературная плазма и плазменные технологии |
| title | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace |
| title_alt | Азимутальная неустойчивость импульсной положительной короны и извилистый след стримера Азимутальна нестійкість імпульсної позитивної корони та звивистий слід стримера |
| title_full | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace |
| title_fullStr | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace |
| title_full_unstemmed | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace |
| title_short | Azimuthal instability of the pulsed positive glow corona and sinuous streamer trace |
| title_sort | azimuthal instability of the pulsed positive glow corona and sinuous streamer trace |
| topic | Низкотемпературная плазма и плазменные технологии |
| topic_facet | Низкотемпературная плазма и плазменные технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81939 |
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