On the contraction of an arc discharge in gaseous mixtures
The influence of properties of a gaseous medium on the process of contraction (self-constriction) of an arc discharge in the atmosphere of the mixtures of noble gases is considered. The calculations are carried out, and it is shown that the degree of constriction of an arc discharge is determined by...
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| Veröffentlicht in: | Вопросы атомной науки и техники |
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| Datum: | 2005 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Zitieren: | On the contraction of an arc discharge in gaseous mixtures / P.V.Porytskyy // Вопросы атомной науки и техники. — 2005. — № 1. — С. 181-183. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860191612829696000 |
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| author | Porytskyy, P.V. |
| author_facet | Porytskyy, P.V. |
| citation_txt | On the contraction of an arc discharge in gaseous mixtures / P.V.Porytskyy // Вопросы атомной науки и техники. — 2005. — № 1. — С. 181-183. — Бібліогр.: 9 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The influence of properties of a gaseous medium on the process of contraction (self-constriction) of an arc discharge in the atmosphere of the mixtures of noble gases is considered. The calculations are carried out, and it is shown that the degree of constriction of an arc discharge is determined by both the thermal characteristics of the gaseous medium and the characteristics of electron-atom collisions. It is revealed that the Ramsauer effect has an influence on a character of the contraction of an arc. Also, it is shown the possibility to neutralize this influence in gaseous mixtures.
Розглянуто вплив характеристик газового середовища на процес контракції (стягування) дугового розряду в сумішах інертних газів. Проведені розрахунки і показано, що ступінь стягування дугового розряду визначається теплофізичними характеристиками газового середовища і характеристиками зіткнень електронів з атомами та іонами. Висвітлено вплив ефекту Рамзауера на характер контракції дугового розряду, а також показана можливість нейтралізації цього ефекту відповідним підбором складу суміші.
Рассмотрено влияние характеристик газовой среды на процесс контракции (сжатия) дугового разряда в смесях инертных газов. Проведены расчеты и показано, что степень сжатия дугового разряда определяется теплофизическими характеристиками газовой среды и характеристиками столкновений электронов с атомами и ионами. Выявлено влияние эффекта Рамзауэра на характер контракции дугового разряда, а также показана возможность нейтрализации этого эффекта соответствующим подбором состава смеси.
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ON THE CONTRACTION OF AN ARC DISCHARGE IN GASEOUS
MIXTURES
P. V. Porytskyy
Institute for Nuclear Research, pr. Nauky 47, Kyiv 03680 , Ukraine,
fax: +380-44-2654463, e-mail: poryts@kinr.kiev.ua
The influence of properties of a gaseous medium on the process of contraction (self-constriction) of an arc discharge in
the atmosphere of the mixtures of noble gases is considered. The calculations are carried out, and it is shown that the
degree of constriction of an arc discharge is determined by both the thermal characteristics of the gaseous medium and
the characteristics of electron-atom collisions. It is revealed that the Ramsauer effect has an influence on a character of
the contraction of an arc. Also, it is shown the possibility to neutralize this influence in gaseous mixtures.
PACS: 52.20.Fs, 52.25.Fi, 52.25.Ya, 52.27.Cm, 52.77.Fv, 52.50.Nr, 52.80.Mg
1. INTRODUCTION
Thermal contraction (self-constriction) of an arc
discharge is caused by the fact that temperature at the
periphery of the discharge falls and the gas density (under
constant pressure) rises [1-5]. Therefore, electrons at the
periphery give up a larger amount of energy to neutral
particles and their temperature falls, which leads, in turn,
to a decrease in the concentration of electrons because of
the intensification of the recombination processes.
The contraction of an arc in one-component gas
media is studied in papers [3-5]. Unfortunately, the
obtained results can not be apply to the case of an arc
discharge in gaseous mixtures due to the fact that the
properties of the mixtures and multicomponent plasmas
are known to be not additive relatively to the
concentration of components [6,7].
In this paper, the real cross-section of electron-atom
collisions are taken into account, and the influence of
characteristics of the gaseous medium on the process of
thermal contraction in the atmosphere of the various
mixtures of noble gases.
It should be mentioned that the contraction is usually
considered as a negative phenomenon that restricts an
application of arc discharges [1]. However, on the other
hand, in certain cases, namely the contraction can be a
base in applications of arc discharges in technology [4].
2. MODEL OF AN ARC DISCHARGE
Consider the plasma of the column of a cylindrical arc
discharge, in which a local thermodynamic equilibrium
(LTE) is maintained. Assuming that the heat release is
proportional to the local current density and ignoring the
radiant transfer, the heat transfer equation (the Elenbaas-
Heller equation) can be written as
( ) ( ) ( )( )
( )
1
0
e
e e p e
d dT dTr T T T
r dr dr dr
q r
κ κ κ ⋅ + +
+ =
(1)
Here, r is the distance from the discharge axis, T is
gaseous temperature, eT is electron temperature, ( ) Tκ ,
( )e eTκ , ( )p eTκ are the coefficients of gaseous, electron
heat conductivity and that due to the ionization-
recombination process, respectively; ( ) ( )q r j r E= is the
power of heat release per unit volume; ( ) Erj σ= is the
electric current density; E is the electric field strength, σ
is the electric conductivity.
Consider a gas at low ionization, when
e IkT U<< , where IU is the effective energy of ionization
of a gaseous medium. If LTE occurs, the number density
of electrons en at the point of discharge is connected with
the number densities of ions in and neutrals an by the
well-known Saha formula
3
2
2
2 2 expe i i e e I
a a e
n n g m kT U
n g h kT
π = −
, (2)
where em is electron mass, h is the Planck constant, ig ,
ag are the effective statistical weights of ion and atom,
respectively.
Since LTE occurs in the plasma region, which is
determined by its heat balance, the temperatures of
electrons and gas are varied weakly. That fact allows to
obtain an approximate solution of Eq.(1) by using the
method stated in [3,5]. Accordingly to this method, we
assume that the dependences of the current density, power
of heat release, and corresponding quantities on the
temperature in the cross-section of a discharge are given,
and the coefficients in Eq.(1) are constant, and their
values are set on the discharge axis. In this way we obtain
the following system of equations that is described an arc
discharge:
2 2
2 *3
e ea
e
e e ea
uM eET T
k m u
ν
ν
− =
, (3.1)
( )
122
16 1 5ge
T e p
I
rkTIE
E R
π κζ κ κ
− = + + +
, (3.2)
2
0 0
0
0 215 ln RS . q r
r
=
, (3.3)
e ep p NkT n kT+ ∆ = + , (3.4)
2
0rEI πσ ⋅= . (3.5)
Here e is an electron charge, M is an effective mass of
atom in gaseous mixtures (
1 1
aM x mα α
α
− −= ∑ , where the
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 181-183 181
subscript α indicates the type of species, am α is an atom
mass, xα is the molar concentration of α -species),
ea eα
α
ν ν= ∑ , ( )*
ea a eM m vα α
α
ν = ∑ , where eαν is the
frequency of electron-atom collisions for the α -species
in mixture, eu is the electron velocity, and the bracket
denotes the averaging over the Maxwellian
distribution of electron velocities; I is the arc current, R
is the radius of the chamber wall, S is the heat function,
2
0 Eq σ= , T edT dTζ = , p∆ is the diminution of pressure in
plasma, and 0r is a characteristic radius of plasma (radius
of contraction), which is determined from the relation
2 2 2
0 1.32 g Jr r r≈ + , where gr and Jr are determined as
2
2
0
16 e T
g
I
kTr
q E
κζ= ,
( )2
2
0
11.6 e e p
J
I
kT
r
q E
κ κ+
= .
The heat function S is determined as
( ) ( )( ) ( )' ' ' ' '
0 0
eT T
e e p e eS T T dT T dTκ κ κ= + +∫ ∫ .
For gaseous conductivity of inert gas mixtures it is
used the Wassiljeva’s formula with coefficients calculated
by the Mason-Saxena method [6] via the conductivities of
inert gases from [8]. To calculate electric conductivities of
the complex arc plasma it is used the first order
approximations from [7]. The pk can be expressed via the
coefficient of ambipolar diffusion [1]. Under calculations
the cross-section data are used from [9]. Upon increasing
the ionization degree it is essential to consider the
Coulomb collisions because it should be respectively
modified the above frequencies.
Also, it should be took into account the following
conditions: the quasineutrality of plasma e in n= , the
electric field strength and the atmosphere pressure are
constant ( E const= , p const= ).
The system (3) with the Saha formula (2) allows us to
obtain the values of 0, , , , , ,e e aE T T n n N r under the
desired values of the arc current I and pressure p and
vice versa.
3. RESULTS AND DISCUSSION
The above-presented model of an arc discharge
describes the discharge where the released heat is
transferred by means of conductivity into the wall of the
discharge tube. This situation corresponds to the
idealization of a long arc (see [5]).
The characteristics of an arc without radiation transfer are
known to describe in unified variables r R , ER and
I R . The calculation of a reduced radius of contraction
0r R in various regimes allows us to depict the following
discharge contraction pattern (Fig.1 and Fig.2). At a
relatively low current the extremely strong constriction of
an arc occurs under dominating the gaseous heat
conductivity. At increasing of current the electron heat
conductivity is raised to a leading hand. If the electron-
atom collisions are still dominated than the value of
reduced radius of contraction is stabilized i.e. r R∝ . At
the follow-up increasing of current the Coulomb collision
is prevailed and the discharge field is diminished.
Fig.1. The calculated values of the reduced radius 0r R
of contraction via reduced current I R ( p =1 atm).
Curves 1-He, 2-Ar, 3-He:Ar(10:90%), 4-He:Ar(20:80%),
5-He:Ar(30:70%), 6-He:Ar(50:50%), 7-He:Ar(70:30%),
8-He:Ar(80:20%) 9-He:Ar(90:10%)
It should be noted that Ar, Kr, and Xe belong to the
gases with a remarkably expressed Ramsauer effect that
causes the expansion of an arc discharge (see Fig.1 and
Fig.2). But, in the gaseous mixtures this influence may be
neutralized. Thus, the relatively small addition of He into
Ar causes the intense constriction of a discharge region
(Fig.1). Otherwise, for the mixture of gases having
Ramsauer effect an additional constriction is absent
(Fig.2).
Fig.2. The calculated values of the reduced radius 0r R
of contraction via reduced current I R ( p =1 atm).
Curves 1-Ar, 2-Xe, 3-Ar:Xe(10:90%), 4-Ar:Xe(20:80%)
4. CONCLUSION
182
The degree of thermal contraction of an arc discharge
is determined by the heat transfer characteristics of the
gaseous mixture and by the characteristics of electron-
atom collisions.
The contraction of a discharge in a certain mixture is
more pronounced in the case where the gaseous thermal
conductivity dominates in the heat transfer processes.
The presence of the Ramsauer effect for a gas
medium where an arc is burning has an essential influence
on the process of contraction, which is revealed in a
decrease in the constriction of an arc discharge in the
corresponded temperature range. But, in the gaseous
mixtures this influence may be neutralized by choosing a
suitable composition of mixture.
REFERENCES
[1] A.V. Yeletsky, L.A. Palkina, B.M. Smirnov. Transfer
phenomena in the slightly ionized plasma. Moscow:
“Atomizdat”, 1975 (In Russian).
[2] A.V. Yeletsky, A.T. Rakhimov. Instabilities in the gas
discharge plasma // Chemistry of Plasma (4). 1977,
pp.123-167 (In Russian).
[3] B.M. Smirnov. Contraction of the high-pressure
positive arc column // High Temp. Phys. (Teplofizika vys.
Temp.) (35). 1997, pp.14-18.
[4] B.E. Paton, V.N. Zamkov, V.P. Prilutsky, and
P.V. Porytskyy. Contraction of the welding arc caused by
the flux in tungsten-electrode-argon arc welding // The
Paton Welding Journal. 2000, No.1(562), pp.5-11.
[5] P.V. Porytskyy. Mechanisms of the contraction of an
arc discharge I. Peculiarities of thermal contraction //
Ukrainian J. Phys. (49). 2004, pp.883-889.
[6] R.C. Reid, J.M. Prausnitz, T.K. Sherwood. The
properties of gases and liquids. NY: McGraw-Hill. 1973.
[7] V.M. Zhdanov. Transport Phenomena in Multi-
component Plasma. Moscow: “Energoatomizdat”, 1982
(In Russian).
[8] V.G. Fastovskii, A.E. Rovinskii, Yu.V. Petrovskii,
Inert Gases. Moscow: “Atomizdat”, 1972 (In Russian).
[9] L.G.H. Huxley, R.W. Crompton. The diffusion and
drift of electrons in gases. NY: Wiley, 1974.
О ТЕПЛОВОЙ КОНТРАКЦИИ ДУГОВОГО РАЗРЯДА В ГАЗОВЫХ СМЕСЯХ
П. В. Порицкий
Рассмотрено влияние характеристик газовой среды на процесс контракции (сжатия) дугового разряда в
смесях инертных газов. Проведены расчеты и показано, что степень сжатия дугового разряда определяется
теплофизическими характеристиками газовой среды и характеристиками столкновений электронов с атомами
и ионами. Выявлено влияние эффекта Рамзауэра на характер контракции дугового разряда, а также показана
возможность нейтрализации этого эффекта соответствующим подбором состава смеси.
ПРО ТЕПЛОВУ КОНТРАКЦІЮ ДУГОВОГО РОЗРЯДУ В ГАЗОВИХ СУМІШАХ
П. В. Порицький
Розглянуто вплив характеристик газового середовища на процес контракції (стягування) дугового розряду в
сумішах інертних газів. Проведені розрахунки і показано, що ступінь стягування дугового розряду
визначається теплофізичними характеристиками газового середовища і характеристиками зіткнень електронів
з атомами та іонами. Висвітлено вплив ефекту Рамзауера на характер контракції дугового розряду, а також
показана можливість нейтралізації цього ефекту відповідним підбором складу суміші.
183
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| id | nasplib_isofts_kiev_ua-123456789-79062 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:06:26Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Porytskyy, P.V. 2015-03-25T19:22:12Z 2015-03-25T19:22:12Z 2005 On the contraction of an arc discharge in gaseous mixtures / P.V.Porytskyy // Вопросы атомной науки и техники. — 2005. — № 1. — С. 181-183. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.20.Fs, 52.25.Fi, 52.25.Ya, 52.27.Cm, 52.77.Fv, 52.50.Nr, 52.80.Mg https://nasplib.isofts.kiev.ua/handle/123456789/79062 The influence of properties of a gaseous medium on the process of contraction (self-constriction) of an arc discharge in the atmosphere of the mixtures of noble gases is considered. The calculations are carried out, and it is shown that the degree of constriction of an arc discharge is determined by both the thermal characteristics of the gaseous medium and the characteristics of electron-atom collisions. It is revealed that the Ramsauer effect has an influence on a character of the contraction of an arc. Also, it is shown the possibility to neutralize this influence in gaseous mixtures. Розглянуто вплив характеристик газового середовища на процес контракції (стягування) дугового розряду в сумішах інертних газів. Проведені розрахунки і показано, що ступінь стягування дугового розряду визначається теплофізичними характеристиками газового середовища і характеристиками зіткнень електронів з атомами та іонами. Висвітлено вплив ефекту Рамзауера на характер контракції дугового розряду, а також показана можливість нейтралізації цього ефекту відповідним підбором складу суміші. Рассмотрено влияние характеристик газовой среды на процесс контракции (сжатия) дугового разряда в смесях инертных газов. Проведены расчеты и показано, что степень сжатия дугового разряда определяется теплофизическими характеристиками газовой среды и характеристиками столкновений электронов с атомами и ионами. Выявлено влияние эффекта Рамзауэра на характер контракции дугового разряда, а также показана возможность нейтрализации этого эффекта соответствующим подбором состава смеси. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies On the contraction of an arc discharge in gaseous mixtures Про теплову контракцію дугового розряду в газових сумішах О тепловой контракции дугового разряда в газовых смесях Article published earlier |
| spellingShingle | On the contraction of an arc discharge in gaseous mixtures Porytskyy, P.V. Low temperature plasma and plasma technologies |
| title | On the contraction of an arc discharge in gaseous mixtures |
| title_alt | Про теплову контракцію дугового розряду в газових сумішах О тепловой контракции дугового разряда в газовых смесях |
| title_full | On the contraction of an arc discharge in gaseous mixtures |
| title_fullStr | On the contraction of an arc discharge in gaseous mixtures |
| title_full_unstemmed | On the contraction of an arc discharge in gaseous mixtures |
| title_short | On the contraction of an arc discharge in gaseous mixtures |
| title_sort | on the contraction of an arc discharge in gaseous mixtures |
| topic | Low temperature plasma and plasma technologies |
| topic_facet | Low temperature plasma and plasma technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79062 |
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