Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields
A mathematical model for plasma parameters calculation in the abnormal glow discharge in crossed electric and magnetic fields is proposed. Numerical model made it possible to obtain the electric potential, electric field, electron density and temperature distributions in the interelectrode space wor...
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| Zitieren: | Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields / A.V. Isakov, V.P. Kolesnik, A.M. Okhrimovskyy, N.P. Stepanushkin, A.A. Taran // Вопросы атомной науки и техники. — 2014. — № 6. — С. 171-174. — Бібліогр.: 21 назв. — англ. |
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irk-123456789-819332015-05-23T03:01:42Z Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields Isakov, A.V. Kolesnik, V.P. Okhrimovskyy, A.M. Stepanushkin, N.P. Taran, A.A. Низкотемпературная плазма и плазменные технологии A mathematical model for plasma parameters calculation in the abnormal glow discharge in crossed electric and magnetic fields is proposed. Numerical model made it possible to obtain the electric potential, electric field, electron density and temperature distributions in the interelectrode space working area. The application validating of the developed numerical model has proved to describe of the processes in the magnetron-type devices. Предложена математическая модель расчета параметров плазмы в аномальном тлеющем разряде в скрещенных электрическом и магнитном полях. Численное решение системы уравнений позволило получить распределения потенциала, электрического поля, плотности и температуры электронов в рабочей зоне рассмотренного межэлектродного промежутка. Проведено обоснование применимости разработанной численной модели для описания процессов в устройствах магнетронного типа. Запропонована математична модель розрахунку параметрів плазми в аномальному тліючому розряді в схрещених електричному і магнітному полях. Чисельне рішення системи рівнянь дозволило отримати розподіли потенціалу, електричного поля, густини і температури електронів у робочій зоні розглянутого міжелектродного проміжку. Проведено обґрунтування застосування розробленої чисельної моделі для опису процесів у пристроях магнетронного типу. 2014 Article Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields / A.V. Isakov, V.P. Kolesnik, A.M. Okhrimovskyy, N.P. Stepanushkin, A.A. Taran // Вопросы атомной науки и техники. — 2014. — № 6. — С. 171-174. — Бібліогр.: 21 назв. — англ. 1562-6016 PACS: 669.187.58 http://dspace.nbuv.gov.ua/handle/123456789/81933 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Isakov, A.V. Kolesnik, V.P. Okhrimovskyy, A.M. Stepanushkin, N.P. Taran, A.A. Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields Вопросы атомной науки и техники |
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A mathematical model for plasma parameters calculation in the abnormal glow discharge in crossed electric and magnetic fields is proposed. Numerical model made it possible to obtain the electric potential, electric field, electron density and temperature distributions in the interelectrode space working area. The application validating of the developed numerical model has proved to describe of the processes in the magnetron-type devices. |
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Article |
| author |
Isakov, A.V. Kolesnik, V.P. Okhrimovskyy, A.M. Stepanushkin, N.P. Taran, A.A. |
| author_facet |
Isakov, A.V. Kolesnik, V.P. Okhrimovskyy, A.M. Stepanushkin, N.P. Taran, A.A. |
| author_sort |
Isakov, A.V. |
| title |
Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields |
| title_short |
Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields |
| title_full |
Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields |
| title_fullStr |
Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields |
| title_full_unstemmed |
Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields |
| title_sort |
computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2014 |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
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http://dspace.nbuv.gov.ua/handle/123456789/81933 |
| citation_txt |
Computer simulation of abnormal glow discharge processes in crossed electric and magnetic fields / A.V. Isakov, V.P. Kolesnik, A.M. Okhrimovskyy, N.P. Stepanushkin, A.A. Taran // Вопросы атомной науки и техники. — 2014. — № 6. — С. 171-174. — Бібліогр.: 21 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T07:41:17Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2014. №6(94)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, №6. Series: Plasma Physics (20), p. 171-174. 171
COMPUTER SIMULATION OF ABNORMAL GLOW DISCHARGE
PROCESSES IN CROSSED ELECTRIC AND MAGNETIC FIELDS
A.V. Isakov, V.P. Kolesnik, A.M. Okhrimovskyy, N.P. Stepanushkin, A.A. Taran
National Aerospace University «KHAI», Kharkov, Ukraine
E-mail: lewka@3g.ua
A mathematical model for plasma parameters calculation in the abnormal glow discharge in crossed electric and
magnetic fields is proposed. Numerical model made it possible to obtain the electric potential, electric field, electron
density and temperature distributions in the interelectrode space working area. The application validating of the
developed numerical model has proved to describe of the processes in the magnetron-type devices.
PACS: 669.187.58
INTRODUCTION
The main distinctive feature of the abnormal glow
discharge in crossed magnetic and electric fields from
the normal glow discharge is the presence of the
transverse magnetic field. That leads to the absence of a
steady leakage electron current to the anode. It allows
obtaining high plasma densities at relatively low
pressures.
In order to reduce the number of experiments for
discharge parameters optimization it is necessary to
understand clearly the basic processes in plasma. This
can be achieved by developing the mathematical models
for computational determination the investigated
processes’ parameters.
There is a variety of different mathematical models
for determination of plasma parameters in crossed
electric and magnetic fields, but no one of them
considers systems of more than two electrodes.
1. RESEARCH OBJECTIVE
DETERMINATION
There are many different approaches to the
discharge plasma processes modelling, like fluid
models, kinetic models, Monte Carlo method, hybrid
models, etc. [1-3].
Based on the literature review in previous work [4],
the fluid model is the most reasonable approach for
modelling the abnormal glow discharge in crossed
magnetic and electric fields at operating pressures of
0.1...0.8 Pa and magnetic field of 0.01...0.05 T.
Let us consider the spatial electrodes configuration,
found on the Fig.1, where the magnetic field distribution
in the interelectrode space, created by the magnetic
system, are shown. The distribution of steady magnetic
field in the discharge space was determined by means of
PARDISO solver [5-7].
The anode (1) is under the positive potential
250...900 V. The cathode (3) potential is also positive,
but lower than the anode potential (1). The cathode (4)
and the polar tip (2) are under "zero" potential relatively
to the anode.
2. MATHEMATICAL MODEL
Let us consider a fluid model presented in [8-15].
The fluid model is based on a system of differential
equations in the form of partial derivatives, including
the continuity equation (1) and the rate of change of the
electron energy density equation (2). For heavy particles
(neutral atom, metastable atom and ion) the continuity
equation (3) is solved.
Fig. 1. The scheme of interelectrode space with crossed
electric and magnetic fields: 1 – anode; 2 – polar tip;
3 – cathode; 4 – cathode; 5 – plane of symmetry;
6 – axis of symmetry
e
e e
n
S
t
Γ , (1)
e e
w e w
n T
S
t
Γ E Γ , (2)
k
k k
n
S
t
, (3)
where ne is electron number density, Γe is electron flux
density, Se is electron creation rate, Te is electron
temperature, Γw is electron energy flux density, E is
electric field strength, Sw is a rate of electron energy
density, nk is the heavy particles number density, Γk is
heavy particles flux density, Sk is rate of k-th particle
creation.
Self-consistent electric field strength E and plasma
potential φ are determined with help of the Poisson
equation:
172 ISSN 1562-6016. ВАНТ. 2014. №6(94)
0
i e
e
n n , E ,
where e is an elementary charge, ε0 is a dielectric
constant, ni is ion density.
In the proposed model only the reactions, given in
the table 1, are taken into account. The cross-sections of
the correspondent collision processes were taken from
the work [12].
Reactions in plasma
Scheme of reaction Type of reaction
e + Ar = e + Ar elastic collision
e + Ar = e + Ar
*
excitation
e + Ar
*
= e + Ar excitation dropping
e + Ar = 2e + Ar
+
direct ionization
e + Ar
*
= 2e + Ar
+
stepwise ionization
Ar
*
+ Ar
*
= e + Ar + Ar
+
Penning ionization
Ar
*
+ Ar = Ar + Ar metastable quenching
The model have to take into account not only
reactions in the bulk discharge but also those ones on
the electrode surface, such as secondary electron
emission, ion neutralization and excitation dropping of
metastable atoms.
The main maintaining mechanism of discharge in
the interelectrode space is the cathode secondary
electron emission under ion bombardment. Secondary
electron emission depends on the energy, ion mass and
on cathode material. Secondary electrons are
accelerated by the electric field in cathode dark space,
where they gain enough energy to ionize argon
molecules.
3. NUMERICAL SOLUTION
The solver PARDISO was applied to determine the
plasma parameters distribution in the discharge space,
which allows to solve the system of differential
equations in the form of partial derivatives in one, two
and three dimensional cases.
In order to simplify the numerical execution of fluid
model, the influence of internal electromagnetic fields
due to motion of charged particles upon the external
steady electromagnetic fields caused by electromagnetic
devices, was not considered [16].
A method, proposed in the works [5-7, 17, 18], for
solving the differential equations was applied. The
calculation program uses the affine invariant of Newton
method [19].
The results depend on the initial approximation in a
complicated manner. Therefore, to reduce the time and
increase the accuracy of fluid model calculation,
approximate value of variables at low computational
accuracy are calculated at the beginning. These
variables serve as initial conditions for the next step
performed with higher accuracy.
It took from 2 to 6 hours to reach a steady state
mode to solve the system of differential equations for
the examined configuration on PC (Intel Core i7-4770K
at 4.3 GHz, RAM 16 GB).
4. RESULTS OF MODELING
Solution of the system of differential equations is
resulted in the electric potential, density and
temperature of electrons distributions in the
interelectrode space, which are presented in Figs. 2-4,
correspondingly.
Fig. 2. Plasma potential distribution in the
interelectrode space
The solutions were obtained under the following
conditions: discharge voltage was up to 400 V,
discharge current was up to 0.4 A, pressure in the
vacuum chamber was of 0.2 Pa.
It’s obvious from the Figs. 2, 3 that the numerical
model give us an opportunity localize the main
ionization area and describe the cathode region near the
cathode (4) and polar tip (2) (see Fig. 1).
Fig. 3. Electron density distribution in the
interelectrode space
From these distributions (see Figs. 2-4) we can
conclude that the "magnetic trap" is formed between the
polar tips. Trapped electron oscillates along the
magnetic field lines and reflects in the polar tips area.
Electron movement to the anode occurs by means of
electrons shifting from one orbit to another due to the
ISSN 1562-6016. ВАНТ. 2014. №6(94) 173
elastic and inelastic collisions. Emitted from the cathode
surface (4), the electrons oscillate along the magnetic
field lines and then reflect from the cathode (3) (see
Fig. 1).
Low electron density in the discharge space is
caused by run away of the part of electrons to the
cathode (3), as it is under the positive potential, which is
several times lower anode potential.
Fig. 4. Electron temperature distribution in the
interelectrode space
From the electric field and magnetic field lines
distribution (Fig. 5) one can conclude that the majority
of ions (up to 45 %) moves to the cathode (4) and the
other part of ions (30 %) moves to the cathode (3),
while the remaining ions move to the polar tips (2).
Fig. 5. Distribution of the electric field strength and
magnetic field lines in the interelectrode space
5. MATHEMATICAL MODEL
VERIFICATION
The experimental data of the discharge parameters in
a cylindrical magnetron, shown in the work [20], were
used in order to verify the proposed mathematical
model. The abnormal glow discharge is initiated at the
noble gas (argon) pressure of 3 Pa and discharge current
of 0.2 A between two coaxial cylindrical electrodes,
which are placed in a homogeneous longitudinal
magnetic field of 0.02 T.
Figs. 6, 7 compares the results (distribution of the
electric potential and electron density) in the midplane
of the cylindrical magnetron obtained using the fluid
model and the results are presented in work [20].
One can conclude from the Figs. 6, 7, that the
numerical verification of the developed mathematical
model has confirmed the qualitative and quantitative
correspondence of the proposed fluid model, within the
measurement error of the probe method [21], with the
results of work [20].
Fig. 6. Plasma potential distribution in the cylindrical
magnetron midplane
Fig. 7. Electron density distribution in the cylindrical
magnetron midplane
CONCLUSIONS
The mathematical model makes it possible to
undertake the numerical experiment for determination
the discharge parameters in the examined interelectrode
space under the operating pressures of 0.1...0.8 Pa and
magnetic induction of 0.01...0.05 T. The solution of the
differential equation system allow determine the
distribution of the plasma potential, electron
temperature and electron density in the abnormal glow
discharge in crossed magnetic and electric fields.
The mathematical model reliability was validated by
applying the proposed model for cylindrical magnetron
calculation and by comparing the calculated data with
the experimental ones. The results confirmed the
qualitative and quantitative correspondence of the
developed fluid model with results presented in the
work [20].
It follows that the developed mathematical model
allow us to specify the near-electrode areas and obtain
174 ISSN 1562-6016. ВАНТ. 2014. №6(94)
the qualitative distribution of the plasma parameters at a
short calculation time. Hence, it is possible to execute
the optimization of magnetic field configuration and
working area for examined spatial electrodes
configurations.
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Article received 18.09.2014
КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ В АНОМАЛЬНОМ ТЛЕЮЩЕМ РАЗРЯДЕ В
СКРЕЩЕННЫХ ЭЛЕКТРИЧЕСКОМ И МАГНИТНОМ ПОЛЯХ
А. В. Исаков, В.П. Колесник, А.М. Охримовский, Н.П. Степанушкин, А.А. Таран
Предложена математическая модель расчета параметров плазмы в аномальном тлеющем разряде в
скрещенных электрическом и магнитном полях. Численное решение системы уравнений позволило
получить распределения потенциала, электрического поля, плотности и температуры электронов в рабочей
зоне рассмотренного межэлектродного промежутка. Проведено обоснование применимости разработанной
численной модели для описания процессов в устройствах магнетронного типа.
КОМП'ЮТЕРНЕ МОДЕЛЮВАННЯ ПРОЦЕСІВ В АНОМАЛЬНОМУ ТЛІЮЧОМУ РОЗРЯДІ
В СХРЕЩЕНИХ ЕЛЕКТРИЧНОМУ І МАГНІТНОМУ ПОЛЯХ
О.В. Ісаков, В.П. Колесник, А.М. Охримовський, М.П. Степанушкін, А.О. Таран
Запропонована математична модель розрахунку параметрів плазми в аномальному тліючому розряді в
схрещених електричному і магнітному полях. Чисельне рішення системи рівнянь дозволило отримати
розподіли потенціалу, електричного поля, густини і температури електронів у робочій зоні розглянутого
міжелектродного проміжку. Проведено обґрунтування застосування розробленої чисельної моделі для опису
процесів у пристроях магнетронного типу.
|