Сharging processes and phase states of macroparticles in low-pressure arc discharge
The effects of plasma density and ionic charge on the floating potential of the solitary macroparticle (MP) in a low-pressure arc discharge have been investigated. The energy balance has been studied taking into account mutual influence on each other of the charging processes and heating of the MP....
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1121842017-01-23T22:30:04Z Сharging processes and phase states of macroparticles in low-pressure arc discharge Bizyukov, А.А. Chibisov, А.D. Sereda, K.N. Romashchenko, E.V. Dimitrova, V. Плазменно-пучковый разряд, газовый разряд и плазмохимия The effects of plasma density and ionic charge on the floating potential of the solitary macroparticle (MP) in a low-pressure arc discharge have been investigated. The energy balance has been studied taking into account mutual influence on each other of the charging processes and heating of the MP. The possibility of the evaporation of the MP is shown. У дуговому розряді низького тиску було досліджено вплив густини плазми та заряду іонів на плаваючий потенціал відокремленої макрочастинки (МЧ). Розглянуто енергетичний баланс з урахуванням взаємного впливу один на одного процесів зарядження та розігріву МЧ. Показано можливість випаровування МЧ В дуговом разряде низкого давления исследуется влияние плотности плазмы и заряда ионов на плавающий потенциал уединенной макрочастицы (МЧ). Рассмотрен энергетический баланс с учетом взаимного влияния друг на друга процессов зарядки и разогрева МЧ. Показана возможность испарения МЧ. 2013 Article Сharging processes and phase states of macroparticles in low-pressure arc discharge / А.А. Bizyukov, А.D. Chibisov, K.N. Sereda, E.V. Romashchenko, V. Dimitrova // Вопросы атомной науки и техники. — 2013. — № 4. — С. 176-178. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.40.Hf http://dspace.nbuv.gov.ua/handle/123456789/112184 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия Bizyukov, А.А. Chibisov, А.D. Sereda, K.N. Romashchenko, E.V. Dimitrova, V. Сharging processes and phase states of macroparticles in low-pressure arc discharge Вопросы атомной науки и техники |
| description |
The effects of plasma density and ionic charge on the floating potential of the solitary macroparticle (MP) in a low-pressure arc discharge have been investigated. The energy balance has been studied taking into account mutual influence on each other of the charging processes and heating of the MP. The possibility of the evaporation of the MP is shown. |
| format |
Article |
| author |
Bizyukov, А.А. Chibisov, А.D. Sereda, K.N. Romashchenko, E.V. Dimitrova, V. |
| author_facet |
Bizyukov, А.А. Chibisov, А.D. Sereda, K.N. Romashchenko, E.V. Dimitrova, V. |
| author_sort |
Bizyukov, А.А. |
| title |
Сharging processes and phase states of macroparticles in low-pressure arc discharge |
| title_short |
Сharging processes and phase states of macroparticles in low-pressure arc discharge |
| title_full |
Сharging processes and phase states of macroparticles in low-pressure arc discharge |
| title_fullStr |
Сharging processes and phase states of macroparticles in low-pressure arc discharge |
| title_full_unstemmed |
Сharging processes and phase states of macroparticles in low-pressure arc discharge |
| title_sort |
сharging processes and phase states of macroparticles in low-pressure arc discharge |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2013 |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112184 |
| citation_txt |
Сharging processes and phase states of macroparticles in low-pressure arc discharge / А.А. Bizyukov, А.D. Chibisov, K.N. Sereda, E.V. Romashchenko, V. Dimitrova // Вопросы атомной науки и техники. — 2013. — № 4. — С. 176-178. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| first_indexed |
2025-07-08T03:30:39Z |
| last_indexed |
2025-07-08T03:30:39Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2013. №4(86) 176
CHARGING PROCESSES AND PHASE STATES OF MACROPARTICLES
IN LOW-PRESSURE ARC DISCHARGE
А.А. Bizyukov1, А.D. Chibisov1, K.N. Sereda1, E.V. Romashchenko2, V. Dimitrova3
1 V.N. Karazin Kharkov National University, Kharkov, Ukraine;
2 V. Dahl East Ukrainian National University, Lugansk, Ukraine;
3 Sofia University St. Kliment Ohridski, Bulgaria
E-mail: bizyukov@mail.ru
The effects of plasma density and ionic charge on the floating potential of the solitary macroparticle (MP) in a
low-pressure arc discharge have been investigated. The energy balance has been studied taking into account mutual
influence on each other of the charging processes and heating of the MP. The possibility of the evaporation of the
MP is shown.
PACS: 52.40.Hf
INTRODUCTION
The usage of arc vacuum discharge in technological
processes requires the control of melted drops in the
plasma flow. There are conditions when the drops of the
cathode substance can be evaporated during its passing
through the plasma from cathode of arc evaporator to
substrate [1, 2]. The analysis of the charging processes
and energy exchange at the MP surface denotes the pos-
sibility of the evaporation of the MP. The influence of
the parameters of low-temperature collisionless plasma
with singly charged ions on the floating potential and
equilibrium temperature of the MP has been investi-
gated in [2]. The authors also considered the mutual
influence on each other of the charging processes and
heating of the MP. In this paper, we consider a more
general plasma situation in which the multi-charged
ions have some streaming speed. This case corresponds
to plasma of the low-pressure arc discharge. The inter-
action of MP with such plasma has been studied. The
effects of plasma density and ionic charge on the MP
floating potential have been investigated. The possibil-
ity of the evaporation of the MP in a low-pressure arc
discharge has been studied.
1. FLOATING POTENTIAL OF MP
Let us consider a charging process of the MP in me-
tallic plasma which produced by a low-pressure arc dis-
charge. There are ions with different charges in such
plasmas. Moreover, the plasma is characterized by high
velocity of plasma flow [3]. The MP is immersed in
plasma charges to the some floating potential mpϕ due
to flows the plasma particles and various kinds of emis-
sion on its surface [2, 4]. The MP is mainly charged by
the collection of electrons and ions from the plasma.
Expressions for the charging currents flowing onto MP
surface in a collisionless plasma can be derived from the
OML (orbit motion limited) approximation [5]. The
electron and ion currents to a MP with a negative poten-
tial are
( )2
08 expe Te mp eI a n e v e Tπ ϕ= − , (1)
( ) ( )2
2
0 21
2
i iDi
i
i
aT
I n Z e a e e
m a
χ χλ
π
π
− −
⎡ ⎤+
= − +⎢ ⎥
⎢ ⎥⎣ ⎦
, (2)
where
( )
12
2 1mp D
i
i
Ze a
T a
ϕ λ
χ
−
⎡ ⎤+
= −⎢ ⎥
⎢ ⎥⎣ ⎦
.
Here, 0n is the plasma density, Z is the ionic charge,
( )e iT is the electron (ion) temperature,
( ) ( ) ( )Te i e i e iv T m= is the electron (ion) thermal veloc-
ity.
The interaction of MP with plasma ions incident
onto the MP surface causes emissions of electrons from
the MP surface. The emitted electrons are known as
secondary. The value of the secondary ion-electron
yield depends on ionic charge. The electron current
emitted from MP surface is written as follows
i e b i e
s i sI I δ− −= , (3)
where i e
sδ
− is the secondary ion-electron yield [6]. The
effective current is defined as
( )1eff i e i e
i i s i sI I I I δ− −= + = + . (4)
There is another significant charging process at high
temperature of MP – it is thermionic emission [2]. Tak-
ing into account the work function reduction by the ef-
fect of the external electric field E (Schottky effect) the
thermionic current is calculated through [7]:
( )
2 3/ 4 1
2
13/ 4 1
2 exp
sin
mp mpsh
e
mpmp
T E T EI a
TE T
φ
π
−
−−
⎡ ⎤−
= ⋅ ⋅ −⎢ ⎥
⎢ ⎥⎣ ⎦
, (5)
where E is the electric field on MP surface, Tmp is the
MP temperature, φ is the work function.
In a case of formation of the space charge around
MP surface, the thermionic current is limited by the
Child-Langmuir Law [8] that in spherical geometry is
given by
( )( )
3 2
3/2
2
4 2
9
mp
e
e D
e
I
m a a
ϕ
α λ
=
+
, (6)
where Dλ is the Debye length, 2α is the transcendental
function [8].
Thus, using (5) and (6), the thermionic emission cur-
rent from the MP surface is determined by conditions:
( ) ( )
( ) ( )
3/ 2 3/ 2
3/ 2
, ;
, .
sh
e e mp e mpth
e sh sh
e e mp e mp
I I I
I
I I I
ϕ ϕ
ϕ ϕ
⎧ >⎪= ⎨
<⎪⎩
(7)
ISSN 1562-6016. ВАНТ. 2013. №4(86) 177
The MP floating potential is determined by the bal-
ance of charging currents (1), (4), (7) to its surface:
( ) ( ) ( ) 0eff th
e mp i mp e mpI I Iϕ ϕ ϕ+ + = . (8)
For ions with charges Z=1, 2, 3, we numerically
solve Eq. (8) for some typical ion energies that are rep-
resentative of low-temperature arc discharge.
109 1010 1011 1012 1013 1014
-60
-50
-40
-30
-20
-10
0
ϕ m
p, V
n0, cm-3
1'
2'
3'
1
2
3
Fig. 1. The dependence of the tungsten MP potential
on plasma density: 1,1' – 1Z = ; 2,2’ – 2Z = ;
3,3’ – 3Z = ; dashed lines 1,2,3 – 20 eV,
solid lines –1’,2’,3’ – 35 eV
Fig. 1 shows that the potential is considerably gov-
erned by the ionic charge. The ions carry charges to MP
and cause the secondary ion-electron emission simulta-
neously. The increase in the ionic charge leads to in-
crease of secondary ion-electron yield. It decreases the
magnitude of MP surface potential. The ionic energy
has no significant effect on the magnitude of potential in
the energy region compared to effect of the ionic
charge.
2. HEATING OF MP
Now consider the contribution of basic processes of
energy exchange between the plasma and MP that lead
to heating of MP. In the OML theory the plasma particle
energy fluxes to MP are determined by:
( )2
08 2 exppl
e Te mp e eP a n v e T Tπ ϕ= − , (9)
( )( ) /pl pl
i i i mp recP I T e Z e Zϕ ε= + + , (10)
where rec
iε is the recombination energy of an ion. The
values of recombination energy of tungsten ions are
given in Table.
Z=1 Z=2 Z=3
,rec
i eVε 7,131 15,72 29,6
The power of thermal radiation from MP surface is
defined by the Stefan-Boltzmann low and is given by:
2 44rad
a mpP a Tπ θσ= , (11)
where θ is the emissivity of MP material, σ is the Ste-
fan-Boltzmann constant.
The MP temperature changes in time and describes
by equation:
( )mp mpcm dT dt P TΣ= ,
where c is the specific heat of MP substance, mpm is
MP mass, ( ) pl pl rad
mp e i aP T P P PΣ = + − is total energy
flow, that includes of basic processes of the energy ex-
change on MP surface (9) - (11). The initially MP tem-
perature is equal 0T , then due to energy flows on its
surface the MP temperature changes until the energy
equilibrium is reached. This occurs when
( ) 0eq
mp mpP TΣ = . (12)
Hence, we obtain the equilibrium temperature eq
mpT .
The MP temperature, affects on the potential of MP
due to the effect of thermionic emission, and its poten-
tial, in turn, affects on to the flow of energy from the
plasma to the MP surface. To consider the mutual influ-
ence of the MP temperature and potential, we numeri-
cally analyze the system of balance equations (8) and
(12). The results of analysis for tungsten MP are pre-
sented in Fig. 2.
109 1010 1011 1012 1013 1014
-60
-50
-40
-30
-20
-10
0
ϕ m
p,V
n0, cm-3
1
2
3
1'
2' 3'
(a)
109 1010 1011 1012 1013 1014
0
1000
2000
3000
4000
5000
T e
q
m
p, o K
n0, cm-3
1
2
3 2'
3'
1'
(b)
Fig. 2. The dependence of potential (a)
and corresponding temperature (b)
of tungsten MP on plasma density: 1,1' – 1Z = ;
2,2’ – 2Z = ; 3,3’ – 3Z = ;
dashed lines 1,2,3…20 eV, solid lines 1,2,3…35 eV
In case of ionic energy 20iT < eV, the results for
MP in plasma with density 13
0 10n < cm-3 do not differ
from results for cold MP. For plasma density
13
0 10n > cm-3, efficient heating of MP (see Fig. 2,b)
leads to an increase of the thermionic current, and as a
result the magnitude of the MP potential decreases. This
case corresponds to plasma of the pulse arc discharge.
Fig. 2 illustrates that the results for MP in plasma
with singly charged ions with energy 30iT ≈ eV and the
results for cold MP are similar. In the case of ions with
charge Z=2 and Z=3 in plasma with density
10
0 10n < cm-3 and 11
0 3 10n < ⋅ cm-3, respectively, the MP
potential decreases to null. This effect associates with
MP discharging by thermionic emission, which causes
due to efficient heating of MP. The MP heating is con-
nected to the energy release caused by recombination of
ions on the MP surface. The energy released on the MP
ISSN 1562-6016. ВАНТ. 2013. №4(86) 178
surface in a plasma with doubly and triply charged ions
is larger than it of single charged ions in 2,2 and 4,15
times, respectively. For plasma with low density, the
electron current does not compensate for thermionic
emission. If we increase the plasma density, the electron
current increases and compensates for discharging by
thermionic emission, and as a result the potential in-
creases. A further increase in the plasma density leads to
increase of the energy flux from plasma and MP tem-
perature. The effect considered above leads to an in-
crease of thermionic emission and as result decrease of
MP absolute potential, whereas the equilibrium tem-
perature considerably increases.
The growth of MP temperature stops when it reaches
the boil temperature of MP substance. The MP radius
changes in time during it boiling and describes by equa-
tion:
( )
24
b
mp mpH P Tdr
dt rπ ρ
Σ
= − , (13)
where ρ is the substance density, H is vaporization heat.
The total evaporation time of the MP with radius a
is given by:
( )
2
0
4
a
b b
mp mp
r drt
H P T
πρ
Σ
= ∫ . (14)
1013 101410-3
10-2
10-1
100
101
t b, s
n0, cm-3
1
2
Fig. 3. The dependence of the tungsten MP evaporation
time on plasma density: 1 – 1 μm; 2 – 10 μm averaged
over an ionic energy
Fig. 3. shows dependence of tungsten MP’s evapora-
tion time versus plasma density. For tungsten MPs with
radii 1 μm and 10 μm, immersed in plasma with den-
sity 14
0 10n = cm-3, the evaporation time are 310− and
22 10−⋅ s, respectively. For plasma densities
14
0 10n < cm-3, the evaporation time rapidly increases.
CONCLUSIONS
To summarize, we have examined the effects of io-
nic charge and energy as well as plasma density on the
MP floating potential.
It is shown that the potential is considerably gov-
erned by the ionic charge. The ionic energy has no sig-
nificant effect on the magnitude of MP potential in the
typical energy region of the arc discharges.
For doubly and triply charged ions due to recombi-
nation of ions on MP surface, efficient heating takes
place. Thus, MP is discharged by thermionic emission.
The MP evaporation is possible in dense plasma.
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Article received 12.04.2013.
ПРОЦЕССЫ ЗАРЯДКИ И ФАЗОВЫЕ СОСТОЯНИЯ МАКРОЧАСТИЦ В ДУГОВОМ РАЗРЯДЕ
НИЗКОГО ДАВЛЕНИЯ
А.А. Бизюков, А.Д. Чибисов, К.Н. Середа, Е.В. Ромащенко, В. Димитрова
В дуговом разряде низкого давления исследуется влияние плотности плазмы и заряда ионов на плаваю-
щий потенциал уединенной макрочастицы (МЧ). Рассмотрен энергетический баланс с учетом взаимного
влияния друг на друга процессов зарядки и разогрева МЧ. Показана возможность испарения МЧ.
ПРОЦЕСИ ЗАРЯДЖЕННЯ ТА ФАЗОВІ СТАНИ МАКРОЧАСТИНОК У ДУГОВОМУ РОЗРЯДІ
НИЗЬКОГО ТИСКУ
О.А. Бізюков, О.Д. Чибисов, К.М. Середа, О.В. Ромащенко, В. Дімітрова
У дуговому розряді низького тиску було досліджено вплив густини плазми та заряду іонів на плаваючий
потенціал відокремленої макрочастинки (МЧ). Розглянуто енергетичний баланс з урахуванням взаємного
впливу один на одного процесів зарядження та розігріву МЧ. Показано можливість випаровування МЧ.
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