Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field
Based on the known experimental and theoretical data, a new model of the plasma jet, which emit by cathode spot (СS) along the magnetic field proposed. According to this model, the plasma jet contains an oppositely directed current of accelerated ions of the cathode material with an excess positive...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2023
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| Цитувати: | Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field / V.V. Vasyliev, V.E. Strel’nitskij // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 92-97. — Бібліогр.: 23 назв. — англ. |
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Vasyliev, V.V. Strel’nitskij, V.E. 2023-12-09T10:05:01Z 2023-12-09T10:05:01Z 2023 Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field / V.V. Vasyliev, V.E. Strel’nitskij // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 92-97. — Бібліогр.: 23 назв. — англ. 1562-6016 PACS: 52.80.Mg DOI: https://doi.org/10.46813/2023-143-092 https://nasplib.isofts.kiev.ua/handle/123456789/196037 Based on the known experimental and theoretical data, a new model of the plasma jet, which emit by cathode spot (СS) along the magnetic field proposed. According to this model, the plasma jet contains an oppositely directed current of accelerated ions of the cathode material with an excess positive charge and a current of accelerated electrons with an excess negative charge, between which an electric field of polarization of the plasma jet formed. Based on this model, the basic parameters of the plasma jet from the external parameters of the magnetic field, the arc current, and the average charge state of the ions calculated. The main mechanisms affecting the speed and direction of movement of the arc CS on the cathode end surface clarified for the first time. На основі відомих експериментальних і теоретичних даних запропонована нова модель плазмового струменя, який емітує катодні плями (КП) вздовж магнітного поля. Згідно цієї моделі він містить протилежно направлені струм прискорених іонів матеріалу катода з надлишковим позитивним зарядом і струм прискорених електронів з надлишковим негативним зарядом, між якими утворюється електричне поле поляризації плазмового струменя. На основі цієї моделі вперше виконані розрахунки основних параметрів плазмового струменя від зовнішніх параметрів магнітного поля, струму дуги та середнього зарядового стану іонів у плазмовому струмені. Вперше з’ясовані основні механізми, що впливають на швидкість і напрямок руху КП дуги по поверхні торця катода, що випаровується. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology Low temperature plasma and plasma technologies Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field Механізми, що впливають на швидкість і напрямок руху катодних плям вакуумної дуги в магнітному полі Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field |
| spellingShingle |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field Vasyliev, V.V. Strel’nitskij, V.E. Low temperature plasma and plasma technologies |
| title_short |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field |
| title_full |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field |
| title_fullStr |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field |
| title_full_unstemmed |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field |
| title_sort |
mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field |
| author |
Vasyliev, V.V. Strel’nitskij, V.E. |
| author_facet |
Vasyliev, V.V. Strel’nitskij, V.E. |
| topic |
Low temperature plasma and plasma technologies |
| topic_facet |
Low temperature plasma and plasma technologies |
| publishDate |
2023 |
| language |
English |
| container_title |
Problems of Atomic Science and Technology |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Механізми, що впливають на швидкість і напрямок руху катодних плям вакуумної дуги в магнітному полі |
| description |
Based on the known experimental and theoretical data, a new model of the plasma jet, which emit by cathode spot (СS) along the magnetic field proposed. According to this model, the plasma jet contains an oppositely directed current of accelerated ions of the cathode material with an excess positive charge and a current of accelerated electrons with an excess negative charge, between which an electric field of polarization of the plasma jet formed. Based on this model, the basic parameters of the plasma jet from the external parameters of the magnetic field, the arc current, and the average charge state of the ions calculated. The main mechanisms affecting the speed and direction of movement of the arc CS on the cathode end surface clarified for the first time.
На основі відомих експериментальних і теоретичних даних запропонована нова модель плазмового струменя, який емітує катодні плями (КП) вздовж магнітного поля. Згідно цієї моделі він містить протилежно направлені струм прискорених іонів матеріалу катода з надлишковим позитивним зарядом і струм прискорених електронів з надлишковим негативним зарядом, між якими утворюється електричне поле поляризації плазмового струменя. На основі цієї моделі вперше виконані розрахунки основних параметрів плазмового струменя від зовнішніх параметрів магнітного поля, струму дуги та середнього зарядового стану іонів у плазмовому струмені. Вперше з’ясовані основні механізми, що впливають на швидкість і напрямок руху КП дуги по поверхні торця катода, що випаровується.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/196037 |
| citation_txt |
Mechanisms affecting the speed and direction of vacuum arc cathode spots movement in a magnetic field / V.V. Vasyliev, V.E. Strel’nitskij // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 92-97. — Бібліогр.: 23 назв. — англ. |
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| fulltext |
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143).
92 Series: Plasma Physics (29), p. 92-97.
https://doi.org/10.46813/2023-143-092
MECHANISMS AFFECTING THE SPEED AND DIRECTION
OF VACUUM ARC CATHODE SPOTS MOVEMENT
IN A MAGNETIC FIELD
V.V. Vasyliev, V.E. Strel’nitskij
National Science Center “Kharkov Institute of Physics and Technоlogy “, Kharkiv, Ukraine
E-mail: Vladimir.Vasyliev@ukr.net
Based on the known experimental and theoretical data, a new model of the plasma jet, which emit by cathode
spot (СS) along the magnetic field proposed. According to this model, the plasma jet contains an oppositely directed
current of accelerated ions of the cathode material with an excess positive charge and a current of accelerated
electrons with an excess negative charge, between which an electric field of polarization of the plasma jet formed.
Based on this model, the basic parameters of the plasma jet from the external parameters of the magnetic field, the
arc current, and the average charge state of the ions calculated. The main mechanisms affecting the speed and
direction of movement of the arc CS on the cathode end surface clarified for the first time.
PACS: 52.80.Mg
INTRODUCTION
Vacuum-arc cathode plasma of electric arc discharge
is one of the most amazing and currently most used
objects for the synthesis of various strengthening
coatings. An arc discharge is characterized by the
formation on the surface of the cathode of very small
non-stationary cathode spots (CS), the surfaces of which
emit plasma jets that concentrate very high current and
power densities at a relatively low cathode fall of the
potential (~ 20 V), which fluctuates [1]. The main
mechanism of arc discharge excitation is the creation of
collective emission processes on the cathode surface,
regardless of the absolute values of current and voltage
[2, 3]. These processes can be thermo emissive or
determined by a strong electric field. Nonlinear
enhancement of thermo ion and field emission can also
lead to the well-known thermal field emission (TFE) [1].
The places where this happens can evaporate with an
explosion, which leads to the appearance of a new form
of electron emission, which is not stationary in nature,
since the place of emission changes explosively. This
non-stationary form of emission is so-called explosive
electron emission (EEE). EEE requires a minimum of
action, which need to invest in the “quantum” of the
explosive process, the so-called ecton.
The ignition of the emission center is not just the
ignition of an arc discharge it is a constant mechanism of
the existence of an arc discharge, based on the existence
of local places of electron emission from the surface of
the cathode with a low work output. In these places, as a
rule, local energy input, this leads to EEE. This stage of
the emission is the basis of the “ecton” model developed
by Mesyats and co-authors [4, 5]. According to the ectons
model [4, 6, 7], thermal acceleration occurs on micro
protrusions until they explode with a delay associated
with the action of the material. The explosion also creates
plasma of the cathode material, as the result of the rapid
heating of a small volume of this material to a
temperature that turns it into a supercritical fluid, which
gradually turns into fully ionized plasma without any
transition through the classical liquid and vapor phases.
At the same time, there is a definite, short-lived state of
the cathode material with a high density, which can best
of all be described as an imperfect plasma [8].
This plasma, expanding explosively, leaves behind a
crater covered with a thin layer of molten cathode
material. Subjected to the high explosive pressure of the
plasma, the remains of the molten material of the cathode
ejected from the explosion crater and quickly cool,
forming macro-particles and micro-protrusions that can
serve as new ignition points. At least one of them will be
the most suitable for thermal acceleration, which leads to
the next explosion and creates conditions for the ignition
of the next ekton. This transition is extremely fast, shorter
than 1 ns, and can occur only at the beginning of the
explosive stage of a new emission region.
Material in this region reaches a maximum
temperature and, due to the extreme pressure gradient in
the environment expands and cools. As the dense non-
ideal plasma of the cathode material expands, it becomes
weakly non-ideal and with further expansion, after about
10 ns, the plasma density decreases so much that the
frequency of collisions drops to the level at which the
condition of equilibrium violated. The plasma enters a
non-equilibrium state, which plays an important role
when considering the properties of the plasma in the
inter-electrode space.
In the process of the transition of the plasma to the
non-equilibrium state, the plasma ions accelerate to
supersonic speeds [9, 10-14]. At the same time, need to
note, that after the end of the explosive stage of the
development of the emission center in the CS, begins the
next quasi-stationary stage, in which continues the
emission of electrons from the molten metal layer of the
newly created crater. The cathode material evaporates
from the surface of this crater and ionizes very close to
the cathode surface due to the intense electron beam
formed in the thin cathode layer. Electrons in this beam
have an energy corresponding to the cathode fall (about
20 V), and its current density is determined by field-
enhanced thermo electron emission.
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 93
Most of the ions returning to the cathode formed as the
result of electron-atom interaction in the relaxation zone
of the electron beam in the immediate vicinity of the
cathode surface [15]. Accelerated by the electric field in
the cathode layer of the potential fall, these ions bombard
the molten surface of the newly created crater, which
sputtered with the formation of macroparticles. At the
same time, need to note, that under the influence of
thermal conductivity, the area, that emits electrons,
expands and its temperature gradually decrease. These
leads to a decrease in the density of the electron beam,
which, in the final stage, is not sufficient for ionization of
vapors of the cathode material in the cathode layer.
Despite the lower cathode surface temperature and
lower electrical voltage, this stage can be important for
the overall cathode erosion because the hot surface can
still deliver metal vapors, especially when the cathode
material has a high vapor pressure [16].
Numerical modeling using a time-dependent two-
dimensional hydrodynamic model showed that the
distribution of the ion current on the cathode at the end of
the explosive stage of the emission site is circular, and
not a peak in the center of the emission site [17, 18]. The
same distribution of the ion current on the cathode can
assumed and for the fractal model of the CS, in which the
CS contains many emission centers that are concentrated
on the periphery of the CS.
In the absence of a transverse magnetic field, any
places on the edge of newly created craters around the СS
can equally likely turn into new active places of emission.
At the same time, in the presence of a magnetic field with
a transverse component at the location of the CS, the ring
symmetry of the formation of emission centers around the
CS is broken. It, as is known [19, 20], causes the
movement of the CS in the direction of the most likely
ignition of new emission areas of spots 2-th type.
At first glance, this seems fair, but it causes a
contradiction in that the СS will move in the most likely
places of ignition of emission centers around the СS
according to the acute angle rule. According to literature
data, this rule declares that the CS during its retrograde
movement across the tangential component of the
magnetic field on the cathode surface shifts toward the
maximum of the tangential component of the magnetic
field on the working surface of the cathode. That is in the
direction of the acute angle between the working surface
of the cathode and the force lines of the magnetic field,
which cross this surface. As a result, the cathode surface
erodes in such a way that the force lines of the magnetic
field eventually become perpendicular to this surface. It
would seem that in this case the CS should move across
the working surface randomly without any definite
direction. However, as experiments show, this is not the
case. The directionality of the predominant speed of the
CS movement is preserved. This indicates that the
existing concepts of controlling the movement of the CS
along the working surface of the cathode only by the
magnetic field do not allow fully identify the mechanisms
affecting the speed and direction of this movement.
The purpose of this work is to identify the main
existing mechanisms that affect the speed and direction of
CS movement on the cathode surface in the case when
the force lines of the magnetic field cross this surface at
right angles, as well as to identify conditions that
effectively increased the deposition rate of coatings.
1. THEORETICAL ESTIMATIONT OF THE
PARAMETERS OF THE VACUUM-ARC
PLASMA JET
In order to ignite a vacuum-arc discharge, it is
necessary that initial plasma of a certain density and
temperature have to be creating near the surface of the
cathode, which has the places with a low work output.
As mentioned above in these places, as a rule, local
energy input, which leads to EEE (ecton). The EEE
creates plasma of the cathode material, as the result of
the rapid heating of a small volume of this material to a
temperature that turns it into a supercritical fluid, which
gradually turns into a fully ionized plasma high density.
This plasma explosively expansions and accelerates ions
along the magnetic field to supersonic speeds Vi,
leaving behind craters.
At the same time, the flow of electrons emitting from
the surface of the craters simultaneously accelerates in
the same direction to the energy of the cathode drop
potential above the EEE site (this is approximately
20 eV). As a result, accelerated flows of ions and
electrons directed in one direction along the magnetic
field form the plasma jet with oppositely directed
electric currents of ions Ii with an excess positive charge
Qi and of electrons Ie with an excess negative charge Qe.
In addition, it known, that in each of these currents,
between charges of the same name, which move in the
same direction with the same speed V and are directed
perpendicular to the line connecting them, there are
forces of magnetic interaction (the forces of attraction)
[21], which focus these currents around their axes.
According to the Bio-Savar-Laplace law [21],
transverse magnetic fields HT form around, the above-
mentioned, oppositely directed currents Ii and Ie, which
push these currents away from each other by Ampere's
force [21]. At the same time, excess opposite electric
charges, that accumulated in these electric currents in a
result of their separation in a plasma jet, that moving
along a non-uniform curvilinear magnetic field, create
electric fields with an intensity E between them. The
force lines of these electric fields are equipotential lines,
so they cross the lines of force of the magnetic field HT,
covering these currents, at a right angle.
The total effect of these electric fields between the
oppositely directed currents Ii and Ie balance the
repulsive Ampere force between them, which is created
at a certain distance a between these currents.
If two focused and oppositely directed electric
currents Ii and Ie are formed in the plasma jet, which can
be considered as separate conductors of finite length
L >> a, where a is the distance between the conductors,
then the Ampere force F of repulsion between these
currents will be approximately equal to [21]:
F =μ02ІіІаL/4πа, (1)
where μ0 = 4π10-7 Hn/m is the magnetic constant.
Thus, it can be assumed that when the plasma jet of
vacuum-arc plasma emitted by the CS along the
magnetic field H that cross an anode it contains two
94 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
separated from each other, oppositely directed electric
currents Іі and Іа >> Іі with opposite excess electric
charges Qi and Qe = - Qi.
When the plasma jet hits a metal surface that is not
an anode, then according to Kirchhoff's first law, the
current of electrons Ie will be equal to the oppositely
current of ions Ii << Іа and their excess electric charges
Qe = - Qi. These charges will create an electromotive
force (EMF) for the oppositely directed currents Ii and
Ie, which ensures their continuity.
On of this assumption, a new model of the plasma
jet created. It allows us to adequately estimate its
parameters from the intensity of the external magnetic
field H0, the arc current Ia, and the configuration of the
magnetic field in the middle of the anode covering this
plasma jet.
To explain this model in Figure shows a schematic
representation of the cross-sectional structure of a
plasma jet emitting CS at a distance from the end of the
cathode along the magnetic field, where the electron are
became magnetized.
Schematic representation of the cross-section of the
plasma jet near the end of the evaporating cathode
In the Figure, FLe is the Lorentz force acting on
electrons; FLi is the Lorentz force acting on ions. Ie and
Ii – respectively, the current of electrons and ions in
their cross section; HT is the intensity of the transverse
magnetic field formed between oppositely directed
electric currents Ie and Ii; a – is the distance between the
centers of electric currents Ie and Ii; E – the intensities
of the transverse electric fields formed between the
outer surfaces, which cover the electric currents Ie and Ii,
respectively, with excess negative and excess positive
charges; H is the strength of the longitudinal magnetic
field in the middle of the plasma jet.
To carry out estimated calculations of the electron
density of the plasma inside the plasma jet and in its
structural elements, the following assumptions used,
that simplify these calculations. It are the following.
a) The entire arc currents Ia ≤ 100 A that passes through
one CS. b) The current of accelerated ions along the
plasma jet is 10% of the arc current, which corresponds
to the experimental results obtained for titanium plasma.
c) The density of plasma diffusion flows across the
magnetic field is much smaller than once compared to
the density of its flows along the magnetic field.
It known that plasma is a diamagnetic medium. This
is due to the cyclotron rotation of charged plasma
particles around the force lines of the magnetic field,
which create magnetic moments of the orbit, μ, the
magnitude of which is determined in vector form as
[22]:
μ = - (Мv┴
2 /2H2) Н. (2)
Thus, the magnetic induction inside the plasma will be
equal to [22]:
B = H0 (1 + 4πχ). (3)
Here χ is the magnetic susceptibility of the plasma.
Since the magnetic moments of all particles directed
against the external field H0, the magnetic susceptibility
χ is negative. It can express in terms of the transverse
pressure of the plasma, P┴, held by the magnetic field
H0 [22]:
χ = P┴/H0. (4)
If the transverse pressure of the plasma inside the
plasma jet is P┴ equal to the pressure of the external
magnetic field, which is equal to H0
2/8π, then the
induction of the magnetic field B inside the plasma jet
will be equal to B = H0/2.
From the condition of equilibrium of the transverse
pressure of the plasma P┴ inside the plasma jet and the
external pressure of the magnetic field with the intensity
H0, it is possible to estimate easily the maximum
density of the plasma and the density of the ion flow
along the plasma jet from the following system of
equations.
Р┴ = nekTе + nikTi + H0
2/16π = H0
2/8π. (5)
To take in account that Te = Ti and ne = niZ
ni = H0
2/16πkTе (Z+1), (6)
j i = IaΛ/sі = ZeniVi, (7)
or from (7)
ni = IaΛ/sіZeVi, (8)
where ji, e, ne, ni, Z, and Te are, respectively, the average
ion current density in the plasma jet, the electron
charge, the density of electrons, the ion density, the
average charge state of ions and the electron
temperature of the plasma; k – Boltzmann's constant; Ia,
and si – are the arc current and the cross-sectional area
of the jet through which the electric current of
accelerated ions passes, and Vi – the average speed of
accelerated plasma ions along the magnetic field,
respectively; Λ – is the value of the plasma ion current
along the plasma jet relative to the arc current.
Equating (6) and (8), we find the value of the cross-
sectional area of the plasma jet si from the magnetic
field strength and the arc current in the plane of its
intersection across the magnetic field H for that part of
it where the current carry by accelerated ions:
sі = 16πIaΛkTе(1+1/Z)/(H0
2eVi). (9)
By substituting the values of si from (9) into (7), we
obtain the value of the average ion current density ji in
the plane of the given cross section of the plasma jet:
ji = H0
2eVi/16πkTе (1+1/Z). (10)
It seen from relations (6), and (10) that the density of
the plasma and ion current in the cross-sectional plane
of the plasma jet do not depend on the arc current
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 95
passing through the CS, but are depends mainly on the
square of the intensity of the external magnetic field H0
in this cross-sectional plane. As can be seen from
relation (9), the cross-sectional area of the plasma jet si
varies as Ia and Λ and is weakly dependent on Z.
Therefore, the coating deposition rate in the cross-
section of the plasma jet also changes depending on
these parameters, other things being equal. Similarly,
we obtain expressions for ne, se, and jе for the second
part of the plasma jet, in which the electric current
carried exclusively by electrons accelerated in the
cathode layer of this jet. These expressions have the
following form:
nе = H0
2/16πkTе (1+1/Z), (11)
sе = 16πIakTе (1+1/Z)/(H0
2eVе), (12)
jе= H0
2eVе/16πkTе (1+1/Z), (13)
where Ve is the speed of electrons accelerating in the
cathode layer of this jet.
When comparing expressions (9) and (12), it seen
that the cross-sectional area of the ion current is
approximately in Λ times smaller than the cross-
sectional area of the electron current, at least near the
cathode surface end.
Substituting in (6) the value of the plasma electron
temperature Te in the plasma jet, which usually does not
exceed 3 eV, can easy to estimate the minimum average
density of plasma in the plasma jet from the intensity of
the external magnetic field from the expression:
ni = 0.83 ∙1010Н0
2/(Z +1). (14)
Substituting in (10) additionally the value of the average
ions speed movement Vi in the plasma jet along the
magnetic field, which, according to experimental data,
is on average equal to 1.5104 m/s [23], can easy to
estimate the minimum average density of the ion current
in the plasma jet from the expression:
ji =0.995∙10-3Н0
2/(1+1/Z). (15)
As an example, the table shows the calculated
average values of the plasma density, ion current
density and the cross-sectional area of the plasma jet at
Ia = 100 A and Λ = 0.1 for two fixed values of the
magnetic field: H0 = 500 E and H0 = 100 E near the
cathode surface end.
Main parameters of the ion current of the plasma jet
from the magnetic field strength H0
Н0, Oe ni, сm-3 ji, А/сm2 si, сm2
500 2.08·1015/
(Z +1)
497.6/(1+1/Z) 3.22·10-2/
(1+1/Z)
100 0.83·1014/
(Z +1)
20/(1+1/Z) 0.8/(1+1/Z)
The results obtained are necessary for elucidating the
main mechanisms affecting the speed and direction of
the CS movement on the cathode end.
2. ADDITIONAL PARAMETERS OF THE
PLASMA JET OF THE VACUUM-ARC
DISCHARGE
The solution of the problem aimed at increasing the
speed of the CS arc movement on the surface of the
evaporating cathode is of urgent importance, since it
ensures a decrease in the droplet phase in the erosion
products of the cathode material, which occurs during
its evaporation from the emission centers of the CS. It
assume that this can be achieved by simultaneously
increasing the probability of ignition of new emission
centers near the CS and the rate of suppression of still
active emission centers in the area of this CS. To
implement this idea, it is necessary to consider in more
detail the parameters of the plasma jet and its structural
elements, which can affect the speed and direction of
CS movement on the surface of the evaporating
cathode, depending on the parameters of the magnetic
field and the arc current.
Electrons moving along the magnetic field in the
plasma jet can reach the anode in two different ways,
which depend on the configuration of the magnetic
field.
The first path of electrons from the cathode to the
anode in a magnetic field is a direct path. It is realized
when the force lines of the magnetic field, along which
the plasma jet emanating from the CS spreads,
simultaneously cross the surfaces of the cathode and
anode. As a result, the current of the vacuum arc
discharge between the cathode and the anode Ia is
provided, mainly, by the electronic current of thermal
electrons, which are accelerated along the magnetic
field by the external electric field. This field creates by
the power source of the vacuum arc discharge between
the cathode and the anode.
At the same time, the bipolarity of plasma jet
provides separately by currents of accelerated ions Ii
with an excess positive charge Qi and electrons Ie with
an excess negative charge Qе. But in order to maintain
excess charges, in the currents at a certain level, the
magnetic field must be divergent, which is characterized
by a transverse gradient directed from the axis of the
cathode, as well as by the radius of curvature of the
force lines of the magnetic field along which the plasma
jet spreads. In this case the bipolar structure of the
plasma jet is supported as a result of the constant
distribution of electric charges in the plasma jet, which
occurs in a non-homogeneous, in particular, in a
divergent, curvilinear, magnetic field, which causes a
gradient and centrifugal drift of magnetized electrons
across the magnetic field relative to slow-moving, non-
magnetized, ions [22].
It should also note that the plasma through which
these currents pass retains its quasi-neutrality, which
violate only at the boundaries of these currents.
Therefore, an excess negative charge Qe accumulates at
the boundary of the electron current Ie, and an excess
positive charge Qi = - Qe accumulates at the boundary of
the ion current Ii. These charges form transverse electric
fields E between the boundaries of these currents, which
provide an electric force of attraction between these
currents.
If the plasma jet falls on the anode, then electric
currents Ii and Ie = Ia also fall on the anode, which
significantly reduces the coatings deposition rate from
accelerated ions of the cathode material on another
surface that is not the anode. As a result, the coatings
deposition rate from accelerated ions will depend only on
the rate of their diffusion from the plasma jet across the
96 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
magnetic field H toward the axis of the cathode. At the
same the validity of the quasi-stationary and final stages
of the development of the CS emission centers are
simultaneously increasing.
The increase of these terms occurs as the result of the
direct outflow of accelerated electrons from the electric
current Ia to the anode that increase the cathode potential
drop between the cathode and the plasma of the plasma
jet. It will lead to an increase in Ie from Ie = Ii to the full
current of the arc discharge Ia >> Ii, which, respectively,
will increase the heating temperature of the cathode
surface, which emits electrons. In this case will
significantly increase the evaporation rate of the cathode
material with the formation of macroparticles.
In the case, when the plasma jet spreads along the
force lines of the magnetic field, that do not cross the
anode, then to ensure the arc current on the anode, the
intensity of the electric field of polarization of the plasma
jet E is of great importance. This electric field will ensure
the drift current of electrons from the plasma jet to the
anode across the magnetic field H. The density of this
drift current JDe is calculated from the well-known
expression [22]:
JDe= еne [ЕН]/ Н2, (16)
where ne is the average plasma density in the plasma jet
between its electric currents Ii and Ie.
In addition, thanks to this drift of the electrons the
polarization electric field E of plasma jet will strengthen
by the external electric field, which will penetrate into
the middle of the plasma jet along the electric field of
the E from the anode side. As a result, the JDe electron
current density to the anode across the magnetic field H
will increase accordingly. The total current of electrons
to the anode Ia along the entire length of the plasma jet
L, taking into account (19), can be approximately
calculated from the following expression:
Іа = aLJDe, (17)
where a is the distance between oppositely directed
electric currents Ii and Ie, in the middle of the across
section of the plasma jet (see Figure).
At the same time, the electric current of accelerated
ions Ii can fully use for the deposition of coatings, and
the electronic current of accelerated electrons Ie, upon
reaching the surface of the coating deposition will
provide a negative potential on it. As a result, the
density of electron currents from the emission centers of
the CS will decrease. It will ultimately lead to a
decrease in the temperature of their surfaces, as quickly
as possible, and a complete cessation of the creation of
vapor phase of the cathode material with the formation
of macroparticles.
If the speed of accelerated electrons in the electron
current Ie is equal to Ve, then the geometric sum of the
Lorentz forces acting on all the electrons accelerated in
this current, FLe, (see Figure) will be equal to:
FLе = еnesе [Ve НT]. (18)
Under the action of this force, all electrons accelerated
along the magnetic field H, will move across the
magnetic field H with the drift speed VDL (see Figure),
which calculated from the known expression [22]:
VDL = [FLе Н]/еН2 = -sе [JeН]/ Н2. (19)
If the current of accelerated electrons Ie and the ion
current of accelerated ions Ii, which are separated from
each other by a distance a, pass through the plasma jet
along the magnetic field H, then the rotation frequency
Ωe of the electron current Ie around the ion current Ii
with non-magnetized ions will be equal to:
Ωе = VDЛ /а = - sе[JeН]/аН2. (20)
According to the directions FLe and H, indicated in
Figure, the direction of rotation of the electron current Ie
around the ion current Ii with non-magnetized ions will
be clockwise. At the same time, the vector of the
maximum electric field of polarization of the plasma jet
E formed between the oppositely directed electric
currents Ii and Ie, respectively, with excess positive
charge Qi and excess negative charge Qe, will also rotate
with the same frequency Ωe around the ion current Ii. As
a result, the direction of CS movement along the
cathode surface towards the positively charged part of
the plasma jet will also change with the same
frequency Ωe.
Thus, the CS, moving against the electric field of the
polarization of the plasma jet E, will constantly change
its direction of movement synchronously with the
change in the direction of this electric field, which, on
average, will ensure the uniform movement of the CS
along the surface end of the evaporating cathode, along
a cycloid trajectory. Such movement of the СS will
ensure uniform erosion of the cathode over its entire
evaporating surface.
CONCLUSIONS
For the first time was assumed, that the plasma jet of
a vacuum-arc plasma contains oppositely directed
currents of the accelerated ions of the cathode material
with an excess positive charge and of accelerated
electrons with an excess negative charge, between which
an electric field of polarization of the plasma jet is
formed.
Based on this assumption, a new model of the plasma
jet proposed for the first time. This model allows
adequately estimate its parameters from the configuration
and intensity of the external magnetic field, the arc
current and the intensity of the electric field of the plasma
jet polarization.
The calculations were made of electron density of the
plasma jet, the density of ion and electron currents along
the magnetic field, as well as the maximum transverse
diameters of these currents from the external parameters
of the magnetic field, the arc current, and the average
charge state of the ions in the plasma jet.
It theoretically shown for the first time that the current
of accelerated electrons under the action of the total
Lorentz force rotates around the axis of the ion current
with a frequency inversely proportional to the distance
between these oppositely directed currents, which ensures
the balance of the forces of magnetic and electric
interaction between them. The electric field formed
between these currents changes its direction relative to
the ion current axis with the same frequency.
It shown that the CS, moving against the electric field
of the polarization of the plasma jet, must constantly
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 97
change its direction of movement synchronously with the
change in the direction of the electric field of the
polarization of the plasma jet. This, on average, will
ensure a uniform movement of CS along the surface end
of the evaporating cathode along a cycloid trajectory.
Such movement of the CS will ensure uniform erosion of
the cathode over its entire evaporating surface.
It theoretically shown for the first time that the highest
coatings deposition rate from accelerated ion flows
obtained only in a curvilinear magnetic field diverging
from the axis of the cathode, at least not crossing the
surface of the anode, which covered the bipolar plasma
jet. In addition, it shown that in this case the evaporation
rate of the cathode material with the macroparticles
formation reduced to a minimum.
At the first time, the main mechanisms affecting the
speed and direction of the CS movement on the surface
end of the evaporating cathode clarified.
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Article received 17.12.2022
МЕХАНІЗМИ, ЩО ВПЛИВАЮТЬ НА ШВИДКІСТЬ І НАПРЯМОК РУХУ КАТОДНИХ ПЛЯМ
ВАКУУМНОЇ ДУГИ В МАГНІТНОМУ ПОЛІ
В.В. Васильєв, В.Є. Стрельницький
На основі відомих експериментальних і теоретичних даних запропонована нова модель плазмового
струменя, який емітує катодні плями (КП) вздовж магнітного поля. Згідно цієї моделі він містить
протилежно направлені струм прискорених іонів матеріалу катода з надлишковим позитивним зарядом і
струм прискорених електронів з надлишковим негативним зарядом, між якими утворюється електричне
поле поляризації плазмового струменя. На основі цієї моделі вперше виконані розрахунки основних
параметрів плазмового струменя від зовнішніх параметрів магнітного поля, струму дуги та середнього
зарядового стану іонів у плазмовому струмені. Вперше з'ясовані основні механізми, що впливають на
швидкість і напрямок руху КП дуги по поверхні торця катода, що випаровується.
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