On the influence of tungsten impurities on the transport properties of thermal plasma
The influence of tungsten impurities on the transport properties of thermal plasma is considered in the ambient atmosphere of argon. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of tungsten causes the essential changes in the values of transport...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
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| Cite this: | On the influence of tungsten impurities on the transport properties of thermal plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2010. — № 6. — С. 162-164. — Бібліогр.: 9 назв. — англ. |
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| author | Porytskyy, P.V. |
| author_facet | Porytskyy, P.V. |
| citation_txt | On the influence of tungsten impurities on the transport properties of thermal plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2010. — № 6. — С. 162-164. — Бібліогр.: 9 назв. — англ. |
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| description | The influence of tungsten impurities on the transport properties of thermal plasma is considered in the ambient atmosphere of argon. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of tungsten causes the essential changes in the values of transport coefficients in comparison with the case of pure argon. 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 вольфрама на транспортные свойства термической плазмы в атмосфере аргона. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное количество примесей вольфрама 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 вольфраму на транспортні властивості термічної плазми в атмосфері аргону. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість домішок вольфраму може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чистого аргону. Висвітлено можливість нейтралізації впливу ефекта Рамзауера на властивості плазми шляхом додавання металевих домішок.
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162 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 6.
Series: Plasma Physics (16), p. 162-164.
ON THE INFLUENCE OF TUNGSTEN IMPURITIES ON THE TRANSPORT
PROPERTIES OF THERMAL PLASMA
P.V. Porytskyy
Institute for Nuclear Research, Kiev, Ukraine
E-mail: poryts@kinr.kiev.ua
The influence of tungsten impurities on the transport properties of thermal plasma is considered in the ambient
atmosphere of argon. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount
of tungsten causes the essential changes in the values of transport coefficients in comparison with the case of pure
argon. 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
1. INTRODUCTION
Tungsten is widely used in plasma devices and
industrial electronic plants. Thus, the walls of discharge
chambers and electrodes are made of heavy metal elements
with a high melting point, typically tungsten (melting point is
3680 K). 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. Usually it is not attended the influence of
tungsten impurities in comparison with others fusible metals.
But the results of experimental investigation in arc plasma
[1] are argued to consider this influence more carefully.
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 [2]. 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 [3,4]. It is
shown that the impurities have an influence on the
transport properties of thermal plasma.
2. 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 rdλ λ λ λ λ λ= + + + + , (1)
where hλ is the translational thermal conductivity of
heavy particles, eλ is the thermal conductivity of
electrons, intλ is the thermal conductivity due to the
transfer among the internal degrees of freedom, riλ is the
reactive thermal conductivity due to ionization, rdλ is the
reactive thermal conductivity due to dissociation.
In turn, the coefficient of viscosity is calculated as
the sum of additions from heavy particle hη and
electrons eη :
h eη η η= + . (2)
It should be underlined that, now, the Grad’s method
of moments [3,4] is an unique alternative in spite of the
most developed Chapman-Enskog’ method [5-9] to solve
the kinetic Boltzmann equation. Both the methods are
based on the formalism of Chapman-Cowling kinetic
integrals
( ) ( )2
1 2
2 3
02
llr rkT e Q dς
αβ αβ
αβ
ς ς ς
πμ
∞
+ −⎛ ⎞
Ω = ⎜ ⎟⎜ ⎟
⎝ ⎠
∫ , (3)
where k is Boltzmann constant, T is temperature,
αβμ is a reduced mass of collided species of
α and β , ( )1 2
2kT gαβς μ= , g is the relative
velocity, and transport cross-section of order l is
determined as
( ) ( ) ( )
0
2 , 1 cos sinl lQ g g d
π
αβ αβπ σ χ χ χ χ= −∫ ,
where χ is scattering angle, ( ),gαβσ χ 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 hα
α
η η= ∑ , (4)
h hα
α
λ λ= ∑ . (5)
The effective coefficients are calculated on the base of
combination of the Chapman-Cowling integrals (3).
The studies of electronic transport coefficients are
known to need using of higher approximations. In that
way for electronic viscosity, electrical conductivity σ ,
163
and electronic conductivity one can be write [4],
respectively,
( )1 225 2
2e e e
p
n m kT
p
η π
′
= , (6)
1 2
2 23 2
2 e
e
q
n e
m kT q
πσ
′⎛ ⎞
= ⎜ ⎟
⎝ ⎠
, (7)
1 2
275 2
8e e
e
qkTn
m q
πλ
′′⎛ ⎞
= ⎜ ⎟ ′⎝ ⎠
. (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 [4]).
Others coefficients are calculated according to the
Lorentzian theory [2].
3. 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+, W, W+, W2+,
W2, W2
+. The results of calculations are shown in
Figs.1-4. The obtained values are in a good agreement
with the data obtained by Chapman-Enskog method
(Figs.1,2).
Fig. 1. Electrical conductivity of thermal plasma
( p =1 atm) for pure argon and the equimolar mixtures of
argon with tungsten. Curves 1-Ar (this work
calculations), 2- Ar –W (99.9:0.1), 3- Ar –W (95:5),
4-Ar-W(90:10), 5- Ar (data from [9])
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 (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 influence can
be neutralized by metal additions in plasma.
Also, one can see that the appearance of tungsten
impurities causes the essential changing of transport
properties with comparison to the case of pure argon.
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 [9]
Fig. 3. Thermal conductivity of thermal plasma
( p =1 atm) for pure argon and the equimolar mixtures of
argon with tungsten. Curves 1-Ar (this work
calculations), 2- Ar –W (99.9:0.1), 3- Ar –W (95:5),
4-Ar-W(90:10), 5- Ar –W (80:20), 6- Ar –W (70:30)
Fig.4. Viscosity of thermal plasma ( p =1 atm) for pure
argon and the equimolar mixtures of argon with tungsten.
Curves 1-Ar (this work calculations), 2- Ar –W (95:5),
3- Ar–W (90:10), 4-Ar-W (80:20), 5- Ar (data from [9])
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.
164
4. CONCLUSIONS
Thus, a small amount of tungsten 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. G. Kuhn, F. Konemann, M. Kock. 2D display of
tungsten impurity in a free-burning arc using laser-
induced fluorescence // J. Phys. D: Appl. Phys. 2002,
v. 35. p. 2096-2104.
2. P. Porytsky, I. Krivtsun, V. Demchenko, U. Reisgen,
V. Mokrov, A. Zabirov. On the application of the theory
of Lorentzian plasma to calculation of transport
properties of multicomponent arc plasmas // Eur. Phys.
Journ. D. 2010, v. 57, N 1, p. 77-85.
3. H. Grad. On the kinetic theory of rarefied gases//
Comm. Pure and Appl. Math. 1949, v. 2, p. 331-407.
4. V.M. Zhdanov. Transport Processes in Multicomponent
Plasma. NY: ”Taylor&Francis”, 2002.
5. S. Chapman, T. Cowling. The mathematical Theory of
Nonuniform Gases. Cambridge: “University Press”,
3rd ed., 1970.
6. J.H. Ferziger, H.G. Kaper. Mathematical theory of
transport processes in gases. Amsterdam: “North-
Holland”, 1972.
7. R.S. Devoto. Transport properties of Ionized
Monatomic Gases // Phys. Fluids. 1966, v. 9, N 6,
p. 1230-1240.
8. R.S. Devoto. Simplified Expressions for the Transport
Properties of Ionized Monatomic Gases // Phys. Fluids.
1967, v. 10, N 10, p. 2105-2112.
9. R.S. Devoto. Transport coefficients of ionized argon//
Phys. Fluids. 1973, v. 16, N 5, p. 2105-2112.
Article received 13.09.10
О ВЛИЯНИИ ПРИМЕСЕЙ ВОЛЬФРАМА
НА ТРАНСПОРТНЫЕ СВОЙСТВА ТЕРМИЧЕСКОЙ ПЛАЗМЫ
П.В. Порицкий
Рассмотрено влияние примесей вольфрама на транспортные свойства термической плазмы в атмосфере
аргона. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное
количество примесей вольфрама 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 ВОЛЬФРАМУ
НА ТРАНСПОРТНІ ВЛАСТИВОСТІ ТЕРМІЧНОЇ ПЛАЗМИ
П.В. Порицький
Розглянуто вплив домішок вольфраму на транспортні властивості термічної плазми в атмосфері аргону.
Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість домішок
вольфраму може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чистого аргону.
Висвітлено можливість нейтралізації впливу ефекта Рамзауера на властивості плазми шляхом додавання
металевих домішок.
|
| id | nasplib_isofts_kiev_ua-123456789-17491 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T08:19:15Z |
| publishDate | 2010 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Porytskyy, P.V. 2011-02-26T22:44:12Z 2011-02-26T22:44:12Z 2010 On the influence of tungsten impurities on the transport properties of thermal plasma / P.V. Porytskyy // Вопросы атомной науки и техники. — 2010. — № 6. — С. 162-164. — Бібліогр.: 9 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/17491 The influence of tungsten impurities on the transport properties of thermal plasma is considered in the ambient atmosphere of argon. The calculations are carried out on the base of Grad’s method, and it is shown that a small amount of tungsten causes the essential changes in the values of transport coefficients in comparison with the case of pure argon. 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 вольфрама на транспортные свойства термической плазмы в атмосфере аргона. Проведенные расчеты основывались на методе моментов Грэда. Показано, что незначительное количество примесей вольфрама 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 вольфраму на транспортні властивості термічної плазми в атмосфері аргону. Проведені розрахунки ґрунтувалися на методі моментів Ґреда. Показано, що невелика кількість домішок вольфраму може суттєво змінити величини транспортних коефіцієнтів порівняно із випадком чистого аргону. Висвітлено можливість нейтралізації впливу ефекта Рамзауера на властивості плазми шляхом додавання металевих домішок. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Низкотемпературная плазма и плазменные технологии On the influence of tungsten impurities on the transport properties of thermal plasma О влиянии примесей вольфрама на транспортные свойства термической плазмы Про вплив домішок вольфраму на транспортні властивості термічної плазми Article published earlier |
| spellingShingle | On the influence of tungsten impurities on the transport properties of thermal plasma Porytskyy, P.V. Низкотемпературная плазма и плазменные технологии |
| title | On the influence of tungsten impurities on the transport properties of thermal plasma |
| title_alt | О влиянии примесей вольфрама на транспортные свойства термической плазмы Про вплив домішок вольфраму на транспортні властивості термічної плазми |
| title_full | On the influence of tungsten impurities on the transport properties of thermal plasma |
| title_fullStr | On the influence of tungsten impurities on the transport properties of thermal plasma |
| title_full_unstemmed | On the influence of tungsten impurities on the transport properties of thermal plasma |
| title_short | On the influence of tungsten impurities on the transport properties of thermal plasma |
| title_sort | on the influence of tungsten impurities on the transport properties of thermal plasma |
| topic | Низкотемпературная плазма и плазменные технологии |
| topic_facet | Низкотемпературная плазма и плазменные технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/17491 |
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