On the influence of beryllium impurities on the transport properties of multicomponent arc plasma
The influence of beryllium impurities on the transport properties of multicomponent arc plasma is considered in the ambient atmosphere of argon and carbon dioxide. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of metal causes the essential changes...
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Porytskyy, P.V. 2015-05-22T17:38:01Z 2015-05-22T17:38:01Z 2014 On the influence of beryllium impurities on the transport properties of multicomponent arc plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2014. — № 6. — С. 198-200. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.25.Fi, 52.25.Vy, 52.25.Ya, 52.27.Cm, 52.77.Fv, 52.50.Nr, 52.80.Mg https://nasplib.isofts.kiev.ua/handle/123456789/81940 The influence of beryllium impurities on the transport properties of multicomponent arc plasma is considered in the ambient atmosphere of argon and carbon dioxide. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of metal causes the essential changes in the values of transport coefficients in comparison with the case of pure gaseous mixtures. It is revealed that the influence of the Ramsauer effect on transport properties can be neutralized by additions of metal into ambient argon. Рассмотрено влияние примесей бериллия на транспортные свойства многокомпонентной дуговой плазмы в атмосфере смесей аргона и диоксида углерода. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное количество примесей металла может существенно изменить величины транспортных коэффициентов в сравнении со случаем чистого аргона. Показана возможность нейтрализации влияния эффекта Рамзауэра на свойства плазмы путем добавки металлических примесей. Розглянуто вплив домішок берилію на транспортні властивості багатокомпонентної плазми в атмосфері сумішей аргону та диоксиду вуглецю. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість металевих домішок може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чистого аргону. Висвітлено можливість нейтралізації впливу ефекту Рамзауера на властивості плазми шляхом додавання металевих домішок. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Низкотемпературная плазма и плазменные технологии On the influence of beryllium impurities on the transport properties of multicomponent arc plasma О влиянии примесей бериллия на транспортные свойства многокомпонентной дуговой плазмы Про вплив домішок берилію на транспортні властивості багатокомпонентної дугової плазми Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma |
| spellingShingle |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma Porytskyy, P.V. Низкотемпературная плазма и плазменные технологии |
| title_short |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma |
| title_full |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma |
| title_fullStr |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma |
| title_full_unstemmed |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma |
| title_sort |
on the influence of beryllium impurities on the transport properties of multicomponent arc plasma |
| author |
Porytskyy, P.V. |
| author_facet |
Porytskyy, P.V. |
| topic |
Низкотемпературная плазма и плазменные технологии |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
| publishDate |
2014 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
О влиянии примесей бериллия на транспортные свойства многокомпонентной дуговой плазмы Про вплив домішок берилію на транспортні властивості багатокомпонентної дугової плазми |
| description |
The influence of beryllium impurities on the transport properties of multicomponent arc plasma is considered in the ambient atmosphere of argon and carbon dioxide. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of metal causes the essential changes in the values of transport coefficients in comparison with the case of pure gaseous mixtures. It is revealed that the influence of the Ramsauer effect on transport properties can be neutralized by additions of metal into ambient argon.
Рассмотрено влияние примесей бериллия на транспортные свойства многокомпонентной дуговой плазмы в атмосфере смесей аргона и диоксида углерода. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное количество примесей металла может существенно изменить величины транспортных коэффициентов в сравнении со случаем чистого аргона. Показана возможность нейтрализации влияния эффекта Рамзауэра на свойства плазмы путем добавки металлических примесей.
Розглянуто вплив домішок берилію на транспортні властивості багатокомпонентної плазми в атмосфері сумішей аргону та диоксиду вуглецю. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість металевих домішок може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чистого аргону. Висвітлено можливість нейтралізації впливу ефекту Рамзауера на властивості плазми шляхом додавання металевих домішок.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/81940 |
| citation_txt |
On the influence of beryllium impurities on the transport properties of multicomponent arc plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2014. — № 6. — С. 198-200. — Бібліогр.: 8 назв. — англ. |
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| first_indexed |
2025-11-25T06:07:00Z |
| last_indexed |
2025-11-25T06:07:00Z |
| _version_ |
1850509145283756032 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2014. №6(94)
198 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, №6. Series: Plasma Physics (20), p. 198-200.
ON THE INFLUENCE OF BERYLLIUM IMPURITIES ON THE
TRANSPORT PROPERTIES OF MULTICOMPONENT ARC PLASMA
P.V. Porytskyy
Institute for Nuclear Research, Kyiv, Ukraine
The influence of beryllium impurities on the transport properties of multicomponent arc plasma is considered in
the ambient atmosphere of argon and carbon dioxide. The calculations are carried out on the base of Grad’s method,
and it is shown that a small amount of metal causes the essential changes in the values of transport coefficients in
comparison with the case of pure gaseous mixtures. It is revealed that the influence of the Ramsauer effect on
transport properties can be neutralized by additions of metal into ambient argon.
PACS: 52.25.Fi, 52.25.Vy, 52.25.Ya, 52.27.Cm, 52.77.Fv, 52.50.Nr, 52.80.Mg
INTRODUCTION
Beryllium is widely used in plasma devices and
industrial electronic plants. Sometimes they are doped
with other materials to lower the work function of the
cathode material. At operation the process of erosion
leads to the evaporation of the metal impurities into the
discharge region that causes the change of plasma
properties.
The improvement in controlling plasma processing
needs for accurate numerical modeling. Transport
properties are indispensable input data for the modeling.
At weakly ionization the Lorentzian theory is suitable to
calculate the properties of multicomponent thermal
plasma [1]. But at increasing of ionization processes a
number of collision processes are known to be included
into consideration. Because of that it is the many
processes are needed to take into account in the
calculation procedure.
In this paper, the transport coefficients for
multicomponent plasma with tungsten impurities are
calculated on the base of the Grad’s method [2, 3]. It is
shown that the impurities have an influence on the
transport properties of thermal plasma.
1. METHOD OF CALCULATION
It should be noted that the present state of the theory
of gas mixtures, as well as multicomponent plasma, is
characterized by the lack of a unified approach to the
description of transport processes. The reason for this is
a very complex nature of dependencies of the properties
of gas mixtures and plasma on the properties of pure
gases and concentrations of the components.
Thus, the coefficient of thermal conductivity is
calculated as the sum
inth e ri rd , (1.1)
where h is the translational thermal conductivity of
heavy particles, e is the thermal conductivity of
electrons, int is the thermal conductivity due to the
transfer among the internal degrees of freedom, ri is
the reactive thermal conductivity due to ionization, rd
is the reactive thermal conductivity due to dissociation.
In turn, the coefficient of viscosity is calculated as
the sum of additions from heavy particle h and
electrons e :
h e . (1.2)
It should be underlined that, now, the Grad’s
method of moments [2,3] is an unique alternative in
spite of the most developed Chapman-Enskog’ method
[4-8] to solve the kinetic Boltzmann equation. Both the
methods are based on the formalism of Chapman-
Cowling kinetic integrals
2
1 2
2 3
0
2
llr rkT
e Q d
, (1.3)
where k is Boltzmann constant, T is temperature,
is a reduced mass of collided species of
and ,
1 2
2kT g , g is the relative
velocity, and transport cross-section of order l is
determined as
0
2 , 1 cos sinl lQ g g d
,
where is scattering angle, ,g is differential
scattering cross-section.
In the 13-moments (13M) approximation of the
Grad’s method the translational transport coefficients
are calculated as the sum of effective coefficients for
each species
h h
, (1.4)
h h
. (1.5)
The effective coefficients are calculated on the base of
combination of the Chapman-Cowling integrals (1.3).
The studies of electronic transport coefficients are
known to need using of higher approximations. In that
way for electronic viscosity, electrical conductivity ,
and electronic conductivity one can be write [3],
respectively,
ISSN 1562-6016. ВАНТ. 2014. №6(94) 199
1 225
2
2
e e e
p
n m kT
p
, (1.6)
1 2
2 23 2
2
e
e
q
n e
m kT q
, (1.7)
1 2
275 2
8
e e
e
qkT
n
m q
. (1.8)
Here em is the mass of electron, en is electronic
density, the elements of determinants
nkp and
nkq are
the functions of the above pointed Chapman-Cowling
integrals. Script “ ‘ ” denotes the absence of elements
with indexes 0 and 1 (see for details [3-8]).
Others coefficients are calculated according to the
Lorentzian theory [2].
2. RESULTS AND DISCUSSION
The calculations are carried out at assumption of
local thermodynamic equilibrium, and the following 8
species have been taken into account: e
-
, Ar, Ar
+
, Be,
Be
+
, Be
2+
, Be
3+
, Be2, Be2
+
and others analogous
mixtures. The results of calculations for the case of
nickel are shown in Figs.1-4. The obtained values are in
a good agreement with the data obtained by Chapman-
Enskog method (see Figs. 1, 2).
Fig. 1. Electrical conductivity of thermal plasma
( p =1 atm) for pure argon and the equimolar mixtures
of argon with beryllium. Curves 1 – pure Ar (this work
calculations); 2 – Ar–Be (99:1); 3 – Ar–Be (90:10);
4 – Ar-Be (75:25); 5 – pure Be
One can see that the properties of multicomponent
plasma have a pronounced non-monotone character with
sharp pikes in certain temperature and pressure ranges.
The pikes are appeared due to the dissociation,
ionization and from others effects connected with metal
impurities. Thus, the viscosity peaks (see Fig.4) are
caused by the minor additions of ions in gases at weakly
ionization.
It should be noted that under scattering of electrons
on argon the Ramsauer effect takes place that is
determined the properties of pure argon. However this
Fig. 2. Thermal conductivity of thermal plasma for
pure argon ( p =1 atm). Curves 1,5 are total
conductivities, 2,6 are gaseous ones, 3,7 are electronic
ones, 4,8 are ionization ones. Curves 1,2,3,4 are
presented calculations, 5,6,7,8 are the data from [8]
Fig. 3. Thermal conductivity of thermal plasma
( p =1 atm) for pure argon and the equimolar mixtures
of argon with beryllium. Curves 1 – Ar (this work
calculations); 2 – Ar–Be (99.9:0.1); 3 – Ar –Be (95:5);
4 – Ar-Be (90:10); 5 – Ar–Be (80:20);
6 – Ar–Be (70:30)
Fig. 4. Viscosity of thermal plasma ( p =1 atm) for pure
argon and the equimolar mixtures of argon with
beryllium. Curves 1 – Ar (this work calculations);
2 – Ar–Be (95:5); 3 – Ar–Be (90:10); 4 – Ar-Be
(80:20); 5 – Ar (data from [8])
influence can be neutralized by metal additions in
plasma.
200 ISSN 1562-6016. ВАНТ. 2014. №6(94)
Also, one can see that the appearance of beryllium
impurities causes the essential changing of transport
properties with comparison to the case of pure argon.
That is needed to take into account under studies of
discharges with tungsten electrodes.
The peculiarity of the Grad’ method is that the
values have the same dimensions at all of stages in
calculation procedure due to the control of calculation
procedure may be improved.
CONCLUSIONS
Thus, a small amount of beryllium causes the
essential changes in the values of transport coefficients
of thermal plasma in comparison with the case of pure
argon.
The calculations of transport properties on the base
of Grad’s method have a good agreement with the
recent calculations based on Chapman-Enskog method.
The influence of the Ramsauer effect on the
transport coefficients can be neutralized by metal
additions in plasma.
REFERENCES
1. P. Porytsky, I. Krivtsun, V. Demchenko, U. Reisgen,
O. Mokrov, and A. Zabirov. On the application of the
theory of Lorentzian plasma to calculation of transport
properties of multicomponent arc plasmas // European
Phys. Journ. D. 2010, v. 57, № 1, p. 77-85.
2. H. Grad. On the kinetic theory of rarefied gases //
Comm. Pure and Appl. Math. 1949, v. 2, p. 331-407.
3. V.M. Zhdanov. Transport Processes in
Multicomponent Plasma. NY: “Taylor&Francis”, 2002.
4. S. Chapman, T.G. Cowling. The mathematical Theory
of Nonuniform Gases / 3
rd
ed. Cambbrige University
Press:”Cambridge”, 1970.
5. J.H. Ferziger, H.G. Kaper. Mathematical theory of
transport processes in gases. North-Holland:
“Amsterdam”, 1972.
6. R.S. Devoto. Transport properties of Ionized
Monatomic Gases // Phys. Fluids. 1966. v. 9, № 6,
p. 1230-1240.
7. R.S. Devoto. Simplified Expressions for the
Transport Properties of Ionized Monatomic Gases //
Phys.Fluids. 1967, v. 10, № 10, p. 2105-2112.
8. R.S. Devoto. Transport coefficients of ionized argon
// Phys.Fluids. 1973, v. 16, № 5, p. 2105-2112.
Article received 23.09.2014
О ВЛИЯНИИ ПРИМЕСЕЙ БЕРИЛЛИЯ НА ТРАНСПОРТНЫЕ СВОЙСТВА
МНОГОКОМПОНЕНТНОЙ ДУГОВОЙ ПЛАЗМЫ
П.В. Порицкий
Рассмотрено влияние примесей бериллия на транспортные свойства многокомпонентной дуговой
плазмы в атмосфере смесей аргона и диоксида углерода. Проведенные расчеты основывались на методе
моментов Грэда. Показано, что незначительное количество примесей металла может существенно изменить
величины транспортных коэффициентов в сравнении со случаем чистого аргона. Показана возможность
нейтрализации влияния эффекта Рамзауэра на свойства плазмы путем добавки металлических примесей.
ПРО ВПЛИВ ДОМІШОК БЕРИЛІЮ НА ТРАНСПОРТНІ ВЛАСТИВОСТІ
БАГАТОКОМПОНЕНТНОЇ ДУГОВОЇ ПЛАЗМИ
П.В. Порицький
Розглянуто вплив домішок берилію на транспортні властивості багатокомпонентної плазми в атмосфері
сумішей аргону та диоксиду вуглецю. Проведені розрахунки ґрунтувалися на методі моментів Ґреда.
Показано, що невелика кількість металевих домішок може суттєво змінити величини транспортних
коефіцієнтів порівняно із випадком чистого аргону. Висвітлено можливість нейтралізації впливу ефекту
Рамзауера на властивості плазми шляхом додавання металевих домішок.
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