Emission characteristics and potential of macroparticle in beam-plasma discharge
Dust plasma now is one of most intensively developing directions of modern plasma physics. We will focus on the main task of the physical processes appearing in gas-discharge plasma with dust particles is definition of the value of electric potential of macroparticles, despite of the significant num...
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| Zitieren: | Emission characteristics and potential of macroparticle in beam-plasma discharge / А.А. Bizyukov, E.V. Romaschenko, К.N. Sereda, А.D. Chibisov, A.V. Nazarov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 162-164. — Бібліогр.: 6 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1109812025-02-09T13:24:55Z Emission characteristics and potential of macroparticle in beam-plasma discharge Електричний потенціал макрочастинки у пучково-плазмових системах Электрический потенциал макрочастицы в пучково-плазменных системах Bizyukov, A.A. Romaschenko, E.V. Sereda, K.N. Chibisov, A.D. Nazarov, A.V. Low temperature plasma and plasma technologies Dust plasma now is one of most intensively developing directions of modern plasma physics. We will focus on the main task of the physical processes appearing in gas-discharge plasma with dust particles is definition of the value of electric potential of macroparticles, despite of the significant number of articles devoted to this problem. In the present work the behaviour of floating electric potential of a particle in beam-plasma systems over the average energies of electron beams taking into account a secondary electron emission and also an auto-electron emission is studied. За теперішнього часу пилова плазма є одним з напрямків сучасної фізики плазми, які найбільш інтенсивно розвиваються. Незважаючи на велику кількість робіт, що присвячені цьому питанню, при вивченні фізичних процесів, що відбуваються у газорозрядній плазмі з пиловими частинками, актуальною проблемою є визначення величини електричного потенціалу макрочастинки. В даній роботі вивчається поведінка плаваючого електричного потенціалу макрочастинки у плазмово-пучкових системах у діапазоні середніх енергій електронних пучків з урахуванням вторинної електронної емісії та автоелектронної емісії. Пылевая плазма в настоящее время является одним из наиболее интенсивно развивающихся направлений современной физики плазмы. Несмотря на множество работ посвященных этому вопросу, при изучении физических процессов, происходящих в газоразрядной плазме с пылевыми частицами, актуальной задачей является определение величины электрического потенциала микрочастиц. В настоящей работе изучается поведение плавающего электрического потенциала макрочастицы в пучково-плазменных системах в диапазоне средних энергий электронных пучков с учетом вторичной электронной эмиссии, а также авто-электронной эмиссии. 2008 Article Emission characteristics and potential of macroparticle in beam-plasma discharge / А.А. Bizyukov, E.V. Romaschenko, К.N. Sereda, А.D. Chibisov, A.V. Nazarov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 162-164. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.27.Lw, 52.40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/110981 en Вопросы атомной науки и техники application/pdf 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 Bizyukov, A.A. Romaschenko, E.V. Sereda, K.N. Chibisov, A.D. Nazarov, A.V. Emission characteristics and potential of macroparticle in beam-plasma discharge Вопросы атомной науки и техники |
| description |
Dust plasma now is one of most intensively developing directions of modern plasma physics. We will focus on the main task of the physical processes appearing in gas-discharge plasma with dust particles is definition of the value of electric potential of macroparticles, despite of the significant number of articles devoted to this problem. In the present work the behaviour of floating electric potential of a particle in beam-plasma systems over the average energies of electron beams taking into account a secondary electron emission and also an auto-electron emission is studied. |
| format |
Article |
| author |
Bizyukov, A.A. Romaschenko, E.V. Sereda, K.N. Chibisov, A.D. Nazarov, A.V. |
| author_facet |
Bizyukov, A.A. Romaschenko, E.V. Sereda, K.N. Chibisov, A.D. Nazarov, A.V. |
| author_sort |
Bizyukov, A.A. |
| title |
Emission characteristics and potential of macroparticle in beam-plasma discharge |
| title_short |
Emission characteristics and potential of macroparticle in beam-plasma discharge |
| title_full |
Emission characteristics and potential of macroparticle in beam-plasma discharge |
| title_fullStr |
Emission characteristics and potential of macroparticle in beam-plasma discharge |
| title_full_unstemmed |
Emission characteristics and potential of macroparticle in beam-plasma discharge |
| title_sort |
emission characteristics and potential of macroparticle in beam-plasma discharge |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Low temperature plasma and plasma technologies |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110981 |
| citation_txt |
Emission characteristics and potential of macroparticle in beam-plasma discharge / А.А. Bizyukov, E.V. Romaschenko, К.N. Sereda, А.D. Chibisov, A.V. Nazarov // Вопросы атомной науки и техники. — 2008. — № 6. — С. 162-164. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-11-26T02:57:31Z |
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2025-11-26T02:57:31Z |
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| fulltext |
162 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6.
Series: Plasma Physics (14), p. 162-164.
EMISSION CHARACTERISTICS AND POTENTIAL
OF MACROPARTICLE IN BEAM-PLASMA DISCHARGE
А.А. Bizyukov, E.V. Romaschenko*, К.N. Sereda, А.D. Chibisov, A.V. Nazarov
V.N. Karazin Kharkov National University, Kharkov, Ukraine;
*V. Dal’ East Ukrainian National University, Lugansk, Ukraine;
E-mail: bizyukov@mail.ru
Dust plasma now is one of most intensively developing directions of modern plasma physics. We will focus on the
main task of the physical processes appearing in gas-discharge plasma with dust particles is definition of the value of
electric potential of macroparticles, despite of the significant number of articles devoted to this problem. In the present
work the behaviour of floating electric potential of a particle in beam-plasma systems over the average energies of
electron beams taking into account a secondary electron emission and also an auto-electron emission is studied.
PACS: 52.27.Lw, 52.40.Mj
1. INTRODUCTION
Investigation of the technological aspects of vacuum-
plasma processes consider to be of great interest for the
dust plasma applications. It is possible to cite vacuum-arc
methods of deposition hardening and a decorative coating
[1, 2] as an example, which based on generation of a
stream of metal plasma with macroparticles (metal drops
with the sizes from micrometers to hundreds micrometers)
at burning of an arc discharge at low pressures. Presence of
the drop phase at a plasma stream results to a deterioration
of performances of coatings [3, 4].
In the present work interacting of an electron beam
with a solitary dust particle being in plasma is observed,
influence of emissive processes on the potential value is
taken into consideration. Modeling of process of charging
is fulfilled for a wide range of energies of an electron
beam, and as consequence, for a wide range of potentials
of a dust particle that results to usage of various
approximations for description of ion collection and beam
and plasma electrons.
2. A STEADY-STATE VALUE OF ELECTRIC
POTENTIAL OF A DUST PARTICLE
The steady-state value of floating potential of dust
particle in beam-plasma system is defined from a
requirement of balance of currents:
( )( ) 01 =+−−++ IIII sbebei ϕεδ (1).
Here, iI , eI and bI – currents of ions and electrons from
plasma and a current of electrons of a beam on a surface
of a dust particle accordingly,
)/1082.239.4(
2
6 2/372/1
10104.1 E
a
EAI φφ
φ
⋅−− ⋅⋅⋅= – an autoelectronic
emission current; E – an electric field strength which on
estimates attains of values of cmV /1010 87 ÷ , φ –
potential of a work function of metal;
( ) ( )
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −
−⋅⋅=
bm
sb
bm
b
mbe Exp
ε
ϕε
ε
εδεδ 24.7 – a secondary
electron emission coefficient representing an empirical-
formula dependence from energy of primary electrons
attaining surface of a material [5], ϕ – potential of a dust
particle, bε – energy of electrons of a beam, bmε – energy
of primary electrons at which the secondary emission
ratio has the greatest value of mδ . Depending on a
relation of currents coming and leaving from a surface of
a particle and the value of energy of electrons of a beam,
its electric potential can be both negative, and positive.
In case of negatively charged particle ( 0<sϕ ) the
electron current from plasma is defined by expression:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
e
s
Tee T
evnaI ϕ
π exp8 0
2 , (2)
where 0n – a plasma density, eT – temperature of
electrons,
e
e
Te m
Tv = – a thermal velocity of electrons.
The electron beam current on a surface of a dust
particle is defined from model of restricted orbits by
analogy to derivation of the formula of a current of
electrons from plasma [5]. In expression (3) electron-
electronic emission called by bombardment of a dust
particle surface by electron beam is considered also:
( )δ
ε
ϕε
−⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−⋅⋅⋅= 11)(
be
b
bab
e
m
nAaI , (3)
here aA – area of surface of a dust particle with radius a ;
bn – a density of electrons of a beam; e and em – a
charge and electron mass accordingly;
e
b
eb m
v ε
= – a
velocity of electrons of a beam.
At low values of potential 1~
e
s
T
eϕ of a dust particle
the path of ions are well enough described by model of
restricted orbits. In this case the ion current on a particle
very close to the expression derived in [5]:
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+−= Φ−Φ− ee
a
sjAI rai 1
2
2
, (4)
where,
2
1
0
2
2
1
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
i
i
r m
kTnj
π
,
i
s
kT
e
as
a ϕ
22
2
−
=Φ , 24 aAa π= ,
iT and im – temperature and an ion mass, accordingly.
163
Let us
eT
ez ϕ
= ,
i
e
m
m
=μ ,
i
e
T
T
=τ ,
b
e
b
T
ε
τ = ,
0
~
n
n
n b= ,
da λξ = . The balance equation of currents (1) will become:
( ) ( )
( )( )
2 2
2
2
1
exp 2 1 exp
2 1
exp (1 ) 1 ,
2 1 2 b e b
b
z z
nz z z
ξμ ξπ τ
τ ξ ξ
ξ τ τ δ τ
ξ τ
⎛ ⎛ ⎞+ ⎛ ⎞
− = − ⋅ +⎜ ⎜ ⎟⎜ ⎟⎜ +⎝ ⎠⎝ ⎠⎝
⎞⎛ ⎞
+ ⋅ − − ⋅ −⎟⎜ ⎟+⎝ ⎠⎠
%
(5)
In a extreme case 1<<τξ that corresponds to a
low densities of plasma, exponential expansion in the
formula (4) result into the well-known formula of an ion
current [3, 6].
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
i
s
Ti
OML
i T
evnaI ϕπ 18 0
2 (6)
In this case the balance equation (5) assumes the
simplified form:
( ) ( ) ( )( )zznzz beb
b
,1)1(
2
~
1exp τδτ
τ
τ
τ
μ
−⋅−−+=− (7)
In a case is positively charged particle 0>sϕ , an
electron current from plasma and a current of a beam look
like:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+=
b
s
ebbb
evnaI
ε
ϕπ 12 , (8)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+=
e
s
Tee T
evnaI ϕ
π 18 0
2 . (9)
Such regime of charging is possible in some range of
energies of an electron beam. Energies 1ε and 2ε also
define an energy ranges of primary electrons, at which
secondary electron emission coefficient ( ) 1, >zbe τδ .
In beam-plasma discharge the temperature of ions is
close to zero, having guessed, that as a result of a secondary
electron emission the potential of a dust particle can to take
value over more 1 V, the ion current on a particle surface can
be neglected. The equation for potential determination of
positively charged dust particle looks like:
( ) ( )( ) 0,11
2
11 =−⋅+++ zzz beb
b
τδτ
τ
. (10)
At enough high potentials 1>>
e
s
T
eϕ , an ion current
transfers in a regime of limitation by volume charge and can
be presented by Chield-Lagmuire law. The requirement of
balance of currents is described by system of two equations
where along with the unknown variable sϕ an unknown
variable s – the size of a volume charge layer occurs:
( ) ( ) ( )
( ) ( )⎩
⎨
⎧
=−
=+++
0
0)(2/3
sIaI
aIaIaIaI
ii
ibe (11)
Here
( )
3
2
3 / 2
2
4 2
( )
9i a
i
e
I a A
m s a
ϕ
α
= ⋅ ⋅ ⋅ – a current
of ions on a surface of the dust particle, expressed by the
law of «3/2» in a spherical case; ( )as2α – a
transcendental function;
i
e
s
b
i m
TnAsI ⋅⋅⋅= 61.0)( – an
ion current going from a layer surface sA .
2000 3000 4000 5000 6000
500
1000
1500
2000
2500
3000
3500
4000
Beam energy, eV
1
2
3
4
5
6
7
8
10
9
ϕ
s
,v
ε, ev
Dependence of potential ( sϕ ) of a dust particle on energy
of a beam ( bε ) for the various sizes of dust particles
1 – ma μ1.0= ,2 – ma μ2.0= ,3 – ma μ3.0= ,
4 – ma μ4.0= , 5 – ma μ5.0= ,6 – ma μ6.0= ,
7 – ma μ7.0= ,8 – ma μ8.0= , 9 – ma μ9.0= ,
10 – ma μ1=
First equation represents balance of currents on a surface
of a dust particle; second one is a continuity equation.
Numerical solution of the equation (11) were made
for plasma with a density of 39
0 10 −= сmn , particle sizes
сma 53 1010 −− ÷= , and 3910 −= cmnb of a density of an
electron beam over the range beam energies.
On the Figure the value of potentials of a dust
particles in beam-plasma discharge are shown. One can
see, that at high potentials, with magnification of energy
of a beam charging of a dust particle is practically
stopped, this effect on small dust particles becomes much
stronger. Presence of this effect is stipulated by rise of
electric field strength near to a surface of a dust particle
and appearance of autoelectronic emission which hinders
the further charging of a dust particle.
REFERENCES
1. A.A. Andreev, L.P. Sablev, V.M. Shulaev,
S.N. Grigoriev. Vacuum-arc devices and coatings.
Kharkov: NSC KIPT, 2005.
2. I.I. Aksenov. Vacuum arc in erosive sources of
plasma. Kharkov: NSC KIPT, 2005.
3. R.L. Boxman and S.Goldsmith // Surf. Coat Technol.
1992, v. 52, p. 39-50.
4. Collected Works of Irving Langmuir /Ed. by G. Suits.
New York, 1961, v. 4.
5. I.M. Bronshtejn, B.S. Frajman Secondary electron
emission. Moscow: “Nauka”, 1969.
6. P.K. Shukla, A.A. Mamun Introduction to Dusty
Plasma Physics/ Institute of Physics Publishing. Series in
Plasma Physics, 2002.
Article received 22.09.08.
ЭЛЕКТРИЧЕСКИЙ ПОТЕНЦИАЛ МАКРОЧАСТИЦЫ В ПУЧКОВО-ПЛАЗМЕННЫХ СИСТЕМАХ
А.А. Бизюков, Е.В. Ромащенко, К.Н. Середа, А.Д. Чибисов, А.В. Назаров
Пылевая плазма в настоящее время является одним из наиболее интенсивно развивающихся направлений
современной физики плазмы. Несмотря на множество работ посвященных этому вопросу, при изучении
физических процессов, происходящих в газоразрядной плазме с пылевыми частицами, актуальной задачей
является определение величины электрического потенциала микрочастиц. В настоящей работе изучается
поведение плавающего электрического потенциала макрочастицы в пучково-плазменных системах в диапазоне
средних энергий электронных пучков с учетом вторичной электронной эмиссии, а также авто-электронной
эмиссии.
ЕЛЕКТРИЧНИЙ ПОТЕНЦІАЛ МАКРОЧАСТИНКИ У ПУЧКОВО-ПЛАЗМОВИХ СИСТЕМАХ
О.А. Бізюков, О.В. Ромащенко, К.М. Середа, О.Д. Чібісов, О.В. Назаров
За теперішнього часу пилова плазма є одним з напрямків сучасної фізики плазми, які найбільш інтенсивно
розвиваються. Незважаючи на велику кількість робіт, що присвячені цьому питанню, при вивченні фізичних
процесів, що відбуваються у газорозрядній плазмі з пиловими частинками, актуальною проблемою є
визначення величини електричного потенціалу макрочастинки. В даній роботі вивчається поведінка
плаваючого електричного потенціалу макрочастинки у плазмово-пучкових системах у діапазоні середніх
енергій електронних пучків з урахуванням вторинної електронної емісії та автоелектронної емісії.
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