On the influence of metal impurities on the thermal contraction of a nitrogen arc
The influence of metal impurities on the process of contraction (self-constriction) of an arc discharge is considered in the ambient atmosphere of nitrogen. The calculations are carried out, and it is shown that the degree of constriction of an arc discharge is determined by both the thermal chara...
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irk-123456789-823052015-05-28T03:02:31Z On the influence of metal impurities on the thermal contraction of a nitrogen arc Porytskyy, P. V. Veklich, A.M. Low temperature plasma and plasma technologies The influence of metal impurities on the process of contraction (self-constriction) of an arc discharge is considered in the ambient atmosphere of nitrogen. 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 shape resonance effect under electron-atom collisions has an influence on a character of the contraction of an arc. 2006 Article On the influence of metal impurities on the thermal contraction of a nitrogen arc / P. V. Porytskyy, A.M. Veklich // Вопросы атомной науки и техники. — 2006. — № 6. — С. 222-224. — Бібліогр.: 13 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 http://dspace.nbuv.gov.ua/handle/123456789/82305 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 Porytskyy, P. V. Veklich, A.M. On the influence of metal impurities on the thermal contraction of a nitrogen arc Вопросы атомной науки и техники |
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The influence of metal impurities on the process of contraction (self-constriction) of an arc discharge is considered in
the ambient atmosphere of nitrogen. 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 shape resonance effect under electron-atom collisions has an influence
on a character of the contraction of an arc. |
| format |
Article |
| author |
Porytskyy, P. V. Veklich, A.M. |
| author_facet |
Porytskyy, P. V. Veklich, A.M. |
| author_sort |
Porytskyy, P. V. |
| title |
On the influence of metal impurities on the thermal contraction of a nitrogen arc |
| title_short |
On the influence of metal impurities on the thermal contraction of a nitrogen arc |
| title_full |
On the influence of metal impurities on the thermal contraction of a nitrogen arc |
| title_fullStr |
On the influence of metal impurities on the thermal contraction of a nitrogen arc |
| title_full_unstemmed |
On the influence of metal impurities on the thermal contraction of a nitrogen arc |
| title_sort |
on the influence of metal impurities on the thermal contraction of a nitrogen arc |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2006 |
| topic_facet |
Low temperature plasma and plasma technologies |
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http://dspace.nbuv.gov.ua/handle/123456789/82305 |
| citation_txt |
On the influence of metal impurities on the thermal contraction of a nitrogen arc / P. V. Porytskyy, A.M. Veklich // Вопросы атомной науки и техники. — 2006. — № 6. — С. 222-224. — Бібліогр.: 13 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT porytskyypv ontheinfluenceofmetalimpuritiesonthethermalcontractionofanitrogenarc AT veklicham ontheinfluenceofmetalimpuritiesonthethermalcontractionofanitrogenarc |
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2025-07-06T08:48:53Z |
| last_indexed |
2025-07-06T08:48:53Z |
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1836886768933142528 |
| fulltext |
222 Problems of Atomic Science and Technology. 2006, 6. Series: Plasma Physics (12), p. 222-224
ON THE INFLUENCE OF METAL IMPURITIES ON THE THERMAL
CONTRACTION OF A NITROGEN ARC
P. V. Porytskyy1, A.M. Veklich2
1Institute for Nuclear Research, pr. Nauky 47, 03680, Kyiv, Ukraine;
2Taras Shevchenko Kyiv National University, Volodymyrs’ka Str. 64, 01033, Kyiv, Ukraine;
e-mails: poryts@kinr.kiev.ua, van@univ.kiev.ua
The influence of metal impurities on the process of contraction (self-constriction) of an arc discharge is considered in
the ambient atmosphere of nitrogen. 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 shape resonance effect under electron-atom collisions has an influence
on a character of the contraction of an arc.
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 [1-4]. 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 [2-4]. 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 [5,6].
In this paper, it is studied the thermal contraction of
an arc in the various mixtures of nitrogen with some
metals on the base of formalism of papers [7,8].
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 [3].
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
g rd
e
e e ri e
dTT Td drr q r
dTr dr T T
dr
κ κ
κ κ
+ ⋅ + =
+ +
.
(1)
Here, r is the distance from the discharge axis, T is
gaseous temperature, eT is electron temperature,
( )g Tκ , ( )rd Tκ , ( )e eTκ , ( )ri eTκ are the coefficients of
gaseous, dissociate, electron, ionization heat
conductivities, respectively; ( ) ( )q r j r E= is the power of
heat release per unit volume; ( ) Erj σ= is the electric
current density; E is electric field strength, σ is 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 [2,4,7,8]. 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
h T e
I
rkTIE
E R
π κ ζ κ
− = + +
, (3.2)
2
0 0
0
0 215 ln RS . q r
r
=
, (3.3)
e ep p NkT n kT+ ∆ = + , (3.4)
mailto:poryts@kinr.kiev.ua
mailto:van@univ.kiev.ua
223
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
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; *
h g rdκ κ κ= + ,
*
e e riκ κ κ= + , 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 h T
g
I
kTr
q E
κ ζ
= ,
2 *
2
0
11.6 e e
J
I
kTr
q E
κ
= .
The heat function S is determined as
( ) ( )* ' ' * ' '
0 0
eT T
e e e hS T dT T dTκ κ= +∫ ∫ .
For gaseous conductivity of inert gas mixtures it is
used the Wassiljeva’s formula with coefficients
calculated by the Mason-Saxena method [5]. To calculate
electric conductivities of the complex arc plasma it is
used the first order approximations from [6]. Under
calculations the cross-section data are used from [9-13].
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 ambient 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 [4]).
The characteristics of an arc without radiation
transfer are known to describe in unified variables r R ,
ER and I R . The arc temperatures are calculated for
some mixtures (Fig.1). In experiment the atmospheric air
arc discharge is studied between melting Ag-CdO
electrodes under 3.5 A. Thus, we can see that the
measurements using Ag I lines are in good agreement
with calculation.
Fig.1.The calculated values of the electron temperature
on the axis of the arc ( p =1 atm). Calculation: the
equimolar mixtures of nitrogen (90%) with metals (10%),
curves 1-N2-Hg, 2- N2-Zn, 3- N2-Cd, 4- N2-Ag, 5- N2-Mo.
Experiment: the arc in Ag-Cd vapours (present work), 6 -
from Ag I lines (520.9 nm, 827.3 nm), 7 - from Cd I lines
(479.9 nm, 508.5 nm, 643.8 nm)
Fig.2. The calculated values of the reduced radius 0r R
of contraction via reduced current I R ( p =1 atm) for
the equimolar mixtures of nitrogen (90%) with metals
(10%), curves 1-N2-Hg, 2- N2-Zn, 3- N2-Cd, 4- N2-Ag,
5-N2-Mo
The calculation of a reduced radius of contraction
0r R in various regimes allows us to depict the
following discharge contraction pattern (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.
224
The most important influence on the properties of an
arc plasmas have the discrepancy between gaseous and
electron temperatures that depends on the peculiarities of
electron-atom cross-sections. It should be noted that
under scattering of electrons on molybdenum the shape
resonance takes place. That causes the strong constriction
of an arc under low current (Fig.2).
4. CONCLUSIONS
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 shape resonance effect for a
gas medium where an arc is burning has an essential
influence on the process of contraction under low
current.
REFERENCES
1. A.V. Yeletsky, L.A. Palkina, B.M. Smirnov. Transfer
phenomena in the slightly ionized plasma. Moscow:
“Atomizdat”, 1975 (In Russian).
2. B.M. Smirnov. Contraction of the high-pressure
positive arc column // High Temp. (Teplofizika vys.
Temp.) 1997, v.35, p.14-18.
3. B.E. Paton, V.N. Zamkov, V.P. Prilutsky,
P.V. Porytskyy. Contraction of the welding arc caused by
the flux in tungsten-electrode-argon arc welding // The
Paton Welding Journal(562). 2000, N1, p.5-11.
4. P.V. Porytskyy // Mechanisms of the contraction of an
arc discharge I. Peculiarities of thermal contraction //
Ukrainian J. Phys. 2004, v.49, p.883-889.
5. R.C. Reid, J.M. Prausnitz, T.K. Sherwood. The
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component Plasma. Moscow: Energoatomizdat, 1982 (In
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7. P.V. Porytskyy. Mechanisms of the contraction of an
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current arc in the mixture of a noble gas with copper //
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