Dissipative structure in the glow discharge
Possibility description of the current cathode spot as dissipative structure caused by distributive feedback is proposed. Two stationary steady states can be associated with normal current density in glow regime and failure of current. Non-steady stationary state can be associated with dark discharg...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Dissipative structure in the glow discharge / O.P. Ponomaryov, I.O. Anisimov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 180-182. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1109752017-01-08T03:02:51Z Dissipative structure in the glow discharge Ponomaryov, O.P. Anisimov, I.O. Low temperature plasma and plasma technologies Possibility description of the current cathode spot as dissipative structure caused by distributive feedback is proposed. Two stationary steady states can be associated with normal current density in glow regime and failure of current. Non-steady stationary state can be associated with dark discharge. Numerical computer model of non-stationary discharge is presented. Розглянута можливість описати катодну пляму жевріючого розряду в нормальному режимі як дисипативну структуру обумовлену розподіленим зворотнім зв’язком. Два стійкі стаціонарні стани при цьому можна трактувати як випадок нормальної густини струму в режимі жевріючого розряду та випадок відсутності струму. Нестійкому стаціонарному стану при цьому відповідає темний розряд. Запропонована числова модель для розрахунку нестаціонарного стану розряду. Рассмотрена возможность описания катодного пятна тлеющего разряда в нормальном режиме как диссипативной структуры, обусловленной распределенной обратной связью. Два устойчивых стационарных состояния при этом можно связать с нормальной плотностью тока в режиме тлеющего разряда и с отсутствием тока. Неустойчивому стационарному состоянию при этом соответствует темный разряд. Предложен численный алгоритм для расчета нестационарного состояния разряда. 2008 Article Dissipative structure in the glow discharge / O.P. Ponomaryov, I.O. Anisimov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 180-182. — Бібліогр.: 13 назв. — англ. 1562-6016 PACS: 52.65.Kj, 52.80.Hc http://dspace.nbuv.gov.ua/handle/123456789/110975 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies |
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Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies Ponomaryov, O.P. Anisimov, I.O. Dissipative structure in the glow discharge Вопросы атомной науки и техники |
| description |
Possibility description of the current cathode spot as dissipative structure caused by distributive feedback is proposed. Two stationary steady states can be associated with normal current density in glow regime and failure of current. Non-steady stationary state can be associated with dark discharge. Numerical computer model of non-stationary discharge is presented. |
| format |
Article |
| author |
Ponomaryov, O.P. Anisimov, I.O. |
| author_facet |
Ponomaryov, O.P. Anisimov, I.O. |
| author_sort |
Ponomaryov, O.P. |
| title |
Dissipative structure in the glow discharge |
| title_short |
Dissipative structure in the glow discharge |
| title_full |
Dissipative structure in the glow discharge |
| title_fullStr |
Dissipative structure in the glow discharge |
| title_full_unstemmed |
Dissipative structure in the glow discharge |
| title_sort |
dissipative structure in the glow discharge |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Low temperature plasma and plasma technologies |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/110975 |
| citation_txt |
Dissipative structure in the glow discharge / O.P. Ponomaryov, I.O. Anisimov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 180-182. — Бібліогр.: 13 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT ponomaryovop dissipativestructureintheglowdischarge AT anisimovio dissipativestructureintheglowdischarge |
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2025-07-08T01:26:51Z |
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2025-07-08T01:26:51Z |
| _version_ |
1837040163420635136 |
| fulltext |
DISSIPATIVE STRUCTURE IN THE GLOW DISCHARGE
O.P. Ponomaryov, I.O. Anisimov
Taras Shevchenko National University of Kyiv, Faculty of Radio Physics, Kyiv, Ukraine,
E-mail: alex.ponomaryov@gmail.com
Possibility description of the current cathode spot as dissipative structure caused by distributive feedback is
proposed. Two stationary steady states can be associated with normal current density in glow regime and failure of
current. Non-steady stationary state can be associated with dark discharge. Numerical computer model of non-stationary
discharge is presented.
PACS: 52.65.Kj, 52.80.Hc
1. INTRODUCTION
Interpretation of the normal current density effect in
the glow discharge [1] attracts attention in the gas
discharge physics for the long time. In the normal mode
of the glow discharge in some range of currents the
discharge voltage remains constant, and current growth
occurs due to the increase of the cathode spot area, while
the current density remains invariable. In spite of the fact
that interpretation of this effect was already proposed [2-
4], discussion of its details is still relevant [5-6]. In this
work we try to discuss this effect in terms of synergetics:
the cathode spot in the normal regime is treated as the
dissipative structure caused by distributed feedback. The
simulation algorithm of the non-steady state of the
discharge burning in hydrodynamic approach is proposed
for checkout of this idea.
2. CATHODE SPOT IN NORMAL MODE
AS A DISSIPATIVE STRUCTURE
The above effect looks similar to the dissipative
structures caused by the distributed feedback that are well
known in synergetics (barretter, heat source in a mesh
with intermixing and others) [7].
Really, the cathode spot area is stable against the
small fluctuations, as well as the high-resistance area
length in a barretter and the heat source area, thus its
shape can vary. The distributed feedback can be caused
by the series resistor connected with a discharge gap to
the voltage source. In fact, the current density variations
in any point of the cathode spot move to the total current
change and accordingly the discharge voltage change. If
the analogy with barretter is correct, that establishing of
the discharge spot takes place via propagation of the
running front type auto-wave. Velocity of this wave goes
to zero when the spot area comes to its equilibrium value.
Nonlinearity and non-locality of the discharge makes
its analytical description too complicate. So it looks
reasonable to use computer simulation for its study. The
first step is to create 1D non-steady code allowing to
study processes of the glow discharge establishment. The
next step needs 2D code.
3. THE BASIC EQUATIONS
AND COMPUTATION PROCEDURE
In frameworks of the diffusion-drift approach the
state of discharge plasma is featured by the continuity
equations for electrons and ions densities
( )n div j S
t
α
α∂ = − +
∂
uur
;
j n v D nα α α α α= − С
uur uur ur
;
= С
ur
v aα αµ ϕ , 1, 1= → = = → = −e a i aα α ;
Bp
e e e iS Ape n v n nϕ β
−
С= −
ur uur
,
(nα are the charged particles densities, α=e for electrons,
and α=i for ions, vα, µα and Dα are velocities, mobilities
and diffusion coefficients, respectively, S is the ionization
– recombination source, A and B are constants from the
Townsend ionization source, and β is the recombination
rate), and the Poisson equation
0
( )i ee n nϕ
ε
−∆ = − ,
where ϕ is the electric field potential and ε0 is the vacuum
dielectric constant.
Boundary conditions have a form
, 0e ij jγ ϕ= =
uur uur
and
0,ij Vϕ= =
uur
on the cathode and on anode, respectively.
Finite difference scheme was gained by the integral-
interpolation method [8] on the uniform chess grid.
The upstream scheme was used [9] taking into
account the considerable contribution of convective
terms. Accumulation of charged particles (mainly
electrons) on electrodes was considered because of the
parameters non-stationarity;
( )n t div jα α∂ ∂ = −
uur
.
The discharge voltage was found from the Ohm’s law
for a full chain. The cathode spot area was taken constant.
Parameters for calculation were used from [4].
180 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6.
Series: Plasma Physics (14), p. 180-182.
mailto:alex.ponomaryov@gmail.com
4. STEADY STATE OF GLOW DISCHARGE
Numerical simulation of glow discharge was carried
out in many articles (see, e.g., [4, 10-12]). Majority of
them is devoted to the stationary state of discharge, and
they can’t be used for study the discharge establishing.
Non-stationary problem was studied only in several works
(see, e.g.,[4, 12]). We also developed the non-stationary
code. The first stage of its testing was to obtain the
stationary picture of discharge.
Fig.1 shows electron and ion density profiles and the
potential spatial distribution in the stationary mode of
glow discharge. These results are similar to previous
simulation and experimental data.
Note that hydrodynamic approach in invalid for small
gas pressures and large current densities [13].
Fig. 1. Spatial distribution of potential and electron and
ion densities for glow discharge in nitrogen (p=1995 Pa,
T=300K, γ=0.33, E=250 V)
5. ESTABLISHING PROCESSES
The discharge gap at low cathode temperatures has
three stationary states for the given total voltage on the
tube and resistor. The first one corresponds to the lack of
current (without any external ionizing agents). It is
formed due to the transversal diffusion of the charged
particles. The second state corresponds to the glow
discharge. The growth of the current is restricted due to
the external resistor that moves to the decrease of the
discharge voltage for large currents. Both states are stable
against the small perturbations. The third state that is
instable against the small perturbations can be associated
with the dark discharge.
The developed 1D code gives the possibility to study
the establishing of the glow discharge. Initial conditions
corresponded to homogeneous distribution of electrons
and ions (without initial velocity) in the discharge
interval.
Fig.2 a shows the spatial distributions of potential
and ionization-recombination source for the time point
1ns. Fig 2 b shows the spatial distributions of electron and
ion densities for the same time point.
In the 1D model this phenomenon is reached by the
following way. At small initial densities of charged
particles electrons promptly transit in an external circuit
and traversal diffusion of ions is reached by introduction
of an additional addend proportional to an ion
concentration into S function. For reception of the dark
discharge initial densities from analytical model were set
from [2].
Evolution of glow discharge depends from initial
densities of charged particles. In case of the homogeneous
and equal initial allocations the core parameters are given
in Fig 4 and 5. One can see the initial stage of formation
of the positive column and cathode layer.
a
b
Fig.2. a – spatial distribution of potential and ionization-
recombination source; b – spatial distribution of electron
and ion densities. t=5 ns, other parameters are the same
as on Fig.1
6. CONCLUSIONS
1. Interpretation of the cathode spot in the normal mode
of glow discharge as the dissipative structure caused by
distributive feedback is proposed.
2. 1D non-stationary hydrodynamic code for simulation
of gas discharge is described. Establishing of the
stationary regime of the glow discharge is studied.
REFERENCES
1. A. von Engel. Ionized gases. Oxford: “Oxford
University Press”, 1965.
2. Ju. P. Raizer. Gas Discharge physics. Berlin:
“Springer – Verlag”, 1991.
181
3. V.N. Melechin, N.Yu. Naumov. On the nature of
cathode spot. // JTP Letters. 1986, v. 12. p. 99 – 103
4. Ju.P. Rayzer, S.T. Surghikov. 2D structure normal
regime of glow discharge and role of diffusion in cathode
spot formation// TVT. 1988, v. 26, p. 428-435.
5. A.V. Azarov, V.N. Ochkin. About the role of emission
coefficient in normal regime of glow disharge: Preprint.
Moscow: Lebedev Physics Institute, Russia: № 36, 2003.
6. P.L. Rubin. Brief reports on physics/ Lebedev Physics
institute, Russia, 2000, v. 9, p. 25
7. A. Yu. Loskutov and A. S. Mikhailov. Introduction to
synergetics. Moscow: “Nauka”, 1990 (in Russian).
8. А.А. Samarskiy, Е.S. Nikolaev. Methods of the
solution of the grid equations. Moscow: “Nauka”, 1977
(in Russian).
9. C.A.J. Fletcher. Computational techniques and fluid
dynamics. Berlin: “Springer – Verlag”, 1988.
10. R. Sh. Islamov. Effective numerical algorithm for 2D
glow discharge modeling // JVMMF. 2006, v. 46, № 11,
p. 2065 – 2080.
11. S.Т. Surghikov, J.S. Shang. Two-component plasma
model for two dimensional glow discharge in magnetic
field // JCP. 2004, v. 199, № 3, p. 437 – 464.
12. G.G. Gladush, А.А. Samohin. Numerical
investigation of the glow discharge in 2D configuration.//
PMTF, 1981, № 5, p. 15 – 23.
13. Z. Donko. On the reliability of low-pressure DC glow
discharge modeling.// XXVIIth ICPIG, Eindhoven, 18 –
22 July, 2005, p. 17 – 22.
Article received 8.10.08.
ДИССИПАТИВНАЯ СТРУКТУРА В ТЛЕЮЩЕМ РАЗРЯДЕ
А.П. Пономарев, И.А. Анисимов
Рассмотрена возможность описания катодного пятна тлеющего разряда в нормальном режиме как
диссипативной структуры, обусловленной распределенной обратной связью. Два устойчивых стационарных
состояния при этом можно связать с нормальной плотностью тока в режиме тлеющего разряда и с отсутствием
тока. Неустойчивому стационарному состоянию при этом соответствует темный разряд. Предложен численный
алгоритм для расчета нестационарного состояния разряда.
ДИСИПАТИВНА СТРУКТУРА В ЖЕВРІЮЧОМУ РОЗРЯДІ
О.П. Пономарьов, І.О. Анісімов
Розглянута можливість описати катодну пляму жевріючого розряду в нормальному режимі як дисипативну
структуру обумовлену розподіленим зворотнім зв’язком. Два стійкі стаціонарні стани при цьому можна
трактувати як випадок нормальної густини струму в режимі жевріючого розряду та випадок відсутності струму.
Нестійкому стаціонарному стану при цьому відповідає темний розряд. Запропонована числова модель для
розрахунку нестаціонарного стану розряду.
182
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