Angular trap for macroparticles
Properties of angular macroparticle traps were investigated in this work. These properties are required to design vacuum arc plasma filters. The correlation between trap geometry parameters and its ability to absorb macroparticles were found. Calculations allow one to predict the behaviour of filter...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2013
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| Цитувати: | Angular trap for macroparticles / D.S. Aksyonov // Вопросы атомной науки и техники. — 2013. — № 2. — С. 123-127. — Бібліогр.: 6 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1117602025-02-09T14:02:39Z Angular trap for macroparticles Кутова пастка для макрочастинок Угловая ловушка для макрочастиц Aksyonov, D.S. Физика радиационных и ионно-плазменных технологий Properties of angular macroparticle traps were investigated in this work. These properties are required to design vacuum arc plasma filters. The correlation between trap geometry parameters and its ability to absorb macroparticles were found. Calculations allow one to predict the behaviour of filtering abilities of separators which contain such traps in their design. Recommendations regarding the use of angular traps in filters of different builds are given. Досліджено властивості кутових пасток макрочастинок, які необхідні при проектуванні реберних систем фільтрів (сепараторів) вакуумно-дугової 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. Наведенo рекомендації щодо використання кутових пасток у фільтрах різних конструкцій. Исследованы свойства угловых ловушек макрочастиц, необходимые для проектирования рёберных систем фильтров (сепараторов) вакуумно-дуговой 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 угловых ловушек в фильтрах различных конструкций. 2013 Article Angular trap for macroparticles / D.S. Aksyonov // Вопросы атомной науки и техники. — 2013. — № 2. — С. 123-127. — Бібліогр.: 6 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/111760 621.793 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Физика радиационных и ионно-плазменных технологий Физика радиационных и ионно-плазменных технологий |
| spellingShingle |
Физика радиационных и ионно-плазменных технологий Физика радиационных и ионно-плазменных технологий Aksyonov, D.S. Angular trap for macroparticles Вопросы атомной науки и техники |
| description |
Properties of angular macroparticle traps were investigated in this work. These properties are required to design vacuum arc plasma filters. The correlation between trap geometry parameters and its ability to absorb macroparticles were found. Calculations allow one to predict the behaviour of filtering abilities of separators which contain such traps in their design. Recommendations regarding the use of angular traps in filters of different builds are given. |
| format |
Article |
| author |
Aksyonov, D.S. |
| author_facet |
Aksyonov, D.S. |
| author_sort |
Aksyonov, D.S. |
| title |
Angular trap for macroparticles |
| title_short |
Angular trap for macroparticles |
| title_full |
Angular trap for macroparticles |
| title_fullStr |
Angular trap for macroparticles |
| title_full_unstemmed |
Angular trap for macroparticles |
| title_sort |
angular trap for macroparticles |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2013 |
| topic_facet |
Физика радиационных и ионно-плазменных технологий |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111760 |
| citation_txt |
Angular trap for macroparticles / D.S. Aksyonov // Вопросы атомной науки и техники. — 2013. — № 2. — С. 123-127. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT aksyonovds angulartrapformacroparticles AT aksyonovds kutovapastkadlâmakročastinok AT aksyonovds uglovaâlovuškadlâmakročastic |
| first_indexed |
2025-11-26T14:17:14Z |
| last_indexed |
2025-11-26T14:17:14Z |
| _version_ |
1849862827785846784 |
| fulltext |
Раздел четвертый
ФИЗИКА РАДИАЦИОННЫХ
И ИОННО-ПЛАЗМЕННЫХ ТЕХНОЛОГИЙ
UDC 621.793
ANGULAR TRAP FOR MACROPARTICLES
D.S. Aksyonov
National Science Center “Kharkov Institute of Physics and Technology”,
Kharkiv, Ukraine
E-mail: d s а k s у о п о v @ g т а i l . с о т
Properties of angular macroparticle traps were investigated in this work. These properties are required to design
vacuum arc plasma filters. The correlation between trap geometry parameters and its ability to absorb macroparticles
were found. Calculations allow one to predict the behaviour of filtering abilities of separators which contain such
traps in their design. Recommendations regarding the use of angular traps in filters of different builds are given.
INTRODUCTION
In most cases, vacuum-arc film deposition needs
applying of special devices – electromagnetic filters
(separators). The necessity of their employment is
caused by the fact that in addition to useful (electron
and ion) components vacuum-arc plasma contains rather
big cathode fragments – so-called macroparticles. Their
contact with a coating can drastically degrade its
quality. At their core, filters are utilizing the concept of
spatial separation of plasma and macroparticle
trajectories. They are designed in such way that there
must not be a direct line-of-sight between the cathode
and a workpiece. Magnetized plasma is being
transported by curvilinear magnetic field from the
cathode to deposition area. Macroparticles are not
affected by transporting field due to their large mass. As
a result, they are moving along straight trajectories and
are not able to reach the substrate.
It is well known [1, 2] that macroparticles are
capable to bounce off filter walls. Undergoing several
rebounds they still can reach the substrate. Colliding
with the walls, macroparticle loses some part of its
initial velocity. After some number of collisions,
macroparticle velocity is decreased so, that it can not
proceed movement: macroparticle either sticks to the
wall or falls due to gravity. It means that it is necessary
to make such conditions, due to which macroparticle
will undergo as much as possible number of collisions
on its way to deposition area. To this end, plasma
guiding channel is usually equipped with additional
obstacles in the form of ribs (baffles).
The effectiveness of separator can be assessed after
its manufacture by counting defects amount which was
left on the coating due to macroparticle impacts. Such
approach has two obvious drawbacks. Firstly, the
counting process is rather time-consuming [3].
Secondly, separator has been already manufactured at
that moment and making modifications of its initial
design is problematic. Therefore filter evaluation should
be made at the stage of its development. But there is a
problem: it is almost impossible (until this work) to
predict with sufficient accuracy an effect of a particular
constructive change on plasma filtering degree.
Computer simulation of macroparticle movement
paths significantly simplifies the problem of separator
designing and assessment of already manufactured ones.
Specialized software, named Macroparticle Tracer
(MPT), was developed for these purposes. The model it
uses and capabilities it possesses were described in
detail earlier [4]. Later [5], basing on the MPT
modelling results analysis, the highly effective baffle
system for T-shaped magnetic filter was developed. It
was found that the highest filtering degree is provided
by baffles tilted on ~ 18º from anode wall and facing the
cathode. At the same time, the location of these baffles
with relation to emission centres (cathode working
surface) is critical for their performance. It was shown
that filtering degree is virtually independent from the
step the baffles are shifted from each other (along the
anode wall) in the range 1...70 mm (with baffles height
equal to 20 mm). But most of the principles responsible
for high filtration coefficient remain unclear.
The most practically valuable capability of baffle
systems is to "absorb" macroparticles, i.e. to act as a
"trap" for macroparticles. The analysis of the developed
baffle systems for T-shaped separator [5] shown, that
two baffle types are absorbing macroparticles most
effectively. In the first case, the bunch from single
baffle and plasma duct wall (generally, it can be a
second baffle instead of wall) are involved in the
absorption process and the baffle is tilted towards
macroparticle emission centres – cathode. In the second
one – the bunch from duct wall and two parallel baffles
which are tilted away from the cathode. According to
this constructive difference, the traps can be
respectively separated into two conventional types:
"angular" and "two-baffle". The scope of this work is to
define properties of angular traps, which are responsible
for their effectiveness and to make some
recommendations regarding baffle systems engineering.
All calculations were made in two-dimensional
approximation and verified by MPT simulations.
Macroparticles were considered as spheres having their
radius tending to zero and therefore represented as
points in calculations. Macroparticle angle of reflection
from surfaces was considered equal to their fall
angle [4, 6].
ISSN 1562-6016. ВАНТ. 2013. №2(84) 123
COMMON PROPERTIES
Angular trap is schematically shown in Fig. 1. It is
made up of junction of baffle and plasma duct wall
(hereinafter the "junction"). Free end of the baffle is
directed toward macroparticle emission centre. The
angle β formed between the trap baffle and the wall can
take values in the range 0 < β ≤ 90º. Macroparticle is
considered to be intercepted if it collided with the trap
walls not less than two times.
This requires to satisfy the following conditions:
0 ,< < ≤ ≤min maxd d d c (1)
0 90 ,α< < ° (2)
where d − is the distance between points of trap junction
and macroparticle impact; c − length of the baffle,
which macroparticle collided first; α − the angle
between wall or baffle (whichever collided first) and
macroparticle trajectory (hereinafter the "glancing" or
"grazing" angle); dmin and dmax − minimum and
maximum possible values of the distance d, which are
defined as:
( )
( ) ( )
sin
,
sin sin
α β
α β
−
=mind h (3)
( )
( ) ( )
sin
,
sin sin
α β
α β
+
=maxd h (4)
where h − the height of the baffle relative to the wall. If
d > dmax, then macroparticle, being reflected from the
wall, will fly past the baffle of the trap (see Fig. 1). In
condition of d < dmin, macroparticle will hit the outer
side of the baffle instead of colliding the wall and
therefore will not get inside the trap.
After each macroparticle rebound inside the trap, the
grazing angle of the particle (α) will be increased by the
value of trap angle (β). Until α < 90º macroparticle will
move deeper inside the trap, i.e. toward the trap
junction. Hence, the number of macroparticle collisions
with the walls of angular trap on the way inwards can be
90 .α β
β
⎢ ⎥° − +
= ⎢ ⎥
⎣ ⎦
n
Fig. 1. Schematic view of the angular trap
(5)
Hereinafter, X⎢ ⎥⎣ ⎦ means rounding of value X to the
nea war
hange its
dir
een from (5), the number of collisions
dur
he length of macroparticle trajectory on
its
rest integer to ds zero (floor function).
After n collisions macroparticle will c
ection to "opposite" one – it will move out of the trap
(away from the junction). After each rebound from the
trap wall, macroparticle glancing angle (α) will decrease
by the trap angle value (β) until α angle become equal to
(or less than) zero. Therefore total number of
macroparticle collisions (N) with the trap can be
obtained from expression (5) if value 180º is used
instead of 90º. However, in most cases, the result will be
valid only for macroparticles with emission point inside
the trap (otherwise, macroparticle will leave the space
between trap baffles earlier than the glancing angle
becomes equal to zero), which is impossible in
considered case.
As it can be s
ing the movement of intercepted macroparticle
inwards the trap does not depend on the trap size (baffle
and plasma duct wall lengths). The number of
macroparticle rebounds on its way out of angular trap,
as it was mentioned above, depends on lengths of the
trap walls and on the point of the first impact d (Fig. 2).
There is some threshold value dt of the distance d
between trap junction and the first collision point. The
number of collisions will be two more (in general) if
d ≤ dt is true.
Knowing t
way inward the trap (see Fig. 2), the angle formed by
trajectory parts during macroparticle movement inside
and outside the trap (γ) and macroparticle glazing angle
at the final rebound (αN), one can obtain the value of
threshold distance dt from the following:
( )
defined as:
( ) ( )
( ) ( )
( ) ( )
( )( )
( )
1
2 2
1
sin sin sin sin
,
sin 2
1
sin
γ
α β α β α
α β
α β
−
= =
sin sin sinα β β⎡+
= + ×⎢
+⎢⎣
⎤⎛ ⎞+ −
⎥× +⎜ ⎟⎜ ⎟+ ⎥⎝ ⎠⎦
∑∏
t
N N
in
i k
d h
k
k
(6)
where
N
180 2N nα α β= °− − , ( )2 9nγ α β= + − ° . 0
3 demonstrates the ure of dependenci (3),
(4)
Fig. 3. Dependency graph of dt, dmax and dmin from
macroparticle grazing angle
Fig. nat es
and (6). It is clear from the figure that function dt(α)
can be approximated by a series of straight lines without
any substantial loss of result accuracy that will
Fig. 2. Trajectory of macroparticle inside angular trap
for d ≤ dt (solid line) and d > dt (dashed line) cases
124 ISSN 1562-6016. ВАНТ. 2013. №2(84)
significantly simplify calculations. It should be
mentioned that distance d will be always less (or equal)
than dt value for glancing angles α ≥ 90 − β, because
dt = dmax in this instance.
In most cases maximum value of N does not
rep
β α β
β α
resent practically meaningful interest. It is connected
to the fact that besides trap geometry and macroparticle
glancing angle, maximum of N depends on relative
location of the trap itself and macroparticle emission
point. So, for the same values of α, β, and h the distance
d can be both lower than threshold value dt and higher
than it depending on H and L values (see Fig. 2). It
means that estimation of filtering capabilities based on
minimum N value is more reliable. In case c >> d total
minimum number of impacts can be written as follows:
( ) 12 90 1 for (90 )α β α β−⎧ ⎢ ⎥
3 for (90 ) 2(90 ) .
2 for 2(90 )
= °
⎪⎪ = °− ≤ < °−⎨
⎪ = °− ≤⎪⎩
N
N
(7)
Here, N possesses the values 3 and 2 because the
min
angular trap having angle β,
the
− + < °−⎣ ⎦N
imum of N, as it was said above, does not exist in
the range of angles α ≥ (90º− β), since dt is always equal
to dmax in this case (Fig. 3).
Since N = f(α), for every
re is a certain critical angle αcr, above which the
number of macroparticle rebounds N will be less than
desired. That is, a trap with angle β will ensure
necessary filtering degree only if condition α < αcr is
true. For values { }*2 1;N k k= + ∈
rom (7):
, critical angle
value can be derived f
90 0.5( 1) .α β− (8)
iagram on Fig. 4 shows the dependency (7) of
ma
s that the glancing angle range at which
ma
2 1
r
,
and for
β β
= °−cr N
D
croparticle-trap collisions number N on
macroparticle glancing angle α for different values of
trap angle β. Region interfaces in the figure are
corresponding to αcr values for different values of N. As
it can be seen from the figure, angular trap is most
effective for low values of α and β angles. Low values
of glancing angle mean that macroparticle flow is
directed along one of the trap baffle. Growth of trap
efficiency in this case confirms earlier results of
modelling [5].
It is obviou
croparticles are able to get into the trap is dependent
on its position relative to macroparticle emission centre.
(This range is always less than 0...90º). As a result, the
trap effectiveness and therefore expediency of its
application in a particular place depends on the place
itself. Knowing the coordinates of emission point,
relative to angular trap, one can determine the angle
range making it possible for macroparticles to travel
inside the trap:
1 2 foα α α
Fig. 4. Minimum number of macroparticle collisions N
with angular trap walls for different values of
macroparticle grazing angle α and trap angle β
Fig. 5. Trajectories of macroparticle with grazing angle
higher than critical before (dashed line) installation of
adjacent trap and after (solid line)
( ) ( )β α α β β α β α β β
<
⎨ < ≤ − < ≤ − >⎪⎩
t
t t t
(9)
where
< ≤⎧⎪
( ) ( )( )( )1 arctan / cotα β= − −H h L h ,
( ) ( )( )( )2 arctan / cotα β= + −H h L h ,
( )arctan /β =t H L ,
where L, H − values that define from the
, it is hardly probable to design a baffle
sys
ULAR TRAP IN -SHAPED PLASMA
ide the anode (or input
sec
distance
emission point to the trap junction (see Fig. 1).
Condition β > βt means that the first macroparticle
collision can occur with both the baffle and duct wall.
Thus if every angle inside the range calculated from (9)
satisfies condition α < αcr, then all macroparticles
leaving given emission point will be absorbed by the
angular trap.
In practice
tem which totally meets α < αcr requirement.
Consequently, there will always be some number of
macroparticles that angular trap can not absorb. But due
to the fact that baffle system consists of a set of traps,
using (3) and (8) one can determine the distance
between neighbouring angular baffles (baffle step) at
which macroparticles with grazing angles α > αcr will
hit the baffle of adjacent trap instead of colliding plasma
duct wall (Fig. 5). In such case macroparticle will
change its glancing angle on more acute one, i.e. its
glancing angle will become lesser than critical. As a
corollary such macroparticle will be absorbed by the
trap. However, for trap angles β ≥ αcr (for example,
when h = 20 mm and N = 7 – β ≥ 22.5º) selection of the
step is not possible because it will have zero or negative
value.
ANG T
DUCT
talled insIf angular trap is ins
tion) of T-shaped separator [5], macroparticle which
leaves trap needs to collide filter walls not less than
two-three times to reach system output. The number of
macroparticle rebounds after it is considered absorbed
by filter (completely loses its initial velocity) is
considered equal to 10 [6]. Thus N = 7 is enough for
macroparticle absorption. According to diagram in
ISSN 1562-6016. ВАНТ. 2013. №2(84) 125
Fig. 7. Dependence of critical glancing angle and the
range of possible glancing angles (greyed) of
macroparticles on the value of trap angle. The trap is
placed at the middle of T-shaped filter anode.
Calculation was made for two utmost points
(H1 and H2) on cathode working surface
Fig. 6. Dependence of critical glancing angle and the
range of possible glancing angles (greyed) of
macroparticles on the value of trap angle. The trap is
placed at far from cathode side of T-shaped filter anode.
Calculation was made for two utmost points
(H1 and H2) on cathode working surface
Fig. 4, a trap having angle β = 18º will absorb all
macroparticles with glancing angle inside range
0 < α ≤ 36º.
Dependencies of critical angle and macroparticle
gla
ade to investigate the
inf
ith performed
cal
movement are the result of their rebounds from outer
ncing angle range on trap angle are shown in Fig. 6.
Calculations were made for a single trap having its
height h = 20 mm and placed on far (from cathode) side
of anode. In the calculation of grazing angle range only
two utmost points of cathode working surface were
taken into account. It is easy to show that macroparticle
glancing angles for emission centres which are between
said ones will be within calculated range. It can be seen
from the figure that condition N ≥ 7 can be provided by
the trap having its angle in range 6º ≤ β ≤ 15º. At this
rate all emitted from cathode surface macroparticles
have grazing angle below critical one. As long as the
angle of the trap grows, the number of intercepted by it
macroparticles with angle above critical value will be
rising. When angle β exceeds the value of 30º, all
macroparticles will have grazing angle higher than
critical (inasmuch as αcr = 0) and requirement N ≥ 7
become unrealizable in principle.
Additional calculations were m
luence of angular trap placement on its efficiency.
Currently, the trap was located at the centre of anode
instead of its far from cathode side. Calculations results
are given in Fig. 7. One can see that condition N ≥ 7 is
not feasible for angular trap placed in such a way. It is
explained by shift of macroparticle grazing angle range
towards higher values at constant αcr. Increase of value
H will obviously lead to similar result. However it
should be kept in mind that a real baffle system will
consist from multiple traps. Therefore, the efficiency
criterion used (N ≥ 7) is overestimated if a whole baffle
system is being considered.
Fig. 8 shows simulation results of macroparticle
collisions with angular trap (β = 15º) for different values
of L. The figure also shows the influence of
effectiveness factor – value N was increased from 7 to
9. Modelling of macroparticle trajectories was
performed using MPT software. It can be seen from the
figure that in conditions where N = 7 and L = 236 mm,
as it was assumed, the trap absorbs all intercepted
macroparticles. At the same time it can not fulfil N ≥ 9
requirement – notable number of macroparticles is
leaving the trap. A similar result is obtained by reducing
distance L. Simulation results are fully confirming the
above calculations (see Figs. 6 and 7).
Obtained dependences along w
Fig. 8. Simulation results of macroparticle trajectories
intercepted by angular trap which is placed at different
distances from cathode and for different efficiency
factors. The trap angle is β = 15º and number of emitted
macroparticles is ~ 104. Trajectories of macroparticles
leaving utmost points of cathode working surface at
maximum grazing angle are highlighted by a thicker
line
culations allow making recommendations regarding
the application of angular traps in designing baffle
systems for separators. Firstly, application of angular
traps is preferred in places where angle between plasma
duct wall and macroparticle trajectory (α) has minimum
value. These places usually are most distant from
cathode (along duct axis) regions like, for example,
"opposite" arm of T-shaped plasma duct or, as shown
above, anode exit. Secondly, one should avoid trap
angle (β) values higher than 30º due to very low
effectiveness of such traps. Generally, the angle of the
trap should be as low as admissible. Thirdly, it is not
recommended to use angular traps in regions of a filter,
where macroparticle movement along plasma duct axis
in unacceptable. Such directions of macroparticle
126 ISSN 1562-6016. ВАНТ. 2013. №2(84)
side of angular trap baffle. This applies to the so-called
"straight" filters and output sections of curvilinear
filters, such as, for example, L- and T-shaped ones. At
the same time, installation of angular traps inside the
input sections of said curvilinear separators will greatly
enhance their filtering abilities if such installation does
not contradict selection of the distance (see above).
Implementation of mentioned recommendations in
published earlier work [5] related to optimization of
filt
In this pap which are
characterizing eff particle filtering
by
REFERENCES
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V.E
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to
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arc
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Flo
Optimization of T-Shaped
Ma
V.E. Strel’nitskij, V.V. Vasilyev,
D.Yu.
Статья поступила в редакцию 21.11.2012 г.
УГЛОВАЯ ЛОВУШКА МАКРОЧАСТИЦ
Исследованы свойства угловых ловушек необходимые для проектирования рёберных
сис
и ю н ц а
КУТОВА ПАСТКА ДЛЯ МАКРОЧАСТИНОК
Досліджено властивості кутових пасток ма необхідні при проектуванні реберних систем
філ
ering abilities of T-shaped separator partially
explains high efficiency of developed baffle system. For
a complete understanding of its functioning it is
necessary to additionally perform analysis of "two-
baffle" trap which was also used in filter design.
However this is beyond the scope of current study and is
the subject of further research.
CONCLUSIONS
er, the dependences
ectiveness of macro
angular trap were established. Growth of filtering
abilities is promoted by decreasing of trap angle,
increasing of distance between the trap and the cathode
along the axis of plasma duct and by decreasing of this
distance transverse to the axis. The effectiveness of
angular trap was calculated and results are confirmed by
simulation in MPT on the example of T-shaped
magnetic separator. Calculation results are explaining
high filtering capabilities of baffle system containing
investigated traps with small angles in its design, as it
was found earlier [5] during optimization of T-shaped
separator. Obtained dependences allow prediction of
efficiency of angular traps application in the process of
baffle systems designing which are used in magnetic
separators.
, A.A. Andreev
. Strel'nitskij, V.M. Khoroshikh. Vacuum arc.
Plasma sources, coatings deposition, surface
modification. Kyiv: “Naukova dumka”, 2012, 728 p.
(in Russian)
2. A. And
Energetic Condensation. New York, Springer, 2008,
542 p.
3. R.L.
deposition // IEEE Trans. Plasma Sci. 2001, v. 29,
p. 762-767.
4. D.S. Ak
w in Filtered Vacuum Arc Plasma Systems // PAST.
2012, N2, p. 108-113.
5. D.S. Aksyonov.
gnetic Separator Filtering Abilities // PAST. 2012,
N2, p.102-107.
6. I.I. Aksenov,
Zaleskij. Efficiency of magnetic plasma filters.
// Surf. Coat. Technol. 2003, v. 163-164, p. 118-127.
ДЛЯ
Д.С. Аксёнов
макрочастиц,
тем фильтров (сепараторов) вакуумно-дуговой плазмы. Установлены зависимости между
геометр ческими параметрами ловушки и эффективность поглоще ия макрочасти . Выполнены р счёты,
результаты которых позволяют прогнозировать поведение фильтрующих качеств сепараторов, содержащих
в своей конструкции такие ловушки. Даны рекомендации относительно применения угловых ловушек в
фильтрах различных конструкций.
Д.С. Аксьонов
крочастинок, які
ьтрів (сепараторів) вакуумно-дугової 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. Наведені
рекомендації щодо використання кутових пасток у фільтрах різних конструкцій.
ISSN 1562-6016. ВАНТ. 2013. №2(84) 127
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