Charging of macroparticles in a high-voltage vacuum arc sheath
Charging of macroparticles (MPs) in front of the negatively biased surface emitted the secondary electrons due to bombardment by multiply charged ions (MCIs) has been investigated. It was found that MPs can be either reflected or attracted to the substrate depending on the substrate bias. Исследуетс...
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| Zitieren: | Charging of macroparticles in a high-voltage vacuum arc sheath / A.A. Bizyukov, I.A. Girka, E.V. Romashchenko, A.D. Chibisov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 246-248. — Бібліогр.: 7 назв. — англ. |
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Bizyukov, A.A. Girka, I.A. Romashchenko, E.V. Chibisov, A.D. 2015-05-27T10:11:37Z 2015-05-27T10:11:37Z 2015 Charging of macroparticles in a high-voltage vacuum arc sheath / A.A. Bizyukov, I.A. Girka, E.V. Romashchenko, A.D. Chibisov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 246-248. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.40.Hf https://nasplib.isofts.kiev.ua/handle/123456789/82250 Charging of macroparticles (MPs) in front of the negatively biased surface emitted the secondary electrons due to bombardment by multiply charged ions (MCIs) has been investigated. It was found that MPs can be either reflected or attracted to the substrate depending on the substrate bias. Исследуется зарядка макрочастиц (MЧ) напротив отрицательно заряженной поверхности, испускающей вторичные электроны из-за бомбардировки многозарядными ионами (MЗИ). Было найдено, что MЧ могут либо притягиваться к подложке, либо отталкиваться в зависимости от потенциала подложки. Досліджено зарядження макрочастинок (МЧ) напроти від’ємно зарядженої поверхні, яка випромінює вторинні електрони завдяки бомбардуванню багатократно зарядженими іонами (БЗІ). Було знайдено, що МЧ можуть або притягатися до підкладки, або відштовхуватися в залежності від потенціалу підкладки. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Низкотемпературная плазма и плазменные технологии Charging of macroparticles in a high-voltage vacuum arc sheath Зарядка макрочастиц в слое вакуумной дуги высокого напряжения Зарядження макрочастинок у шарі вакуумної дуги високої напруги Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Charging of macroparticles in a high-voltage vacuum arc sheath |
| spellingShingle |
Charging of macroparticles in a high-voltage vacuum arc sheath Bizyukov, A.A. Girka, I.A. Romashchenko, E.V. Chibisov, A.D. Низкотемпературная плазма и плазменные технологии |
| title_short |
Charging of macroparticles in a high-voltage vacuum arc sheath |
| title_full |
Charging of macroparticles in a high-voltage vacuum arc sheath |
| title_fullStr |
Charging of macroparticles in a high-voltage vacuum arc sheath |
| title_full_unstemmed |
Charging of macroparticles in a high-voltage vacuum arc sheath |
| title_sort |
charging of macroparticles in a high-voltage vacuum arc sheath |
| author |
Bizyukov, A.A. Girka, I.A. Romashchenko, E.V. Chibisov, A.D. |
| author_facet |
Bizyukov, A.A. Girka, I.A. Romashchenko, E.V. Chibisov, A.D. |
| topic |
Низкотемпературная плазма и плазменные технологии |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
| publishDate |
2015 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Зарядка макрочастиц в слое вакуумной дуги высокого напряжения Зарядження макрочастинок у шарі вакуумної дуги високої напруги |
| description |
Charging of macroparticles (MPs) in front of the negatively biased surface emitted the secondary electrons due to bombardment by multiply charged ions (MCIs) has been investigated. It was found that MPs can be either reflected or attracted to the substrate depending on the substrate bias.
Исследуется зарядка макрочастиц (MЧ) напротив отрицательно заряженной поверхности, испускающей вторичные электроны из-за бомбардировки многозарядными ионами (MЗИ). Было найдено, что MЧ могут либо притягиваться к подложке, либо отталкиваться в зависимости от потенциала подложки.
Досліджено зарядження макрочастинок (МЧ) напроти від’ємно зарядженої поверхні, яка випромінює вторинні електрони завдяки бомбардуванню багатократно зарядженими іонами (БЗІ). Було знайдено, що МЧ можуть або притягатися до підкладки, або відштовхуватися в залежності від потенціалу підкладки.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/82250 |
| citation_txt |
Charging of macroparticles in a high-voltage vacuum arc sheath / A.A. Bizyukov, I.A. Girka, E.V. Romashchenko, A.D. Chibisov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 246-248. — Бібліогр.: 7 назв. — англ. |
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| first_indexed |
2025-11-26T14:05:26Z |
| last_indexed |
2025-11-26T14:05:26Z |
| _version_ |
1850624321667465216 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №1(95)
246 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 246-248.
CHARGING OF MACROPARTICLES IN A HIGH-VOLTAGE VACUUM
ARC SHEATH
A.A. Bizyukov, I.A. Girka, E.V. Romashchenko, A.D. Chibisov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: romaschenko@bk.ru
Charging of macroparticles (MPs) in front of the negatively biased surface emitted the secondary electrons due to
bombardment by multiply charged ions (MCIs) has been investigated. It was found that MPs can be either reflected
or attracted to the substrate depending on the substrate bias.
PACS: 52.40.Hf
INTRODUCTION
A vacuum arc discharge emits a plasma as well as
macroparticles (MPs) in the form of molten droplets of
cathode material [1]. The significant MP fraction sub-
stantially limits the possibilities of vacuum arc plasma
in coating technologies. The MPs occur in the range of
size from several microns to a few hundred microns, the
velocity of MPs reaches maximum value of 700-
800m/s. Cathodic vacuum arc plasma are known to con-
tain multiply charged ions. These ions have kinetic
energies of a few tens of eV. The mean ion charge state
Z is generally higher than 1 for most materials. In
many vacuum arc experiments, ions are collected at a
negatively biased metal surface. The purpose of the
present study is to investigate the behavior of charged
MPs in front of the negatively biased surface emitted
the secondary electrons due to bombardment by multip-
ly charged ions (MCIs).
1. SHEATH MODEL
Let us consider a high-voltage substrate is immersed
in a vacuum arc produced plasma. For a high-voltage
sheath, the current to the substrate is almost all ion cur-
rent [2]. The MPs are assumed to have no effect on the
sheath structure. In our coordinate system a plasma-
sheath interface (interface between quasi-neutral and
nonneutral regions) is taken to be the origin, 0x , and
the positive direction is away from the it. The substrate,
which is supposed to be at the constant potential bV , is
located at dxx ( eb TeV eVb>>Te, where eT is
the electron temperature in energy units, e is the ele-
mentary charge). The ion temperature is assumed neg-
ligible in comparison with eT . The generalized Bohm’s
criterion is over satisfied for vacuum arc plasmas [3].
The ions, hitting the substrate surface with kinetic
energies below 300 eV, may cause a potential electron
emission [4]. Such ion energies are typical for deposi-
tion a thin metallic film coating.
The total ion beam current density is the sum of each
ion species k
,
11
N
k
ikikk
N
k
iki unZejj
(1)
where kZ is the charge state, ikn is the ion density of
the k-th species, iku is the velocity of each species. The
density fraction of the k-th species 0nnf ikk , where
0n is the bulk plasma density.
A secondary electron beam produced at the substrate
by the secondary emission is ejected from that place
dxx towards the plasma in the x direction [4].
,
12
N
k
ik
k
k
N
k
eke j
Z
jj
(2)
where ikj is the current density of secondary electrons
produced by the ions of the k-th species, k k is the
secondary ion-electron emission yield [4].
The potential variation in the sheath is found by
solving Poisson’s equation
0
21
2
2
N
i
ek
N
k
ikk nnZe
dx
d
,
(3)
where ekn is the secondary electron density; o is the
permittivity constant. The boundary conditions are
0)0(;0)0( .
The flux of ions is assumed to be continuous across
the sheath in the collisionless model. From the equa-
tions of continuity and energy conservation for the ions
we derive the ion density
eZ
m
eZ
j
n
kk
i
k
ik
ik
02
,
(4)
where im is the ion mass, ko is the initial ion energy
of the k-th species.
On the analogy we obtain the secondary electron
density ekn produced by the secondary emission
b
eek
ek
Ve
m
e
j
n
2
,
(5)
where em is the electron mass.
Substituting in Eq. (3) the densities (4) and (5), we
obtain the sheath equation for numerical integration.
2. MP CHARGING
We consider the MP with radius a as a spherical
probe immersed in the plasma sheath [5]. The MP ra-
dius is much smaller than the electron Debye radius
mailto:romaschenko@bk.ru
ISSN 1562-6016. ВАНТ. 2015. №1(95) 247
D . We assume instantaneous transfer of charge onto
and off the MP at any MP position in the sheath. The
steady-state potential to which a MP is charged is de-
termined from the balance of particle fluxes to the grain
2 1
1 1 ,
N N
k
ek ik
k k k
j j
Z
(6)
where is the secondary electron-electron emission
coefficient [6].
The ions and electrons can be described as beam-
like due to their high directed velocities. The expres-
sions for the ion and electron fluxes are
,kkkkk unqj
(7)
where ie, represents the electrons and ions, re-
spectively; the collection cross section for charging col-
lisions between the macroparticle with the particle
based on the orbital motion limited (OML) approach is
2
2
)(
)()(2
1
xum
xxq
a s
,
(8)
where )(xs is the potential at the MP surface.
If
1
)(
)()(2
2
xum
xxq s
, 0 .
(9)
Solving for )(x Eq. (3) and for )(xs Eq. (6), we
obtain MP charge
)()(14)( 0 xxaxQ sD
.)()(4 0 xxs (10)
The MP travels through the plasma sheath and is
subject to electric force [7]
)()(
)1(3
1
2
xExQ
a
a
EQF
D
D
,
(11)
where )(xE
is the electric field in the sheath.
The potential energy of given size at the local sheath
position is
xdxExQzU
x
0
)()()(
.
(12)
The profile of potential energy and initial kinetic
energy of MP define the trapping of MP.
For numerical solutions it is convenient to introduce
the new variables
21
0
2
0 eD Tenxxz , eTez )( ,
ess Tez )( , )()()( zzz sd . (13)
Copper is the most commonly used cathode material
in vacuum arc experiments and consequently the calcu-
lations were carried out for copper ions, bombarding a
copper substrate [1, 4]. Here, we present the results of
numerical calculations of the dynamics of charging of a
Cu-macroparticle of radius a=1 m in the sheath with
account of secondary electron emission due to ion and
electron bombardment for the values of the parameters
presented in Table. The electron temperature is usually
not more than 1…2 eV. Thus, we gave 1eT eV.
Fig. 1. The local sheath potential )(z (z)(solid
line), the potential at the MP surface )(zs (dotted
line), the MP potential with respect to the local plasma
potential )(zd (dashed line) as a function of dis-
tance z for a substrate bias: Vb = -90 V(а);
Vb = -140 V(b)
Energies and secondary electron emission coefficients
for the different fractions of Cu-ions: Ref [1, 4]
Ion
charge
Z
Ion state
fraction, kf
Ion ene-
rgy,
0k (eV)
Secondary
electron
emission
coefficient, k
1 0.30 37
2 0.55 56 0.21
3 0.15 66 0.69
The results of the numerical solution of Eqs. (3) and
(6) are shown in Fig.1. This plot demonstrates the di-
mensionless local sheath potential, the potential at the
MP surface, the dust potential with respect to the local
plasma potential as a function of normalized distance
Dxz . In first case, substrate bias Vb = -90 V
(Fig.1,a), the potential at the MP surface )(zs is neg-
ative, and the MP potential with respect to the local
plasma potential )(zd is negative too.
For a substrate bias Vb = -140 V (Fig. 1,b), the dust
potential at the MP surface )(zs is negative. Howev-
er, the MP potential with respect to the local plasma
potential )(zd is positive near the substrate because
the sheath potential becomes more negative than the MP
potential. In Fig. 2,a, the MP charge profile for a sub-
strate bias Vb = -90 V is shown. The MP charge is nega-
tive. The MP charge determines the electric force.
Therefore, the electric force will be negative too (see
Fig. 2,b). The dependence of the potential energy of MP
on the position Dxz is shown in Fig. 2,c.
a
b
248 ISSN 1562-6016. ВАНТ. 2015. №1(95)
Fig. 2. The dependence of the MP charge on the posi-
tion Dxz for a substrate bias Vb = -90 V (a);
The dependence of the electric force, acting on this MP
charge (b); The dependence of the corresponding poten-
tial energy (c)
Fig. 3. The dependence of the potential energy of the
MP on the position Dxz z=x/D for a substrate
bias Vb = -140 V
If the MP kinetic energy is large enough to over-
come the potential barrier, a negatively charged MP
may be attracted to the substrate. For copper, velocity
range of MPs is 250…450 m/s. Mps with velocity above
400 m/s overcome the potential barrier and attracted to
the substrate. For velocity range of MPs is
250…400 m/s, MPs are reflected.
For bias Vb = -140 V, the profile of potential energy
of MP are shown in Fig. 3. This profile means that the
MPs can be attracted to the substrate in all velocity
range.
CONCLUSIONS
Charging of copper MPs and its influence on the MP
motion in front of the negatively biased copper surface
emitted the secondary electrons due to bombardment by
MCIs have been investigated. It was found that the pos-
sibility of MP attraction increases with negative bias
voltage. We show that the results presented here may be
applicable to the control of the MPs by modifying the
bias of the substrate.
REFERENCES
1. R.L. Boxman, P.J. Martin. Handbook of Vacuum Arc
Science and Technology: Fundamentals and Applica-
tions. New Jersey: “Noyes Publications”, 1995.
2. М.А. Lieberman, A.J. Lichtenberg. Principles of
plasma discharge and material processing / John Wiley
& Sons, Inc., New York, 1994.
3. G.Yu. Yushkov. Ion velocities in vacuum arc plas-
mas// J. Appl. Phys. 2000, v. 88, № 10, p. 5618-5622.
4. J.S. Sherman. Secondary electron emission by multi-
ply charged ions and its magnitude in vacuum arcs// J.
Appl. Phys. 1977, v. 10, p. 355-359.
5. I. Langmuir. Collected Works of Irving Langmuir /
Ed. by G. Suits. New York: “Pergamon”, 1961.
6. A. Piel. Plasma Physics: An introduction to Labora-
tory, Space and Fusion Plasmas. “Springer”, 2010.
7. J.E. Daugherty, R.K. Porteous. Electrostatic Forces
on Small Particles in Low-pressure Discharges // J.
Appl. Phys. 1993, v. 73, p. 161.
Article received 22.11.2014
ЗАРЯДКА МАКРОЧАСТИЦ В СЛОЕ ВАКУУМНОЙ ДУГИ ВЫСОКОГО НАПРЯЖЕНИЯ
А.А. Бизюков, И.А. Гирка, Е.В. Ромащенко, А.Д. Чибисов
Исследуется зарядка макрочастиц (MЧ) напротив отрицательно заряженной поверхности, испускающей
вторичные электроны из-за бомбардировки многозарядными ионами (MЗИ). Было найдено, что MЧ могут
либо притягиваться к подложке, либо отталкиваться в зависимости от потенциала подложки.
ЗАРЯДЖЕННЯ МАКРОЧАСТИНОК У ШАРІ ВАКУУМНОЇ ДУГИ ВИСОКОЇ НАПРУГИ
О.А. Бізюков, I.О. Гірка, О.В. Ромащенко, О.Д. Чібісов
Досліджено зарядження макрочастинок (МЧ) напроти від’ємно зарядженої поверхні, яка випромінює
вторинні електрони завдяки бомбардуванню багатократно зарядженими іонами (БЗІ). Було знайдено, що МЧ
можуть або притягатися до підкладки, або відштовхуватися в залежності від потенціалу підкладки.
a
b
c
|