Two-baffle trap for macroparticles
In this work, properties of two-baffle macroparticle traps were investigated. These properties are needed for designing and optimization of vacuum arc plasma filters. The dependencies between trap geometry parameters and its ability to absorb macroparticles were found. Calculations made allow one to...
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irk-123456789-799482015-04-10T03:02:41Z Two-baffle trap for macroparticles Aksyonov, D.S. Физика радиационных и ионно-плазменных технологий In this work, properties of two-baffle macroparticle traps were investigated. These properties are needed for designing and optimization of vacuum arc plasma filters. The dependencies between trap geometry parameters and its ability to absorb macroparticles were found. Calculations made allow one to predict the behaviour of filtering abilities of separators containing such traps in their design. Recommendations regarding the use of two-baffle traps in filters of different builds are given. Исследованы свойства двухрёберной ловушки макрочастиц, знание которых необходимо при проектировании фильтров (сепараторов) вакуумно-дуговой эрозионной плазмы. Установлены зависимости между геометрическими параметрами ловушки и эффективностью поглощения макрочастиц. Выполнены расчёты, результаты которых позволяют прогнозировать поведение фильтрующих качеств сепараторов, содержащих в своей конструкции такие ловушки. Даны рекомендации относительно применения двухрёберных ловушек в фильтрах различных конструкций. Досліджено властивості двореберних пасток макрочастинок, знання яких є необхідним при проектуванні реберних систем фільтрів вакуумно-дугової ерозійної плазми. Встановлено залежності між геометричними параметрами пастки та ефективністю поглинання макрочастинок. Виконано розрахунки, результати яких дозволяють прогнозувати поведінку фільтруючих якостей сепараторів, які мають у своєму складі такі пастки. Надано рекомендації стосовно використання двореберних пасток у фільтрах різних конструкцій. 2014 Article Two-baffle trap for macroparticles / D.S. Aksyonov // Вопросы атомной науки и техники. — 2014. — № 2. — С. 143-148. — Бібліогр.: 7 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/79948 621.793 en Вопросы атомной науки и техники National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine |
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Физика радиационных и ионно-плазменных технологий Физика радиационных и ионно-плазменных технологий Aksyonov, D.S. Two-baffle trap for macroparticles Вопросы атомной науки и техники |
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In this work, properties of two-baffle macroparticle traps were investigated. These properties are needed for designing and optimization of vacuum arc plasma filters. The dependencies between trap geometry parameters and its ability to absorb macroparticles were found. Calculations made allow one to predict the behaviour of filtering abilities of separators containing such traps in their design. Recommendations regarding the use of two-baffle traps in filters of different builds are given. |
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Aksyonov, D.S. |
author_facet |
Aksyonov, D.S. |
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Aksyonov, D.S. |
title |
Two-baffle trap for macroparticles |
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Two-baffle trap for macroparticles |
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Two-baffle trap for macroparticles |
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Two-baffle trap for macroparticles |
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Two-baffle trap for macroparticles |
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two-baffle trap for macroparticles |
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National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine |
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2014 |
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Физика радиационных и ионно-плазменных технологий |
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citation_txt |
Two-baffle trap for macroparticles / D.S. Aksyonov // Вопросы атомной науки и техники. — 2014. — № 2. — С. 143-148. — Бібліогр.: 7 назв. — англ. |
series |
Вопросы атомной науки и техники |
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AT aksyonovds twobaffletrapformacroparticles |
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2025-07-06T03:52:16Z |
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2025-07-06T03:52:16Z |
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ISSN 1562-6016. ВАНТ. 2014. №2(90) 143
UDC 621.793
TWO-BAFFLE TRAP FOR MACROPARTICLES
D.S. Aksyonov
National Science Center “Kharkov Institute of Physics and Technology”,
Kharkov, Ukraine
Е-mail: d s а k s у о п о v @ g т а i l . с о т
In this work, properties of two-baffle macroparticle traps were investigated. These properties are needed for
designing and optimization of vacuum arc plasma filters. The dependencies between trap geometry parameters and
its ability to absorb macroparticles were found. Calculations made allow one to predict the behaviour of filtering
abilities of separators containing such traps in their design. Recommendations regarding the use of two-baffle traps
in filters of different builds are given.
INTRODUCTION
One of the most prevalent methods of film
deposition is vacuum arc technique. Coatings obtained
by this method possess high service characteristics.
Application range of such films is rather wide: from
diffusion barriers in microelectronics and tool wear
protection to decorative coatings on dishes and door
handles. But vacuum arc technique has intrinsic
drawback – there are some relatively big fragments
among cathode erosion products, a so-called
macroparticles. Their ingress on the workpiece
commonly results in degradation of film quality.
Macroparticle filters, or separators, are employed in
order to filter off macroparticles from plasma [1, 2].
Their operation principle implies spatial separation of
movement trajectories of macroparticles and useful
plasma components, i.e. ions and electrons. Some kind
of obstacle is placed between cathode and the
workpiece, which purpose is to eliminate the direct line-
of-sight between these areas. Plasma is being
transported bypassing this obstruct by curved magnetic
field. Due to the fact that mass to charge ratio of
macroparticle is high, they are nearly not affected by the
transporting field. Moving along straight trajectory,
macroparticles are unable to get to the substrate without
colliding with the obstacle. However macroparticles can
reach the substrate by rebounding from plasma duct
walls. Due to the collisions, macroparticles are loosing
some part of their velocity and at some point become
incapable to move further any longer. To increase the
number of collisions, additional obstacles are being
placed on the route of macroparticles. These obstacles
represent a set of ribs (also known as baffles), mounted
on the walls of plasma-guiding channel.
Effectiveness of separators can be evaluated by
counting a number of macroparticles or defects they left
in a coating [3]. The method suggests presence of
manufactured filter, therefore making construction
changes in such case is difficult. That is why it is
reasonable to perform evaluation of filtering abilities of
separator before its manufacture, i.e. at the stage of
separator development. Computer simulation of
macroparticle movement trajectories can drastically
assist in problem of filters engineering and estimation of
their efficiency. Specialized software MPT
(Macroparticle Tracer) was developed for these
purposes earlier [4]. Several highly effective baffle
constructions for T-shaped magnetic filter [5] were
designed with its aid.
It was established during engineering, that two types
of baffle constructions (traps) are involved in the
process of macroparticle absorption (filtering off). In the
first case, construction contains a bunch of baffle and
plasma duct wall. Here, the baffle is tilted towards
macroparticles emission source – the cathode. Another
baffle system represents a set of two parallel baffles
which are tilted away from the cathode. According to
the constructive differences these two baffle species
possess, they can be respectively separated into two
types: an "angular" trap and a "two-baffle" trap. It was
found that the effectiveness of the traps emphatically
relies on the angle which is formed between the trap
baffle and plasma duct. There was also observed a
strong dependency of filtering abilities these traps have
on their location relative to macroparticle emissions
centres. The concepts being responsible for such
behaviour are currently unknown. Their understanding
may significantly simplify the problem of vacuum arc
plasma filters engineering. The influence of angular
type traps geometry and location inside separator on
their effectiveness was studied earlier [6]. Therefore the
scope of current work is the investigation of two-baffle
traps properties. All calculations this work contains
were made in two-dimensional approximation.
COMMON PROPERTIES
Two-baffle trap is schematically shown in Fig. 1. It
consists of two parallel baffles with equal length which
are attached to plasma duct wall at some distance s from
each other. Free ends of baffles are directed away from
macroparticle emission source. Angle β between baffle
and plasma duct wall can take values in range
0 < β ≤ 90º. Macroparticle is assumed intercepted by the
trap if it gets into space between baffles. At this rate,
macroparticle will either collide with trap baffles not
less than two times or once with the stopper (described
below). This requires satisfaction of next conditions:
{ }min , ,< ≤min maxd d d c (1)
0 90 ,α< < ° (2)
where d − distance between the baffle attachment and
macroparticle collision points; c − baffle length;
α − angle between the baffle and macroparticle
trajectory (hereinafter "glancing" or "grazing" angle);
144 ISSN 1562-6016. ВАНТ. 2014. №2(90)
dmin and dmax − minimum and maximum possible values
of distance d which are defined as:
( )
( )
( )
sin
,
sin sin
α β
β α
+
= −min
hd s (3)
( )
( )
( )
sin
,
sin sin
α β
β α
−
= −max
hd s (4)
where h − height of the trap (baffle) against plasma duct
wall. If d < dmin is true, then macroparticle will hit outer
side of the baffle and will not get inside the trap. If
d > dmax, two variants are possible: in case dmax > c
(α < β) macroparticle will fly past the trap, otherwise
(i.e. dmax ≤ c), after collision with the first baffle,
macroparticle will fly past the second one (see Fig. 1).
It should be noted, that value d can take negative
values. If so, it means that macroparticle collided
plasma duct wall, not trap baffles. Thus macroparticle,
in fact, gets into the angular trap [6] consisting from one
baffle of two-baffle trap and duct wall. Such situation
corresponds to the worst-case scenario: as it has been
established during simulation [5] and will be shown
below, effectiveness of two-baffle traps is extremely
low for low values of macroparticle grazing angles.
Positive effect of angular trap presence will be observed
only when macroparticle incidence angle is small
relative to the angular trap [6], which is possible only in
a narrow range of β angle values. Therefore it is
advisable to use two-baffle traps having some kind of
"stopper" (diaphragm) (Fig. 2) at their base. However
such approach imposes an additional limitation on the
trap geometry:
( )
2 .
sin 2β
<
hs
(5)
Fulfilment of this condition ensures that effective
baffle length Δ (Fig. 3) will always greater than zero.
All subsequent calculations are made for traps with
stoppers. Negative values of d for such traps
correspond to macroparticle collision with the
stopper.
As in case of angular trap, there is some threshold
value dt of distance d for two-baffle trap. Depending
on which one is greater, the number of macroparticle
collisions N with the trap may vary (± 1 in general
case). But since only minimum value of N represents
practical value, only it will be considered further.
Being intercepted by the trap, macroparticle will
alternately hit baffles and travel some distance δ
inward the trap between these collisions (see Fig. 3).
Once macroparticle has travelled distance equal Δ, it
will collide with the stopper and change its initial
direction to backward one (i.e. outward the trap) and
after it travels distance Δ − 2ε + δ, it will leave the trap
space. So, full distance the macroparticle covers is equal
2Δ − 2ε + δ. Knowing geometrical parameters of the
trap one can obtain a relation for minimum number of
macroparticle collisions inside the trap:
( ) ( )
( )2
0.5 sin 2
2 tan 2 for
,sin
1 for
β
α α α
β
α α
⎧ ⎢ ⎥−
= + >⎪ ⎢ ⎥
⎨ ⎢ ⎥⎣ ⎦
⎪ = ≤⎩
t
t
h s
N
s
N
(6)
( ) ( )( )( )12arctan sin 2 0.5 sin 2t s h sα β β
−
= − ,
where αt − threshold angle at α values below which,
macroparticle is able leave the trap right after colliding
the stopper (i.e. no collisions with baffles occur). Here
X⎢ ⎥⎣ ⎦ means rounding of value X to the nearest integer
towards zero (floor function).
It can be seen from (6) that the number of
intercepted macroparticle collisions with the trap
depends on all geometry parameters of the trap. The
number N grows along with an increase of the trap
height h and a decrease of its step s or angle β. It is
connected to the fact that an increase of h when
β = const, as well as a decrease of β when h = const,
leads to growth of effective baffle length Δ. Reduction
of N during step s growth is the result of accompanying
increase of distance δ, which macroparticle travels
between collisions. Thereby the determining factor is
Fig. 1. Schematic representation of two-baffle trap
Fig. 2. Trajectory of macroparticle which was intercepted by two-baffle trap with (solid line) and without
(dashed line) the stopper
ISSN 1562-6016. ВАНТ. 2014. №2(90) 145
not specific value of the trap step or height, but their
"correct" relation: if h/s = const, then N = const too if
other conditions are equal. The h/s relation should be
chosen depending on the trap angle, macroparticle
grazing angles range and needed value of N. According
to this, dependency N = f(α,β) is of interest, it is shown
in Fig. 4.
From the diagram in Fig. 4 one can assess
macroparticle absorption effectiveness of two-baffle
traps having their height to step ratio equal to 1. It is
clear that if values of step and height are changed, the
diagram will have somewhat different look: as long as
h/s increases, the interfaces of the regions will be lower
and lower. But the nature of relationships will remain
unchanged. It is also can be seen from the diagram, that
traps with β ≥ 45º have nearly same efficiency: there is
no essential variation of the range of absorbed
macroparticles. At this rate, if specified value of N is
achieved, the use of the traps with angles other than 90º
is not economically feasible, because classical "straight"
trap (β = 90º) is the most simple one with respect to its
cost and material input. As for the traps with angles
lower than 45º, their efficiency rapidly increases with
angle β fall off. This is related to the constancy of h
value, because a decrease of β leads to higher values of
effective baffle length Δ (see Fig. 3). Moreover, the
distance between baffles (not step) decreases, which
means value of δ become lower. Such change in Δ and δ
causes significant gain of collisions number N. Because
N raises for all macroparticles (for all glancing angles)
the range of macroparticles which are being absorbed
widens. However one should keep in mind that along
with trap angle decrease, the number of macroparticles
which are capable to get into such trap from a particular
point also decreases. Besides, β lowering brings about
higher values of "unused" baffle length. Collision of
macroparticle with baffle in this area corresponds to
d > dmax, i.e. the macroparticle will not get into space
between trap baffles and therefore can not be absorbed.
As a result, despite the high values of N, performance of
such baffles design as a trap for macroparticles is
extremely low. Baffles of this kind are playing the role
of macroparticle "reflectors" [5] which is equally
important in designing of effective filters.
Previously [6], in the work devoted to study of
angular trap, it was established that for every trap with
angle β and given efficiency factor N, there is some
critical value of macroparticle glancing angle αcr. If an
angle at which macroparticles are get into angular trap
exceeds value of this critical angle, then the number of
macroparticle-trap collisions N will have lower value
than desired. Calculation of critical grazing angle value
is needed for estimation of filtering abilities of traps
with known location of emission centres relative to the
traps. Obviously, critical angle also exists for two-baffle
traps. The dependence of its magnitude on values of β is
corresponding to interfaces of regions for different N
values in Fig. 4. From relation (6) it is easy to obtain
value of critical angle for { }*2 ;N k k= ∈ :
( )
( )
2sin
arctan .
2 sin 2
β
α
β
⎛ ⎞
= ⎜ ⎟⎜ ⎟−⎝ ⎠
cr
sN
h s
(7)
In contrast to angular trap, where condition α < αcr
was needed to be true, two-baffle trap requires
satisfaction of condition α > αcr. In other words,
efficiency of angular traps rises with macroparticle
Fig. 3. Real trap and its equivalent construction used
for the calculation of macroparticle collisions number,
which consists of the trap and its reflection with respect
to the stopper
Fig. 4. Minimum macroparticle-trap collisions number
against macroparticle glancing angle (α) and the trap
angle (β) for h/s = 1
146 ISSN 1562-6016. ВАНТ. 2014. №2(90)
grazing angle decrease, while effectiveness of two-
baffle traps – with its increase.
As it was mentioned above, α angle at which a
macroparticle is able to get inside two-baffle trap
depends on both the trap geometry and relative location
of the trap and emission centres – cathode working
surface. Value of the angle is always within 0 < α ≤ 90º
range. Knowing the coordinates of the trap one can
narrow glancing angles range to:
1 2
1 4
for
,
for
α α α β β
α α α β β
< ≤ ≤⎧
⎨ < ≤ >⎩
t
t
(8)
where
( )
( ) ( ) ( )1 2
cot
arctan
cot sin
β
α
β β−
⎛ ⎞+ −
= ⎜ ⎟⎜ ⎟− − −⎝ ⎠
H L s
H L s h
,
( )
( ) ( ) ( )2 2
cot
arctan
cot sin
H L s
H L s h
β
α
β β−
⎛ ⎞+ +
= ⎜ ⎟⎜ ⎟− − −⎝ ⎠
,
( )
( ) ( )4 2
cot
arctan
cot sin
β
α
β β−
⎛ ⎞+
= ⎜ ⎟⎜ ⎟− −⎝ ⎠
H L
H L h
,
2 2 2
arctanβ
⎛ ⎞+ + −
⎜ ⎟=
⎜ ⎟−⎝ ⎠
t
L L H h
H h
,
where L, H − values defining the distance from emission
point and the trap (see. Fig. 1); βt − the trap angle higher
than which dmax > c becomes possible, i.e. macroparticle
will pass by the baffle. As it can be seen from (8), the
difference of ranges for β ≤ βt and for β > βt is only in
their upper limit. So, if all angles within the range (8)
have higher values than αcr, then all macroparticles
being emitted from the point moved away from the trap
on distance defined by H and L will be absorbed by this
trap.
TWO-BAFFLE TRAP IN T-SHAPED
PLASMA DUCT
Depending on relative location of macroparticle
emission centre and the trap, performance of the last one
may vary in a wide range, what determines
appropriateness of the trap placement in the particular
position of plasma guiding channel. In order to
determine the effectiveness of two-baffle trap it is
necessary to define criterion N, determine grazing
angles range macroparticles are getting into the trap and
which part of this range the trap is able to absorb.
In case of two-baffle trap placement near the anode
exit or inside the output section of T-shaped plasma
duct [5], macroparticle can hit the substrate without any
additional collision after it has left the space between
the trap baffles. At the same time, it is sufficient for
macroparticle to bounce off filter walls 10 times [7] to
loose its initial velocity. Thereby, macroparticle will be
absorbed by separator if N ≥ 10 condition is true.
Further calculations utilize efficiency criterion of said
value.
Fig. 5 shows the dependencies of critical (αcr) and
threshold (αt) angles as well as macroparticle glancing
angles range for different values of the trap angle β.
Two-baffle trap has its height h and step s equal to
20 mm. Calculation was made for two utmost points of
the cathode working surface (H1 = 78.5 mm and
H2 = 131.5 mm) because grazing angles of
macroparticles for other emission centres (H1 < H < H2)
are within this range. So as to determine influence
degree of the trap location on its effectiveness,
calculations were made for the traps placed at two
positions: at the middle of anode (L = 118 mm) and at
the distance closest to the cathode (L = 20 mm). It
follows from the figure, that for satisfaction of N ≥ 10
condition by the trap placed at distance L = 20 mm it is
necessary for it to have angle in range 23º ≤ β ≤ 34º. If
the trap is moved on distance L = 118 mm away from
the cathode, it must have angle 46.4º ≤ β ≤ 54.2º. It also
can be seen from the figure that in case of interchanging
of the baffles designed for L = 20 mm and L = 118 mm
(leaving their angle unchanged) two variants are
possible: either the performance of the trap will be
greatly reduced or macroparticles will not be intercepted
by the trap at all.
It is interesting that the most frequently used
"straight" trap (β = 90º) possesses minimum efficiency.
In order to meet appointed above effectiveness factor
(with considered values of H, h and s) it needs to be
placed at distance L ≥ 550 mm, what is not always
Fig. 5. The dependences of critical angle value and
macroparticle glancing angles range (greyed) on the
value of two-baffle trap angle, which is placed inside
the anode of T-shaped separator at different distance
away from the cathode. Calculation was made for the
nearest and the farthest (relative to anode) points on the
cathode working surface
Fig. 6. The dependences of critical angle value and
macroparticle glancing angles range (greyed) on the
value of two-baffle trap angle, which is placed inside
the output section of T-shaped separator. Calculation
was made for the nearest and the farthest (relative to
anode) points on the cathode working surface
ISSN 1562-6016. ВАНТ. 2014. №2(90) 147
possible. However application of such traps in some
cases is the only acceptable option [5]. In the considered
T-shaped separator, these traps were used inside the
input sections of the plasma duct. They were installed at
distance L within the range 269 mm ≤ L ≤ 541 mm
(H = 98.5 mm, h/s =1). Effectiveness of the traps is
respectively in range from N ≥ 4 to N ≥ 8.
As for the efficiency of two-baffle traps in the output
section of T-shaped separator, supplementary
calculations were performed. The results are given in
Fig. 6. The figure shows that for N ≥ 10 angle of the
trap must be in 18º ≤ β ≤ 24.3º range. During separator
optimization process [5] the one with β = 24º was used,
that explains high level of observed performance, when
macroparticle trajectories were modelled in MPT
program. According to Fig. 6, application of "classical"
baffles with angle β = 90º inside the output section of
the duct is inappropriate, at least in its initial part.
Effectiveness of these baffles will be minimal (N = 1)
since macroparticle glancing angle in all possible range
has the value lower than αt. It should be noted, that the
trap angle β in this case must not be equal to 45º due to
contradiction to statement (5). That is the effective
baffle length Δ of considered trap will be equal to zero if
β = 45º (see Fig. 3).
Based on the calculation results performed in this
study several recommendations as for application of
two-baffle traps can be given. Traps of this type can be
utilized at almost any part of a plasma duct if their angle
and step are adjusted correctly. As the distance along
duct axis between the trap and the cathode becomes
longer, angle and step may be significantly increased
what will definitely reduce baffle system cost.
Application of 90-degree traps, in common case, is not
recommended due to their low efficiency for acceptable
values of height to step ratio and typical separator
dimensions. The "unused" surfaces of the traps possess
the feature to redirect unfiltered macroparticles athwart
plasma duct axis. In this regard, installation of two-
baffle traps is preferable inside output sections of
curvilinear plasma ducts (for example L- and T-shaped)
and inside a so-called straight (or rectilinear) separators,
where longitudinal movement of macroparticles is
unacceptable. It is due to the fact that this kind of
macroparticles can not be intercepted by the baffles if
their trajectories are close to the axis of the plasma
guide.
Designed earlier [5] baffle system for T-shaped
magnetic filter meets the above recommendations and
the guidelines as for application of angular traps [6]
what explains high filtering properties the system has.
The correctness of relationships obtained in this work is
confirmed by the results of simulations in MPT.
CONCLUSIONS
During current study, the dependences
characterizing effectiveness of macroparticle absorption
by two-baffle traps were established. Absorption
capacity of the traps grows with a decrease of their
angle and with an increase of their height to step ratio.
The traps are most effective in absorption of
macroparticle flows, which are directed to their baffles
at angles close to right one. The efficiency of two-baffle
traps that placed in different locations of the anode and
inside the output section of the plasma duct was
calculated on an example of T-shaped separator.
Calculation results are in agreement with MPT
simulation results. Acquired relations allow one to
predict efficiency of angular traps application on a stage
of design of baffle systems used in magnetic separators.
The list of recommendations regarding the engineering
of baffle systems that are based on such traps was
composed.
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Статья поступила в редакцию 21.11.2012 г.
148 ISSN 1562-6016. ВАНТ. 2014. №2(90)
ДВУХРЁБЕРНАЯ ЛОВУШКА ДЛЯ МАКРОЧАСТИЦ
Д.С. Аксёнов
Исследованы свойства двухрёберной ловушки макрочастиц, знание которых необходимо при
проектировании фильтров (сепараторов) вакуумно-дуговой эрозионной плазмы. Установлены зависимости
между геометрическими параметрами ловушки и эффективностью поглощения макрочастиц. Выполнены
расчёты, результаты которых позволяют прогнозировать поведение фильтрующих качеств сепараторов,
содержащих в своей конструкции такие ловушки. Даны рекомендации относительно применения
двухрёберных ловушек в фильтрах различных конструкций.
ДВОРЕБЕРНА ПАСТКА ДЛЯ МАКРОЧАСТИНОК
Д.С. Аксьонов
Досліджено властивості двореберних пасток макрочастинок, знання яких є необхідним при проектуванні
реберних систем фільтрів вакуумно-дугової ерозійної плазми. Встановлено залежності між геометричними
параметрами пастки та ефективністю поглинання макрочастинок. Виконано розрахунки, результати яких
дозволяють прогнозувати поведінку фільтруючих якостей сепараторів, які мають у своєму складі такі
пастки. Надано рекомендації стосовно використання двореберних пасток у фільтрах різних конструкцій.
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