Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources
The possibility of transportation of charged macroparticles (MPs) through a magnetic filter is studied. It is shown that when MPs moves through the curved magnetic filter its can be charged either positively or negatively. The trajectories of charged MPs are changed due to the negative space charge...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2015 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Цитувати: | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources / A.A. Bizyukov, D.V. Chibisov, A.D. Chibisov, E.V. Romashchenko, V.V. Kovalenko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 298-301. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859979334080528384 |
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| author | Bizyukov, A.A. Chibisov, D.V. Chibisov, A.D. Romashchenko, E.V. Kovalenko, V.V. |
| author_facet | Bizyukov, A.A. Chibisov, D.V. Chibisov, A.D. Romashchenko, E.V. Kovalenko, V.V. |
| citation_txt | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources / A.A. Bizyukov, D.V. Chibisov, A.D. Chibisov, E.V. Romashchenko, V.V. Kovalenko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 298-301. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The possibility of transportation of charged macroparticles (MPs) through a magnetic filter is studied. It is shown that when MPs moves through the curved magnetic filter its can be charged either positively or negatively. The trajectories of charged MPs are changed due to the negative space charge in the plasma duct. It is found that positively charged MPs may be retained in plasma duct, depending on the parameters of plasma and MPs. The conditions determining their transportation through the filter are obtained.
Вивчено можливість транспортування заряджених макрочастинок (МЧ) через магнітний фільтр. Показано, що при русі МЧ у криволінійному магнітному фільтрі вони можуть заряджатися як позитивно, так і негативно. За умови існування радіального електричного поля в плазмоводі відбувається зміна траєкторій заряджених МЧ. Встановлено, що позитивно заряджені МЧ можуть бути утримані в плазмоводі залежно від їхніх параметрів та параметрів плазми. Отримано умови, що визначають транспортування МЧ через фільтр.
Изучена возможность транспортировки заряженных макрочастиц (МЧ) через магнитный фильтр. Показано, что при движении МЧ в криволинейном магнитном фильтре они могут заряжаться как положительно, так и отрицательно. При условии существования радиального электрического поля в плазмоводе происходит изменение траекторий заряженных МЧ. Установлено, что положительно заряженные МЧ могут быть удержаны в плазмоводе в зависимости от их параметров и параметров плазмы. Получены условия, определяющие транспортировку МЧ через фильтр.
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| first_indexed | 2025-12-07T16:25:34Z |
| format | Article |
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 298
DYNAMICS OF MACROPARTICLES IN A MAGNETIC FILTER
FOR A VACUUM ARC PLASMA SOURCES
A.A. Bizyukov, D.V. Chibisov, A.D. Chibisov, E.V. Romashchenko, V.V. Kovalenko
V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: chibisov.alexandr@mail.ru
The possibility of transportation of charged macroparticles (MPs) through a magnetic filter is studied. It is
shown that when MPs moves through the curved magnetic filter its can be charged either positively or negatively.
The trajectories of charged MPs are changed due to the negative space charge in the plasma duct. It is found that
positively charged MPs may be retained in plasma duct, depending on the parameters of plasma and MPs. The con-
ditions determining their transportation through the filter are obtained.
PACS: 52.40.Hf
INTRODUCTION
Vacuum arc discharge is an effective source of
plasma with a wide range of scientific and technological
applications [1, 2]. One of the most important techno-
logical applications of vacuum arc plasma is associated
with its use for ion-plasma deposition of coatings that
improve the properties of products. When the vacuum
arc is burning the main plasma source are cathode spots,
however, in the cathode spot an erosion of the cathode
surface leads to the formation not only of the plasma
flow but also macroparticles − droplets of cathode mate-
rial. Ratio of the droplet fraction in the total erosion of
the cathode is a significant part (is about 90%), as in
terms of the characteristics of the plasma source is a
negative factor. This is due to the fact that the deposited
droplets on the surface of the products impair some im-
portant characteristics of the surface layer, such as porosi-
ty and surface roughness, the adhesion of the coating to
the surface corrosion and other surface properties [3].
In practice, most of the specific ways of reducing the
flow of droplets on the products are based on the separa-
tion of the ion trajectories and streams of the droplets.
First of all, is used the fact that (due to the different na-
ture of the formation of the ion flow and droplet flow)
most of the droplets moves at a low angle to the surface
of the cathode, while the main ion flow is moving nor-
mal to the surface. More effective are the various filters
where the ion flow separates from the droplet flow by
the magnetic field. However, the higher the required
degree of the ion flow purification from drops, the more
complex and expensive construction of the filter is, and
the greater the become losses ionic component of the
filtered flow [3].
However, experiments show that a small portion of
the MPs passes through the filter. One of the mecha-
nisms of the transportation of the MP through the filter
is changing their trajectories due to elastic collisions of
the MPs with the walls of the filter [3]. In this paper, we
study the possibility of transportation of the MPs
through the magnetic filter as a result of their retention
by the electric field inside the plasma duct.
1. CHARGE OF THE PARTICLES IN THE
VACUUM-ARC PLASMA SOURCES
It is known that the MP immersed in plasma is
charged as a result of absorption of electrons and ions of
plasma, as well as various types of electron emission
from the MP surface [4].
The charge of the MPs varies widely depending on
the energy of the particles of plasma as well as ratio of
their densities and can take both negative and positive
values [5]. The value of the charge and its sign deter-
mine the character of interaction of the MP with an elec-
tric field presented in the plasma duct and hence deter-
mine the trajectory of the MP in the filter. Charge of the
MP is determined by the balance of ion and electron
currents on its surface. Calculation of the currents from
plasma on the MP in presence of the magnetic field is a
intricate problem, however in some cases various ap-
proximations are used successfully. In particular, if the
magnetic field is not large enough such that condition
g dr aλ>> >> (1)
is true, where gr is the Larmor radius of electron, dλ is
the Debye length, a is the radius of the MP, in colli-
sionless plasma the OML theory for calculating the ion
and electron currents on the spherical probe is used. In
this paper we consider plasma created by a stationary
arc discharge with the density 10 12
0 10 ...10n = cm-3 and
electron temperature 1...5eT = eV. Ion component has a
directed velocity with the energy distribution close to
Maxwellian. The average energy of directed motion of
the ions is equal to 25...50fl
iε = eV [4]. The strength of
the magnetic field B in the filter is equal to 100 G.
With these parameters, typical for vacuum-arc systems,
the condition (1) is true and OML theory is correct.
Currents of electrons and ions from plasma to the
surface of the MP have the form:
( )2
08 expe Te a eI a en v e Tπ ϕ= , (2)
2
0 1 a
i Ti
i
Z e
I en Z v a
T
ϕ
π π
< >
= < > −
, (3)
where e is the elementary charge, 0n is the plasma
density, ( )e iT are the temperatures of the plasma elec-
trons and ions, ( ) ( ) ( )Te i e i e iv T m= are their thermal
velocities 1 2 31 2 3Z α α α< >= ⋅ + ⋅ + ⋅ is the averaged ion
charge of ions, 1α , 2α , 3α are the relative concentra-
tions of ions with charges Z=1, 2, 3 respectively, aϕ is
the potential on the surface of the MP.
To focus the plasma flow created by vacuum arc
discharge a negative potential to the substrate subu
ISSN 1562-6016. ВАНТ. 2015. №4(98) 299
(Fig. 1) is applied, that leads to an acceleration of the
ions up to energies fl
i subeZuε = .
Fig. 1. Scheme of formation of the electron flow
on a substrate in vacuum-arc systems with curved
magnetic filters
The interaction of the ion component of the plasma
flow with the substrate causes the formation of the flow
of secondary electrons (see Fig. 1), whose density is
determined by the secondary electron yield. Taking into
account that in the plasma flow the ions with varying
degree of ionization exist, it is advisable to introduce the
average secondary electron yield:
1 1 2 2 3 3
i e i e i e i e
s s s sδ α δ α δ α δ− − − −= ⋅ + ⋅ + ⋅ , (4)
where i e
sZδ − is the secondary electron yield for the ions
with charge Z.
The energy of the secondary electrons fl
eε is deter-
mined by the negative potential on the substrate subu
and has negligible variation that corresponds to the en-
ergy spectrum of the secondary electrons.
The density of the secondary electron flow is related
with an ion current density jj on the substrate by the
relation:
fl i e
e s ij jδ −= . (5)
Current of these secondary electrons on the surface
of the MP is determined by the OML theory:
2 1fl fl a
e e
i
e
I j a
T
ϕ
π
= +
. (6)
An important process that affects on the magnitude
of the charge of the MP is the emission of electrons
from the surface. We will consider the following main
mechanisms of electron emission: ion-electron emis-
sion, electron-electron emission. Value of the current of
the ion-electron emission from the surface of the MP is
given by:
i e i e
s s iI Iδ− −= . (7)
Using (3) and (7) for ease, we assume that on the
surface of the MP the effective current flows.
.eff i e
i i sI I I −= + (8)
Expression for the current of the secondary electron-
electron emission has a similar form:
e e fl e e
s e sI I δ− −= , (9)
where i e
sδ
− is the secondary electron yield. By analogy
with ion current, we introduce an efficient electron cur-
rent:
eff pl fl e e
e e e sI I I I −= + − . (10)
The floating potential of the MP is determined by
equating the currents (8) and (10) on its surface:
( ) ( ) 0eff eff
e a i aI Iϕ ϕ+ = . (11)
The potential of the particle and its charge are relat-
ed by the following equation:
mp aQ a ϕ= ⋅ . (12)
Equation (11) was solved numerically. The results of
this solution are shown in Fig. 2.
From the figure follows, that interval of energies of
the electron flow, where the MP has the positive charge
and potential, exists. This interval corresponds to the
energy of the electron flow, where the secondary yield
e e
sδ
− greater than unity.
The maximum value of the charge of the MP in the
energy interval 1 2
fl
eε ε ε> > is determined by the ener-
gy of the secondary electrons.
Fig. 2. Dependence of the potential and charge tungsten
MP versus the energy of the electron flow
( 11 3
0 10n cm−= , 3eT eV= , 25fl
i eVε = )
2. MOTION OF THE MACROPARTICLES
IN A CURVED FILTER
Plasma in a magnetic filter is transported through a
duct which is a part of the torus, therefore for descrip-
tion of the motion of the MP in duct it is advisable to
introduce the toroidal coordinate system ( , , )r ξ θ with
an axis of symmetry 1O (Fig. 3,a). Let us consider the
forces that determine the trajectory of the MP in the
filter, depending on its parameters (size, velocity). It is
known that in the plasma duct of the magnetic filter a
ISSN 1562-6016. ВАНТ. 2015. №4(98) 300
radial electric field exists due to space charge and ap-
plied positive potential to the wall of the plasma duct
(see Fig. 1) [3]. The magnetic filter operating principle
is that the MP moves rectilinearly, in contrast to ion
flow, and therefore has to deposit on the wall. However,
if the MP has a positive charge, that is possible, as
shown above, due to the effect of secondary electron-
electron emission, then Coulomb force acts on the MP
towards to the axial line of the duct 2O (Fig. 3,b). As a
result MP can be retained inside the duct. Besides the
Coulomb force when the MP moves along the axial line
of the torus, the centrifugal force directed away from the
axis 1O of the torus acts on it.
In order to determine the conditions when retention
of the MP inside the filter is possible, let us consider the
laws of conservation of energy as well as of conserva-
tion of angular momentum. We consider the case when
there is no azimuthal motion of the MP, i.e. when
0vξ = . The law of conservation of energy in this case
has the form:
( ) ( )
2 2 2
0
0 12 2 2
mp mp mp rM v M v M v
E U r U r θ= + = + + , (13)
where mpM is the mass of the MP, vθ and rv are θ and
r components of velocity respectively and 0vθ and 0rv
their initial values, 2 2 2
0 0 0rv v vθ= + , ( ) ( )1 1mpU r Q rϕ= , 1r
is the distance from the point of formation of the MP to
the axial line of the plasma duct 2O , ( )1rϕ is the poten-
tial at the point of MP formation, r is the current dis-
tance from the MP to the axial line of the plasma duct.
The law of conservation of angular momentum in
our case has the form:
0 1mp mpM v R M v Rθ θ= , (14)
where 1R is the distance from the axis 1O to the MP in
point of it formation, R is the current distance from the
axis to the MP. From the law of conservation of angular
momentum (14) we find the longitudinal velocity of the
MP:
1
0
Rv v
Rθ θ= . (15)
Taking into account (15) the law of conservation of
energy (10) takes the form:
( )
22 2
0 1
0 2 2
mp mp rM v M vRE U r
R
θ = + +
. (16)
MPs are retained inside of the plasma duct when the
condition 0rv = in the range 0r r< is true, so the equa-
tion that determines the boundary of the MP motion
inside of the plasma duct has the form:
( )
22
0 1
0 0
1 02
mpM v RE U r
R r
θ
= + +
, (17)
where ( ) ( )0 0mpU r Q rϕ= is the potential on the wall of
the plasma duct.
After simple transformations, the condition (17)
takes the form:
( )
22
0 1
0 02
1 00
1 MP
v RE Q r
R rv
θ ϕ
− = +
. (18)
Fig. 3. The coordinate system is in the curvilinear filter.
0R and 0r are major radius and minor radius
of the torus respectively
The main problem now is to determine from (18) the
parameters of the particles that can be retained in the
plasma duct. These parameters are the initial velocity of
the MP and its size. Based on this the equation (18) was
solved numerically for several substances. Fig. 3 shows
the results of the numerical solution of equation (18) for
tungsten particles in the two extreme cases when the
velocity vector is directed normally to the plane of the
cathode (in this case 0 0rv = ), and the case when the
velocity vector is directed at a small angle to the surface
of the cathode (in this case 0 0vθ = ).
The curves shown in Fig. 4 determine boundary of
the parameters (velocity of the MP and its size) that
separates the MPs into two groups: MPs that pass
through the filter and MPs that are deposited on its
walls. MPs parameters of that are below the curves pass
through the filter and accordingly, MPs with velocities
and sizes from the region above the curves are deposited
on the walls of the filter.
Thus by comparing the results of calculations pre-
sented in the paper with data of experimental observa-
tions [3] we can see that in the plasma flow formed by
stationary arc the MPs that can pass through the mag-
netic filter are present. The calculations carried out for
particles of other materials differ from those calcula-
tions insignificantly.
It should also be noted, that even the MP, whose en-
ergy is sufficient to overcoming the potential barrier, at
collision with the wall of duct can not only to subside
but reflected from it also (elastically or inelastically).
a
b
ISSN 1562-6016. ВАНТ. 2015. №4(98) 301
Fig. 4. Dependence of the critical size of the tungsten
MP versus its initial velocity (1 – 0 0rv = ; 2 – 0 0vθ = )
As a result of the collision the direction as well as
the value of speed is changed, so the favorable condi-
tions for the further transportation of MP may be creat-
ed.
CONCLUSIONS
It was found that the MPs which formed during the
operation of stationary vacuum arc plasma sources can
be positively charged due to the effect of secondary
electron-electron emission as a result of their interaction
with the electron flow that is formed on the substrate.
The main processes that determine the trajectory of
the positively charged MPs in the curved plasma duct
are the interaction MP with the radial electric field
which created by a negative space charge as well as
centrifugal repulsion. Coulomb force turns the MPs so
that its moves along a curved path in plasma duct and
can be trapped in the potential well and then transported
to the substrate. The conditions on the size and initial
velocity of the MPs that can pass through the magnetic
filter are determined.
REFERENCES
1. Handbook of Vacuum Arc Science and Technology:
Fundamentals and Applications / Eds. R.L. Boxman,
D.M. Sanders, P.J. Martin. NJ: Noyes Publ. 1995,
p. 742.
2. A. Anders. Cathodic Arcs: From Fractal Spots to
Energetic Condensation. Springer Science Business
Media, LLC, 2008, p.540.
3. I.I. Aksenov, A.A. Andreyev, et al. Vakuumnaya
duga: istochniki plazmy, osazhdeniye pokrytiy, pov-
erkhnostnoye modifitsirovaniye. Kiev: «Naukova
dumka», 2012, p. 238-273 (in Russian).
4. V.E. Fortov, A.G. Khrapak, et al. Dusty plasma //
UFN. 2004, v. 174, № 5, p. 495-544.
5. A.A. Bizyukov, A.D. Chibisov, et al. Electric poten-
tial of a macroparticle in beam-plasma systems //
Plasma Physics Reports. 2009, v. 35, № 6, p. 499-
501.
Article received 05.05.2015
ДИНАМИКА МАКРОЧАСТИЦ В МАГНИТНЫХ ФИЛЬТРАХ ВАКУУМНО-ДУГОВЫХ
ИСТОЧНИКОВ ПЛАЗМЫ
А.А. Бизюков, Д.В. Чибисов, А.Д. Чибисов, Е.В. Ромащенко, В.В. Коваленко
Изучена возможность транспортировки заряженных макрочастиц (МЧ) через магнитный фильтр. Пока-
зано, что при движении МЧ в криволинейном магнитном фильтре они могут заряжаться как положительно,
так и отрицательно. При условии существования радиального электрического поля в плазмоводе происходит
изменение траекторий заряженных МЧ. Установлено, что положительно заряженные МЧ могут быть удер-
жаны в плазмоводе в зависимости от их параметров и параметров плазмы. Получены условия, определяю-
щие транспортировку МЧ через фильтр.
ДИНАМІКА МАКРОЧАСТИНОК У МАГНІТНИХ ФІЛЬТРАХ ВАКУУМНО-ДУГОВИХ ДЖЕРЕЛ
ПЛАЗМИ
О.А. Бізюков, Д.В. Чібісов, О.Д. Чібісов, О.В. Ромащенко, В.В. Коваленко
Вивчено можливість транспортування заряджених макрочастинок (МЧ) через магнітний фільтр. Показа-
но, що при русі МЧ у криволінійному магнітному фільтрі вони можуть заряджатися як позитивно, так і не-
гативно. За умови існування радіального електричного поля в плазмоводі відбувається зміна траєкторій за-
ряджених МЧ. Встановлено, що позитивно заряджені МЧ можуть бути утримані в плазмоводі залежно від
їхніх параметрів та параметрів плазми. Отримано умови, що визначають транспортування МЧ через фільтр.
INTRODUCTION
2. Motion of the macroparticles in a curved FILTER
conclusions
references
ДИНАМИКА МАКРОЧАСТИЦ В МАГНИТНЫХ ФИЛЬТРАХ ВАКУУМНО-ДУГОВЫХ ИСТОЧНИКОВ ПЛАЗМЫ
ДИНАМІКА макрочастинок у Магнітних фільтрах вакуумно-дуговИх ДЖЕРЕЛ ПЛАЗМИ
|
| id | nasplib_isofts_kiev_ua-123456789-112211 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:25:34Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bizyukov, A.A. Chibisov, D.V. Chibisov, A.D. Romashchenko, E.V. Kovalenko, V.V. 2017-01-18T19:35:17Z 2017-01-18T19:35:17Z 2015 Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources / A.A. Bizyukov, D.V. Chibisov, A.D. Chibisov, E.V. Romashchenko, V.V. Kovalenko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 298-301. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.40.Hf https://nasplib.isofts.kiev.ua/handle/123456789/112211 The possibility of transportation of charged macroparticles (MPs) through a magnetic filter is studied. It is shown that when MPs moves through the curved magnetic filter its can be charged either positively or negatively. The trajectories of charged MPs are changed due to the negative space charge in the plasma duct. It is found that positively charged MPs may be retained in plasma duct, depending on the parameters of plasma and MPs. The conditions determining their transportation through the filter are obtained. Вивчено можливість транспортування заряджених макрочастинок (МЧ) через магнітний фільтр. Показано, що при русі МЧ у криволінійному магнітному фільтрі вони можуть заряджатися як позитивно, так і негативно. За умови існування радіального електричного поля в плазмоводі відбувається зміна траєкторій заряджених МЧ. Встановлено, що позитивно заряджені МЧ можуть бути утримані в плазмоводі залежно від їхніх параметрів та параметрів плазми. Отримано умови, що визначають транспортування МЧ через фільтр. Изучена возможность транспортировки заряженных макрочастиц (МЧ) через магнитный фильтр. Показано, что при движении МЧ в криволинейном магнитном фильтре они могут заряжаться как положительно, так и отрицательно. При условии существования радиального электрического поля в плазмоводе происходит изменение траекторий заряженных МЧ. Установлено, что положительно заряженные МЧ могут быть удержаны в плазмоводе в зависимости от их параметров и параметров плазмы. Получены условия, определяющие транспортировку МЧ через фильтр. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Приложения и технологии Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources Динаміка макрочастинок у магнітних фільтрах вакуумно-дугових джерел плазми Динамика макрочастиц в магнитных фильтрах вакуумно-дуговых источников плазмы Article published earlier |
| spellingShingle | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources Bizyukov, A.A. Chibisov, D.V. Chibisov, A.D. Romashchenko, E.V. Kovalenko, V.V. Приложения и технологии |
| title | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources |
| title_alt | Динаміка макрочастинок у магнітних фільтрах вакуумно-дугових джерел плазми Динамика макрочастиц в магнитных фильтрах вакуумно-дуговых источников плазмы |
| title_full | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources |
| title_fullStr | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources |
| title_full_unstemmed | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources |
| title_short | Dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources |
| title_sort | dynamics of macroparticles in a magnetic filter for a vacuum arc plasma sources |
| topic | Приложения и технологии |
| topic_facet | Приложения и технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112211 |
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