Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок
The article discusses the various methods of estimating the surface cathode temperature of the high-voltage glow discharge electron gun, which forms a ribbon electron beam with a linear focus. Numerical estimations have been made to design the cathode assembly of an industrial gun. It is shown that...
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| author | Melnyk, Igor Tuhai, Serhii Kovalchuk, Dmytro Surzhykov, Mykola Shved, Iryna Skrypka, Mykhailo Kovalenko, Oleksandr |
| author_facet | Melnyk, Igor Tuhai, Serhii Kovalchuk, Dmytro Surzhykov, Mykola Shved, Iryna Skrypka, Mykhailo Kovalenko, Oleksandr |
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| description | The article discusses the various methods of estimating the surface cathode temperature of the high-voltage glow discharge electron gun, which forms a ribbon electron beam with a linear focus. Numerical estimations have been made to design the cathode assembly of an industrial gun. It is shown that the most effective way to make approximate estimates of the temperature of the cathode surface in high-voltage glow discharge electron guns for various technological purposes is to use arithmetic-logical ratios for modeling the geometry of the cathode assembly and locus functions for estimating the temperature distribution. The accuracy of such estimates, made using the heat balance equation, was 5–10%, sufficient at the initial stage of designing an electron gun. It is shown that using the SolidWorks CAD software complex for designing high-voltage glow discharge electron guns is effective only for solving the complex engineering design tasks and preparing the corresponding technical documentation. The results of the theoretical research published in the article are of interest to a wide range of specialists engaged in developing electron beam equipment and its implementation in industrial production. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2024.1.08 |
| first_indexed | 2025-07-17T10:28:31Z |
| format | Article |
| fulltext |
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko, 2024
Системні дослідження та інформаційні технології, 2024, № 1 99
TIДC
МАТЕМАТИЧНІ МЕТОДИ, МОДЕЛІ,
ПРОБЛЕМИ І ТЕХНОЛОГІЇ ДОСЛІДЖЕННЯ
СКЛАДНИХ СИСТЕМ
UDC 004.942:537.525
DOI: 10.20535/SRIT.2308-8893.2024.1.08
EVALUATION OF THE THERMAL REGIME OF THE CATHODE
OPERATION OF A HIGH-VOLTAGE GLOW DISCHARGE
ELECTRON GUN, WHICH FORMS A RIBBON ELECTRON BEAM
I.V. MELNYK, S.B. TUHAI, D.V. KOVALCHUK, M.S. SURZHIKOV,
I.S. SHVED, M.Yu. SKRYPKA, O.M. KOVALENKO
Abstract. The article discusses the various methods of estimating the surface cath-
ode temperature of the high-voltage glow discharge electron gun, which forms a rib-
bon electron beam with a linear focus. Numerical estimations have been made to de-
sign the cathode assembly of an industrial gun. It is shown that the most effective
way to make approximate estimates of the temperature of the cathode surface in
high-voltage glow discharge electron guns for various technological purposes is to
use arithmetic-logical ratios for modeling the geometry of the cathode assembly and
locus functions for estimating the temperature distribution. The accuracy of such es-
timates, made using the heat balance equation, was 5–10%, sufficient at the initial
stage of designing an electron gun. It is shown that using the SolidWorks CAD
software complex for designing high-voltage glow discharge electron guns is effec-
tive only for solving the complex engineering design tasks and preparing the corre-
sponding technical documentation. The results of the theoretical research published
in the article are of interest to a wide range of specialists engaged in developing
electron beam equipment and its implementation in industrial production.
Keywords: electron gun, high-voltage glow discharge, CAD-systems, thermody-
namic equation, heat balance equation, arithmetic-logical relation, locus.
INTRODUCTION
Today, high-voltage glow discharge (HVGD) electron guns are widely used in
various branches of industry [1–3]. The main fields of application of such electron
guns are electron-beam welding of thin-walled parts and their assemblies, deposi-
tion of ceramic coatings in an environment of active or inert gases, depending on
the requirements of the technological process, as well as electron-beam cleaning
of refractory metals and ceramic materials for the further use of high-refining ma-
terials in modern production technologies. The main advantages of HVGD elec-
tron guns over traditional electron sources with incandescent cathodes are the fol-
lowing [1–3].
1. Stability and reliability of operation in conditions of low vacuum in the
environment of various gases, in particular inert and active ones.
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 100
2. Simplicity of the design of HVGD electron guns with the possibility of
replacing spent units, in particular the cold cathode of the HVGD.
3. Simplicity of vacuum technological equipment, without the need to ensure
the operation of the electron gun in conditions of high vacuum.
4. Simple control of the power of the electron beam. In general, there are two
ways to provide such control in order to improve the quality of industrial products
that are subject to heat treatment with an electron beam. There are the following:
changing the pressure in the discharge gap [4] or changing the concentration of ions
in the anode plasma due to the lighting of the additional auxiliary discharge [5].
In connection with the physical features of the operation of HVGD electron
guns listed above and the existing advantages of these types of guns over tradi-
tional electron sources with incandescent cathodes as well as over other beam
technologies, including laser ones [2; 3], the main industrial areas of application
of HVGD electron guns in modern electron beam technologies are the following.
1. High-speed electron beam welding of capsules and contacts of modern
electronic devices, in particular cryogenic ones [6; 7].
2. Production of ceramic films for high-quality and durable capacitors with
the aim of creating a new component base of the modern electronic industry [8–11].
3. Production of ceramic films for receiving and transmitting antennas of
modern microwave communication electronic means [8–11].
4. Deposition of heat-resistant and heat-protective coatings in the modern
automotive, aviation, and space industries. For example, advanced modern tech-
nologies are the application of heat-protective coatings on the blades and other
parts of automobile and aircraft engines [12–15].
5. Electron beam refining of refractory metals and ceramic materials in order
to increase their purity and quality [16–20]. For example, in works [17–20], the
features of applying electron-beam remelting technologies to obtain pure poly-
crystalline silicon were considered. The aim of this advanced electron-beam tech-
nology is to improve the manufacturing technology of modern semiconductor
electronics devices, in particular, electronic microcircuits.
6. The modern technologies of three-dimensional printing on the metal’s
substrates [21].
STATEMENT OF THE PROBLEM
One of the features of the HVGD electron gun is a rather low current density from
the metallic surface of the cold cathode, the maximum value of which is about
2
310
m
А
. In connection with this, an advanced direction for the introduction of
HVGD electron guns in modern electron-beam technologies is the formation of
profiled electron beams with a linear and circular focus from a large cathode sur-
face. The main advantage of using such types of HVGD electron guns in modern
electron-beam welding and surface treatment technologies is the extremely high
productivity of the technological process, since the use of profiled electron beams
allows for a short period of time to process the products of a long duration with
complex geometry without the need to provide the additional scanning of the
electron beam on the surface of detail, which is treated [2; 3].
The main advantages of HVGD electron guns, which form profile electron
beams, are the following [2; 3].
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 101
1. A wide range of power, from 10 kW to 600 kW, which allows designing
optimal equipment for a specific technological application.
2. Stability of operation in a wide vacuum range, the partial gas pressure can
be from 10–4 to 10–1 Pa, including in conditions of dynamic pressure changes in
the process chamber.
3. The use of different active and noble gases, as well as mixtures of them, is
also possible.
4. The HVGD electron guns are compact and light in weight.
5. The HVGD electron guns are simple to exploit and repair, and they are
also reliable in operation.
6. The cold cathodes of HVGD electron guns have a significant time of op-
eration without necessary cleaning, up to 100 amps for hours or more.
The construction diagram of the electrode system of the HVGD electron
gun, which forms an electron beam with a linear focus, is shown in Fig. 1. The
main features of the electrode systems of HVGD electron guns, which form elec-
tron beams with a ring and linear focus, as well as methods of evaluating their
geometric design parameters, were
considered in papers [22–24].
In connection with this, the
most important tasks related to the
mathematical model of HVGD elec-
tron sources, from a practical point
of view, are estimates of the thermal
modes of operation of the cold cath-
ode, which form electron beams
with a linear focus. In general, from
the point of view of HVGD physics,
the thermal mode of operation of the
cold cathode significantly affects its
emission properties [1].
Methods of analysis of the self-
aligned electron-ion optics of
HVGD, taking into account the as-
sessment of the position of the
plasma boundary relative to the
cathode, have been studied quite thoroughly and were described in the papers
[1, 25–27]. Generally, anode plasma in HVGD electrode systems is considered
a moving electrode with a given potential that is transparent to electrons. The pe-
culiarities of estimating the position of the plasma boundary in HVGD electrode
systems, which form electron beams with a linear and circular focus, were con-
sidered in a paper [20]. The general theoretical approach to estimating the operat-
ing temperature of the cold cathodes of the HVGD electron guns was considered
in [28].
Another approach to simulation and experimental study of the properties of
powerful and intensive electron beams in vacuum and plasma devices, including
microwave ones, is presented in the papers [29–31]. In the paper [29], the radia-
tion of plasma diodes in the microwave range has been studied experimentally. In
the paper [30] the penetration of an intensive electron beam into an irradiated ob-
4
3
2
1
Fig. 1. Structural diagram of the HVGD electrode
system, which forms an electron beam with
a linear focus: 1 — cathode; 2 — anode; 3 —
electron beam; 4 — product being processed
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 102
ject in dependence on the incidence angle of the electron beam has been studied.
In the paper [31] model of an electron beam for an advanced method of computa-
tional dosimetry for radiation processing has been elaborated and tested.
Therefore, the main goal of this work is to evaluate the thermal modes of operation of
the cold cathode in HVGD electrode systems that form electron beams with a linear focus.
GENERAL THEORETICAL APPROACHES AND THE BASIC EQUATIONS FOR
CALCULATING THE TEMPERATURE DISTRIBUTION ON THE COLD CATHODE
SURFACE OF HIGH-VOLTAGE GLOW DISCHARGE ELECTRON SOURCES
The main conclusion, which is a consequence of the general theory of HVGD, is
that the accelerated electrons in HVGD do not significantly affect the temperature
of the working gas [1]. Accordingly, limitations on the power of HVGD electron
guns can only be associated with ensuring the dissipation of energy on the elec-
trodes. In addition, the maximum power of HVGD electron guns is limited by the
emissive properties of the cold cathode, as well as by contraction of the discharge
and step ionization under conditions of high pressure [1]. The maximum value of
the current density of the secondary ion-electron emission is 103 A/m2. In any
case, in the general theory of the HVGD, it is justified that, according to the rela-
tions for the current-voltage characteristic of the HVGD, the HVGD electron
guns, within the physical conditions of the existence of the discharge under a de-
fined range of the pressure and the accelerating voltage, are operated stably, with-
out unwanted surges of current up to extremely high values [1].
The second conclusion of the general theory of HVGD is that to reduce the
temperature of the electrodes and, accordingly, the effect of their heating on the
discharge parameters, it is desirable to use light gases, for example, hydrogen or
helium, in the powerful electron guns. In addition, it is known that when light
gases are used, the sputtering coefficient of the cathode surface S decreases, and,
accordingly, the operation time of the HVGD electron gun without replacing the
cathode increases [1]. However, the choice of operation gas or gas mixture is al-
ways combined with the task of ensuring a high value of the coefficient of secon-
dary ion-electron emission γg, which allows, under the condition of stable opera-
tion of the cathode, to increase the power of the electron beam that is formed [1–
3]. Another way to reduce the operating temperature of the electrodes’ surfaces is
to increase the gas flow rate. However, the application of this method must be
compatible with the gun current stabilization system, since the gun current de-
pends on the pressure of the operation gas, and, according to the main equation of
vacuum technology, the gas pressure in the HVGD gun directly depends on the
gas flow rate [4]. Usually, in modern electron-beam technological equipment, the
control of the current of the HVGD gun is carried out by changing the gas pres-
sure by automatically adjusting the gas flow into the electron gun [4]. Therefore,
this method of cooling is generally not used in industrial HVGD electron guns.
That is why ensuring the effectiveness of water cooling of the cold cathode
due to the thermal power released on it as a result of bombardment with residual
gas ions is the main technical factor that ensures the stable operation of HVGD
electron guns [28].
Generally, the following four approaches are used to solve applied problems of
thermodynamics [32–35].
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 103
1. A simplified approach based on the transition to a one-dimensional model without
taking edge effects into account and solving the heat balance equation [32; 33]:
b
s
mmt P
dt
dT
mTcP )( ; dl
T
TTS
P
ml
m
clss
t
0 )(λ
)(
, (1)
where mc is the specific heat capacity of the heated material; mλ is the thermal
conductivity of the heated material; sS is the surface area irradiated by the flow
of energetic particles; ml is the thickness of the body being heated; sT is the tem-
perature on the surface of the substance, mm is the mass of the heated material;
clT is the temperature coolant; bP is the power absorbed by the substance; and tP
is the lost power due to thermal conductivity.
Estimates of the surface temperature, which are based on relations (1), are
most accurate for metals that have high thermal conductivity, and, due to this, the
temperature of the surface of the metal, which is heated by a high-energy stream
of charged particles, can be assumed to be the same with great accuracy [28].
Therefore, for the preliminary analysis of the temperature of the emission surface
of the cathode of the HVGD electron guns, the ratio (1) is used. For electrode sys-
tems with direct cooling of the cathode by a coolant, the heat balance equation (1)
is written as follows [28]:
,
22
arcsinα
λλγ+1
γ
2
к
к
22
c
cc
cc
c
ccc
g
g
c
c T
R
R
R
R
R
lRRR
W
T
l
cc vkk 21α , (2)
where cα is the heat transfer coefficient of the liquid through the base of the
cathode; c is the thermal conductivity of the cathode material; cR — the radius
of the cathode emission surface; R — the transversal size of the cathode; cv is
the rate of the cooling liquid, sm /3 , k1 and k2 are the empiric coefficients. For
example, for water, at room temperature and atmospheric pressure, 3501 k and
210002 k [34; 35].
In the case of a complex geometry of the cathode, a mathematical approach
for describing the geometric form of complex three-dimensional objects, based on
the application of arithmetic-logical relations [36] and Rvachov functions [37–39],
or the locus, can be effectively used to find the temperature of its surface using
relations (2). The appropriate software means can be effectively implemented us-
ing the programming tools of the MatLab system of scientific and technical calcu-
lations [40].
2. Analytical solution of the heat conduction equation [32; 33]:
),,()( zyxF
z
T
zy
T
yx
T
x
Tc
t v
, (3)
where yx, , and z are the space coordinates; T is the temperature of medium; is
the thermal conductivity of the substance; is its density by mass; ),,( zyxF —
the density of the thermal sources on the surface boundary.
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 104
Solving the generalized equation of thermal conductivity with partial deriva-
tives (3) is carried out analytically by expanding its solution under given bound-
ary conditions into a functional series. To carry out this operation, consider the
kernel of equation (3), which, in its general form, is written as follows [28; 32; 33]:
,
4
exp
)π2(
1
),(
2
2
ta
x
ta
tx
t
n
t
v
t c
a
ρ
λ2 , (4)
where x is the coordinate, that is under consideration and by which the equation
(3) is solved; t is the time; ta is the coefficient of thermal diffusion; vc is the gas
heat capacity by the volume, and n is the number of the basic function. In the the-
ory of thermal conductivity, it has been proven that the series based on the use of
functions (3) are orthogonal and coincide [41–44]. Generally, the coefficients of
thermodynamic tasks in the functional row (4) must corresponded to partial dif-
ferential equation (3), given above [28; 32; 33]. The general disadvantage of this
approach is the difficulty of automating the formation of functional series using
computer programs [32; 33]. That is, the application of such an approach requires
a large amount of routine work from professional mathematicians and engineers.
On the other hand, the obtained functional series can be analyzed, in particular,
take the derivatives of analytical functions and search for their extrema [41; 42].
This sometimes, to some extent, simplifies the search for optimal engineering so-
lutions regarding the geometry of the cathode assembly details [32; 33].
3. Numerical solution of the heat conduction equation (3). Usually, the right-
hand difference method or the implicit Crank–Nicholson method is used to solve
the complex non-stationary heat-conduction equation (3) [30; 31; 38]. However,
if a stationary thermodynamic problem is considered, the hyperbolic heat conduc-
tion equation (3) is generally reduced to the elliptic Poisson equation [32; 33; 40;
43; 44]. The advantage of numerical methods for solving engineering problems in
thermodynamics is that, if they are correctly set, it is possible to obtain high accu-
racy in modeling the temperature distribution, taking into account all edge effects.
The general disadvantage of this approach is that, in order to obtain optimal de-
signs of thermodynamic systems, it is necessary to analyze a large number of
variants, which is usually associated with huge time costs. Today, even with the
use of advanced computers and network technologies in cloud computing, solving
one variant of an engineering task with the complex spatial geometry of the simu-
lated object can take several hours [36; 39]. Another disadvantage of using this
approach is that the research engineer has only the final results of the provided
calculations, and after those, it is usually extremely difficult to find the optimal
design from the point of view of the laws of thermodynamics. It is much easier to
do this through the analysis of the simple analytical solution of a thermodynamic
problem or the corresponding functional series.
4. Today, with the development of computer systems for engineering design
and modeling, computer modeling methods using built-in computer calculation
systems and engineering systems for automated design (CAD) are often used to
estimate the temperature regimes of the HVGD cold cathode. Such methods of
modeling thermodynamic systems are based on the numerical solution of the heat
conduction equation (3) using the implicit Crank–Nicholson scheme, and calcula-
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 105
tions are performed using the finite element method [40; 43; 44]. When using this
method, the accuracy of calculations for axially symmetric cathode cooling sys-
tems is proportional to the minimum dimensions of the calculation elements of
the finite-difference cells and is estimated by the following ratio [43; 44]:
2
1
2
12
),(),(
zr h
z
zrT
h
r
zrT , (5)
where 1 is the temperature calculation error at nodal points; 2 is the error of
approximation of the temperature dependence between nodes; rh is the discreti-
zation step along the r coordinate, and zh is the discretization step along the z
coordinate.
It is clear from relation (5) that to increase the accuracy of simulation of
HVGD cathode cooling systems, the density of the finite-difference grid should
be increased in regions with a high temperature gradient. Usually, such areas are
the boundaries between elements of the cooling system, which have different val-
ues of thermal conductivity.
The work [28] presented the results of modeling the cooling system of the
cathode unit through the copper base in the case of considering a gap between the
cathode and the base and without such a gap. The simulation was carried out in
the pdetool program of the MatLab system for scientific and technical calcula-
tions [28; 40].
COMPUTER SIMULATION TOOLS OF THE SOLIDWORKS CAD SOFTWARE
The work [28] considered the means of modeling the cooling system of the cath-
ode unit of the powerful HVGD electron gun, implemented in the modern Solid-
Works software complex, in the Flow Simulation program [45; 46]. The advan-
tage of using this software tool in engineering activities is that it is designed
specifically for drawing and has high-quality graphic means for visualizing com-
plex three-dimensional parts, assemblies and structures. In the SolidWorks soft-
ware complex, drawings of individual parts of the cathode assembly are first cre-
ated, and then, through the connection of these parts, an assembly drawing is
performed with the possibility of three-dimensional visualization of the entire
structure [45; 46]. After that, the final version of the drawing of the cathode as-
sembly is uploaded to the Flow Simulation program, where the power of the heat
flow that is applied to the surface of the cathode is set. Manual and automatic set-
tings of the rate of the coolant are also possible. The Flow Simulation software
has its own database on the necessary values of thermodynamic parameters of
metals, ceramics, organic materials, as well as liquids and gases [45; 46], so it is
enough to specify most of the material from which the corresponding part of the
cathode assembly is made, the coolant and, if necessary, the type of operation gas
and its pressure [45; 46]. Basic mechanical, thermodynamic, aerodynamic, and
electrophysical properties of structural materials, given in reference literature [34,
35], already entered into the database of the SolidWorks CAD software [45; 46].
A generalized review of the possibilities of using all the approaches described
above regarding the analysis and optimization of the temperature regime of the
cathode cooling systems of HVGD electron guns was generally carried out in [28].
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 106
PRELIMINARY ESTIMATES OF THE TEMPERATURE OF THE COLD
CATHODE SURFACE OF A HIGH-VOLTAGE GLOW DISCHARGE
ELECTRON GUN, INTENDED FOR THE FORMATION OF A RIBBON
ELECTRON BEAM, USING THE HEAT BALANCE EQUATION,
ARITHMETIC-LOGICAL RELATIONS, AND RVACHOV FUNCTIONS
The structural diagram of the electrode system of the HVGD device, which forms
a ribbon electron beam, is shown in Fig. 2. The device intended for the formation
of a ribbon beam contains a cathode 1, which is fixed on a high-voltage insulator
4, and is located in a capsule 2. The cooling of the cathode surface with water is
carried out directly, cold water enters through tubes that are passed through the
insulator. The length of the rubber hoses used to supply water should be such that
they provide reliable electrical insulation, taking into account the fact that a volt-
age of 15 kV is applied to the cathode.
The capsule of the device, taking into account the near-cathode diaphragm 4
and the base flange 6 with a hole for outputting the electron beam, forms a
discharge chamber in which a high-voltage discharge burns [1–3]. Diaphragm 4,
located near the cathode, ensures the distribution of the electric field necessary for
the formation and focusing of the ribbon electron beam [2; 3].
3
2
1
5
4
6
7
Fig. 2. Structural diagram of the HVGD electrode system designed to form a ribbon
electron beam: 1 — insulator; 2 — capsule; 3 — cathode; 4 — near-cathode diaphragm;
5 — anode; 6 — base flange for mounting the gun on the technological chamber with a
hole for the output of the electron beam; 7 — ribbon electron beam with a linear focus
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 107
The calculation of water cooling of the cathode surface for the HVGD elec-
trode system, whose design scheme is shown in Fig. 2, was carried out taking into
account the geometric features of the cathode assembly. Fig. 3 shows the
construction of the cathode assembly used and the corresponding geometric
parameters of the cathode. Therefore, the boundary conditions for solving
thermodynamic task are presented in Fig. 4.
Analytical relation (2) has been used to estimate the temperature of the sur-
face of the HVGD cold cathode, and the geometry of the cathode assembly was
described using arithmetic and logical functions [36]. Under such conditions, the
arithmetic-logical relationship that was used to calculate the temperature of the
cold cathode of the HVGD device, which forms a ribbon electron beam with
a linear focus, has the following form:
Fig. 3. Geometrical parameters of the cathode of the HVGD electrode system, the struc-
tural scheme of which is shown in Fig. 2: Rc is the radius of the cylindrical emission surface
from which the flow of electrons is formed; R is the cathode radius as a structural element; lс is the
thickness of cathode; lez is the wideness of the cathode emission zone; hez is the longitude
length of the cathode emission zone; and Rr is the radius of cathode rounding
hez
R
Rr
hez – Rr
x
y
R – hez
z
Rc
R
lez
lc x
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 108
,
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25
cl
gcc
cgc
ez T
R
lW
hyC 54321),( CCCCCyxTc ,
where ),( yxTc is temperature distribution function on the cathode surface by x
and y coordinates; cα is the heat transfer coefficient of the coolant liquid
through the base of the cathode according to the second ratio of equations set (2).
Insulator
Coolant
C
a
th
o
d
e
Coolant
Electron
Beam
Region of Discharge
Lighting
Anode
H
e
at
F
lo
w
Fig. 4. The boundary conditions for calculation the heat regime of electrodes system
of high voltage glow discharge electron gun
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 109
Calculations using relations (6) were carried out using logical and matrix
programming tools of the MatLab -system of scientific and technical calculations
for the following parameters of the cathode assembly: 10clT С, 51cW kW,
3γ g , 05.0cR m, 03.0R m, 012.0rR m, 005.0cl m, 012.0ezl m,
026.0ezh m, 03.0cv m3/s, 3501 k k and 210002 k .
The simulation results obtained using arithmeticlogical relations (6) are
shown in Fig. 5.
y,
m
x,m a
x,m b
y,
m
y,
m
x,m c
Fig. 5. Contour graphs of the temperature distribution on the cold cathode surface Тc(x, y),
obtained using arithmetic-logic relation (6): a — 1cW kW; b — 5cW kW; c — 7cW kW
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 110
From the graphic dependences obtained using arithmetic-logic relations (6)
and shown in Fig. 5, it can be seen that the preliminary, generalized estimates
based on the use of the heat balance equation indicate that in the range of power
released at the cathode, within the range of 71cW kW, the surface tempera-
ture of the water-cooled aluminum cathode does not exceed 60°С. Such a tem-
perature mode of operation is normal for the cold cathode of technological elec-
tron sources, based on HVGD [1–3].
Another, more accurate approach to describing the geometry of complex
three-dimensional objects is the use of Rvachev functions, or locus [37–39]. The
essence of this approach is that instead of the logical ratios used in the analytical
expression (6), atomic functions or locus are used. Locus is smooth functions with
a high value of the derivative. Therefore, with their help, a jump-like coordinate
difference is approximated for the surface being modulated. Locus functions are
formed on the basis of arithmetic-logical relations. This approach makes it
possible to effectively use locus for solving problems of electrophysics and
thermodynamics in real devices with complex electrode geometry [37–39].
Analytical expressions for locus functions are given in Table 1 [35–37].
T a b l e 1 . Rvachov R -functions R , or locus
The accompanying
logical function of
the Boolean algebra
Set of functions R
21211 ),( xxxxF
21
2
2
2
1212α1211 α2
α1
1
),( xxxxxxxxxxy
21212 ),( xxxxF
21
2
2
2
1212α1212 α2
α1
1
),( xxxxxxxxxxy
113 )( xxF 1113 )( xxxy
The coefficient α in the ratios given in Table 1 is selected in the range [0; 1],
depending on the formulation of the modeling task.
Let's rewrite the logical expressions of the arithmetic-logical functions (6) in
terms of the Rvachev R functions defined in Table 1.
);(11 xlL ez );(12 yhL ez
)()(
α1
1
),( 12α1112111 yhxlLLLLR ezez
)()(α2)()( 22 yhxlyhxl ezezezez ;
),(21 ezlxL ),(22 yhL ez )(23 xRL ;
)()(
α1
1
),( езез22α21222121 yhlxLLLLR
)()α(2)()( 22 yhlxyhlx ezezezez ;
)(
α1
1
),( 2123α2123212 xRRLRLRR (7)
)(α2)( 21
22
21 xRRxRR ;
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 111
;)(,,)( 3332
2
ез
2
31 yRhLhyLhyRxL ezezr
)()(
α1
1
),( 22
32α31323131 ezezr hyhyRxLLLLR
;)()(α2)()( 222
2
22
ezezrezezr hyhyRxhyhyRx
))((
α1
1
),( 3133α3133313 yRhRLRLRR ez
;))((α2))(( 31
22
31
yRhRyRhR ezez
;)(,,)( 4342
22
41 yRhLhyLxhyRL ezezezr
)()(
α1
1
),( 22
42α41424141 ezezr hyxhyRLLLLR
;)()(α2)()( 222
2
22
ezezrezezr hyxhyRhyxhyR
))((
α1
1
),( 4143α4143414 yRhRLRLRR ez
;))((α2))(( 41
22
41
yRhRyRhR ezez
;5 ezhyL
.1)(α2))((1)(
α1
1
1)1,( 2
α555 ezezez hyhyhyLLR
Then the sophisticated arithmetic-logical relation (6), taking into account (7),
will be rewritten as follows:
+
2
arcsin)γ+1(α
λ
2
γ
),(
2
22
1
cl
c
ez
gcc
c
ccc
gc
c T
R
Rl
R
RR
W
RyxT
xl
+
2
arcsin)γ+1(λα
)(γ
2
2
cl
c
r
gccc
ezgc T
R
RR
R
lRW
R
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 112
cl
c
r
gccc
ccrgc
T
R
RR
R
xRRRW
R
2
arcsin)γ+1(α
γ
λ2
22
3 (8)
cl
c
r
ezrgcc
cgc T
R
RR
hyRR
lW
R
2
arcsin)()γ+1(λα
γ
2
22
4
.
)γ+1(α
γ
25
cl
gcc
cgc T
R
lW
R
The results of calculating the temperature distribution on the surface of the
cathode using content (8), which have been obtained under the condition α = 0.95,
are shown in Fig. 6.
Fig. 6. Contour graphs of temperature distribution on the surface of the cold cathode Tc(x, y),
obtained using relation (8): а — 1cW kW; b — 3cW kW; с — 5cW kW
y,
m
x,m a
y,
m
x,m b
x,m c
y,
m
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ESTIMATION OF THE SURFACE TEMPERATURE OF THE COLD CATHODE
USING MODELING TOOLS OF THE SOLIDWORKS CAD SOFTWARE
The CAD software system SolidWorks is a well-known and widely used package
that allows one to create 3D models of parts based on drawings or sketches. That
is why this engineering CAD is often used by designers and industrialists. The
system also has the powerful algorithms for calculating loads of various types.
The calculations are based on the physical parameters of materials implemented
in the program, which include almost all widely used metals, alloys, nonmetals,
and liquids. Mechanical loads and deformations, as well as thermal loads can be
simulated. It is also possible in this CAD system to study the aerodynamics or
hydrodynamics of a simulated object in a liquid or gas flow [45; 46].
Today, the creation of an engineering design of any device cannot be done
without the prior use of its simulation tools. High-voltage devices, in case of fail-
ure during testing, pose a significant danger, therefore, it is much more efficient
and safer to make their preliminary modeling and corresponding simple calcula-
tions. Modern systems of automatic design and their corresponding tools allow,
with sufficient accuracy, to simulate the conditions and loads to which a real
model of the device will be subjected. The SolidWorks CAD system has several
internal applications for modeling loads of various types [45; 46].
In the course of the provided engineering researches described in this section
of paper, the application Flow Simulation has been used [45; 46]. This program
allows you to simulate flows of liquids or gases within certain geometric limits,
taking into account the heat exchange between interacting solid-states materials,
liquids, and gases. Since this software is primarily focused on the development of
three-dimensional models, it calculates the physical parameters of materials with
a certain value of error, which does not allow obtaining an absolutely accurate
result. However, usually this accuracy of calculations is sufficient to draw general
conclusions regarding the correctness of testing and applying the system being
researched and designed [45; 46].
To simulate the design of the device in the SolidWorks CAD system, one
need to make an assembly drawing or a necessary detail in the form of a three-
dimensional model. In the provided and described engineering research, an as-
sembly drawing of an electronic device intended for the formation of an electron
beam with a ribbon focus has been made. First of all, one needs to open the as-
sembly drawing file and click on the option Flow Simulation.
In the next step, one needs to create a new project with specification of
physical quantities, materials, and initial conditions for modeling.
Then, by selecting the Calculation Area option, one can select the space
where the object of research is located. Before this, it is necessary to make an axi-
symmetric section of the assembled drawing for better visualization [28; 45; 46].
As noted in Section 4 of the paper, the SolidWorks CAD system has its own
powerful database of mechanical, electrical, and electrophysical properties of
various structural materials. Therefore, the next step in simulation is the selection
of materials from which separate parts of the structure are made. If the necessary
material is not available, it is possible to create a new record in the database and
enter the necessary parameters of the material there [45; 46].
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 114
Having chosen the materials for the parts and assemblies of the device, one
can move on to defining the boundary conditions for the operation of the device
being modeled [45; 46]. The parameters of the model for studying the temperature
mode of operation of the cathode unit of the HVGD electron gun, which forms a
ribbon beam with a linear focus, are given in Table 2.
T a b l e 2 . The parameters of the cathode assembly model of the HVGD elec-
tron gun, which forms an electron beam with a linear focus, created in the
SolidWorks CAD system
Model parameter Value
A model of the heat conduction in a solid body Enabled
Only heat conduction in a solid Disabled
Radiation heat exchange Disabled
Heat exchange in gas by radiation Disabled
Non-stationarity Disabled
Gravitational effects Disabled
Rotation Local Area (Averaging)
The power released at the cathode 2 kW
Type of liquid flow Laminar and turbulent
High-value Mach number flow model Disabled
Cavitation Enabled
Concentration of dissolved gas by mass, kg/m3 10–4
Free surface Disabled
Surface roughness, μm 0.1
Water flow rate in the normal direction to the
cathode surface, m/s
10
Water consumption, m3/s 10–5
Thermal conditions on the outer walls Adiabatic wall
Number of nodes in the finite-elements mesh 5·103
Static pressure, Pa Temperature, °K
Thermodynamic parameters
101325 293.2
Intensity, % Scale (length, m)
Intensity and scale of turbulence
2 1.5·10–4
ANALYSIS OF OBTAINED SIMULATION RESULTS AND PRACTICAL
RECOMMENDATIONS
Fig. 7 shows the results of modeling the thermal modes of operation of the cathode
node of an electronic device that forms a ribbon beam with a linear focus, ob-
tained using the Flow Simulation program in the SolidWorks engineering com-
puter CAD system. The obtained results largely coincide with the results obtained
by numerically solving the heat balance equation and modeling the geometry of
the cathode node by arithmetic-logical relations or locus functions, which are
shown in Fig. 6.
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 115
a
b
c
Fig. 7. The temperature distribution of the cathode assembly Tc (x, y, z), obtained using
modeling tools and the design toolkit of the SolidWorks CAD software
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 116
The results of modeling the temperature regime of the cathode assembly ob-
tained in the provided research generally indicate that a simplified approach to
solving the heat conduction equation (3), connected with the transition to the ana-
lytical solution of the heat balance equation (2), taking into account the real ge-
ometry of the cooling constructive elements of the electronic gun through the use
of arithmetic-logical relations, is quite effective, and the accuracy obtained from
modeling is usually sufficient for preliminary generalized estimates of the thermal
mode of operation of structural units at the initial stage of gun design. The method
of describing the complex geometry of construction details by locus or Rvachev
functions [28; 37–39] is also effective. To calculate the thermal regime of the
cathode assembly, we used relation (2), which is quite universal and was used in
work [28] to calculate the surface temperature of the cathode with direct cooling
in electron guns that form beams with a point focus. The difference of the pro-
posed model lies in the fact that the real geometry of the cathode assembly for the
HVGD electron guns, which forms a ribbon electron beam, was described using
the appropriate arithmetic-logical ratios. It should also be noted that the accuracy
of thermal calculations in the SolidWorks software complex is also low, about
20%. However, an important advantage of this system, from a practical point of
view, is the possibility of numerical calculations for real structures. In this regard,
if the appropriate mathematical apparatus is available, the proposed model of the
cathode node, based on the use of locus, or Rvachev functions [28; 37–39], can be
recommended to designers of electron beam technological equipment for further
practical use. To carry out more accurate estimates of the temperature of the sur-
face of the cathode, taking into account the boundary effects, in work [28] it was
recommended to use the pdetool toolkit of the MatLab system of scientific and
technical calculations, however, working with this program requires certain quali-
fications and knowledge of the appropriate mathematical apparatus from the de-
signers.
The testing experiments in SolidWorks software were realized in the
such range of geometry parameters of cathode item: m, 01.005.0 cR 03.0R
m, 01.0 m, 01.0012.0 rR m, 001.0005.0 cl m. 001.0012.0 ezl By
the power of electron gun regimes, range of 1–150 kW are considered. Pointed
out above error of simulation, corresponding to the obtained experimental results,
have been in the same range. The dependences of focal beam parameters on
geometry of electrodes’ system and technological tolerances have been analyzed
in the papers [22–24].
The scientific results, given in this article, have been obtained in the
Scientific Laboratory of Electron Beam Technological Devices of National
Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnical Institute”
customed by “Chervona Khvyla” Open Joint Stock Company.
These results are of interest to a wide range of specialists who are engaged
in the development and introduction into production of modern electron-beam
technological equipment.
CONCLUSION
The paper considers various theoretical approaches to estimating the operating
temperature of the surface of the cold cathode of the HVGD electron gun, which
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 117
forms a ribbon-like converging electron beam with a linear focus. Based on the
test calculations that have been performed, it is shown that the accuracy of esti-
mates using ratio (2), obtained as a solution of the system of heat balance equa-
tions (1), is quite high. For the considered models of HVGD electron guns, the
calculated surface temperature of the cathode, in the case of using Rvachev arith-
metic-logical relations and functions (8) to describe the geometry of the cathode
assembly, is about 5–10% and is close to the estimated results obtained using the
SolidWorks software complex. To carry out more accurate estimates, taking into
account edge effects and the influence of the temperature of the peripheral region
of the cathode on the emission of electrons from its surface, you can use either
estimates through functional series using relation (4) or the pdetool toolkit of the
MatLab scientific and technical calculations system. The method of using ratio
(4) to estimate the surface temperature of the cathode of the HVGD electron gun,
which forms a beam with a point focus, as well as the corresponding mathemati-
cal approaches for the use of special functions, were considered and analyzed in
work [28]. Such evaluations can be interesting and useful for developers of new
types of HVGD electron guns with improved emission characteristics. To carry
out such calculations, a sufficiently high qualification of development engineers
with appropriate knowledge of mathematical functions and corresponded software
is required. In the case of preliminary evaluations, without taking into account the
influence of the temperature of the peripheral region of the cathode surface on its
emission characteristics, calculations using arithmetic-logical relations and Rva-
chev functions similar to relations (8) are sufficient. To carry out such assess-
ments, it is also necessary to develop suitable mathematical approaches and ap-
propriate modifications of the software, since each design of the HVGD electron
guns for technological purposes has its own specific features [2; 3].
Main recommendations to engineers, who designed HVGD electron guns,
have been obtained as a results of scientific research, are as follows.
1. For electron guns with the power range of 1–5 kW using of cathode item
without cooling for simplifying the gun construction is possible.
2. For electron guns with the power range of 5–30 kW using of cooling cath-
ode through cooper base for simplifying the gun construction is possible.
3. For electron guns with the power, grater, then 30 kW, the direct cooling of
the cathode surface with coolant is necessary. The scheme of corresponded gun
construction is given in Fig. 2, and the geometrical parameters are noted at Fig. 3.
The temperature of cathode emission surface for the cathode from aluminum has
to be in range 150–200 °C [2; 28].
The theoretical assumptions presented in the article are of great practical im-
portance regarding the creation of new types of structures for HVGD electron
guns and their industrial application. The results presented in the article may be
interesting and useful for a wide range of specialists who are engaged in the de-
velopment of modern electron-beam equipment and its application in industry.
REFERENCE
1. I. Melnyk, S. Tuhai, and A. Pochynok, “Universal Complex Model for Estimation
the Beam Current Density of High Voltage Glow Discharge Electron Guns,” Lecture
Notes in Networks and Systems; Eds: M. Ilchenko, L. Uryvsky, and L. Globa, 152,
pp. 319–341, 2021. Available: https://www.springer.com/gp/book/ 9783030583583
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 118
2. S. Denbnovetsky et al., “Principles of operation of high voltage glow discharge electron guns
and particularities of its technological application,” Proceedings of SPIE, The International
Society of Optical Engineering, pp. 10445–10455, 2017. Available:
https://spie.org/Publications/Proceedings/Paper/10.1117/12.2280736
3. S.V. Denbnovetsky, V.G. Melnyk, and I.V. Melnyk, “High voltage glow discharge
electron sources and possibilities of its application in industry for realizing of differ-
ent technological operations,” IEEE Transactions on plasma science, vol. 31, no. 5,
pp. 987–993, October, 2003. Available: https://ieeexplore.ieee.org/document/1240048
4. S.V. Denbnovetsky, V.I. Melnyk, I.V. Melnyk, and B.A. Tugay, “Model of control of
glow discharge electron gun current for microelectronics production applications,”
Proceedings of SPIE. Sixth International Conference on “Material Science and Mate-
rial Properties for Infrared Optoelectronics”, vol. 5065, pp. 64–76, 2003. doi:
10.1117/12.502174.
5. I.V. Melnyk and S.B. Tugay, “Analytical calculations of anode plasma position in
high-voltage discharge range in case of auxiliary discharge firing,” Radioelectronic
and Communication Systems, vol. 55, no. 11, pp. 50–59, 2012. Available:
http://radio.kpi.ua/article/view/S0021347012110064
6. A.A. Druzhinin, I.P. Ostrovskii, Y.N. Khoverko, N.S. Liakh-Kaguy, and A.M. Vuyt-
syk, “Low temperature characteristics of germanium whiskers,” Functional materials, 21
(2), pp. 130–136, 2014. Available: https://nanoscalereslett.springeropen.com/ arti-
cles/10.1186/s11671-017-1923-1
7. A.A. Druzhinin, I.A. Bolshakova, I.P. Ostrovskii, Y.N. Khoverko, and N.S. Liakh-
Kaguy, “Low temperature magnetoresistance of InSb whiskers,” Materials Science
in Semiconductor Processing, 40, pp. 550–555, 2015. Available: https://academic-
accelerator.com/search?Journal=Druzhinin
8. A. Zakharov, S. Rozenko, S. Litvintsev, and M. Ilchenko, “Trisection Bandpass Fil-
ter with Mixed Cross-Coupling and Different Paths for Signal Propagation,” IEEE
Microwave Wireless Components Letters, vol. 30, no. 1, pp. 12–15, 2020.
9. A. Zakharov, S. Litvintsev, and M. Ilchenko, “Trisection Bandpass Filters with All
Mixed Couplings,” IEEE Microwave Wireless Components Letters, vol. 29, no. 9,
pp. 592–594, 2019. Available: https://ieeexplore.ieee.org/abstract/document/8782802
10. A. Zakharov, S. Rozenko, and M. Ilchenko, “Varactor-tuned microstrip bandpass
filter with loop hairpin and combline resonators,” IEEE Transactions on Circuits
Systems, II, Exp. Briefs, vol. 66, no. 6, pp. 953–957, 2019. Available:
https://ieeexplore.ieee.org/document/8477112
11. A. Zakharov, S. Litvintsev, and M. Ilchenko, “Transmission Line Tunable Resona-
tors with Intersecting Resonance Regions,” IEEE Transactions on Circuits Systems
II, Exp. Briefs, vol. 67, no. 4, pp. 660–664, 2020.
12. T.O. Prikhna et al., “Electron-Beam and Plasma Oxidation-Resistant and Thermal-
Barrier Coatings Deposited on Turbine Blades Using Cast and Powder
Ni(Co)CrALY(Si) Alloys I. Fundamentals of the Production Technology, Structure,
and Phase Composition of Cast NiCrAlY Alloys,” Powder Metallurgy and Metal Ce-
ramics, 61(1-2), pp. 70–76, 2022. Available: https://www.springer.com/journal/11106
13. T.O. Prikhna et al., “Electron-Beam and Plasma Oxidation-Resistant and Thermal-
Barrier Coatings Deposited on Turbine Blades Using Cast and Powder
Ni(Co)CrAlY(Si) Alloys Produced by Electron-Beam Melting II. Structure and
Chemical and Phase Composition of Cast CoCrAlY Alloys,” Powder Metallurgy
and Metal Ceramicsthis, 61(3-4), pp. 230–237, 2022.
14. I.M. Grechanyuk et al., “Electron-Beam and Plasma Oxidation-Resistant and Ther-
mal-Barrier Coatings Deposited on Turbine Blades Using Cast and Powder
Ni(Co)CrAlY(Si) Alloys Produced by Electron Beam Melting IV. Chemical and
Phase Composition and Structure of Cocralysi Powder Alloys and Their Use,” Pow-
der Metallurgy and Metal Ceramics, 61(7-8), pp. 459–464, 2022.
15. M.I. Grechanyuk et al., “Electron-Beam and Plasma Oxidation-Resistant and Ther-
mal-Barrier Coatings Deposited on Turbine Blades Using Cast and Powder Ni
Evaluation of the thermal regime of the cathode operation of a high-voltage glow …
Системні дослідження та інформаційні технології, 2024, № 1 119
(Co)CrAlY (Si) Alloys Produced by Electron Beam Melting III. Formation, Struc-
ture, and Chemical and Phase Composition of Thermal-Barrier Ni(Co)CrAlY/ZrO2–
Y2O3 Coatings Produced by Physical Vapor Deposition in One Process Cycle,”
Powder Metallurgy and Metal Ceramics, 61(5-6), pp. 328–336, 2022.
16. V. Vassilieva, K. Vutova, and V. Donchev, “Recycling of alloy steel by electron beam
melting,” Electrotechnics and Electronics (E+E), vol. 47, no. 5–6, pp. 142–145,
2012.
17. H. Sasaki, Y. Kobashi, T. Nagai, and M. Maeda, “Application of electron beam melting to the
removal of phosphorous form silicon: toward production of solar-grade silicon by metallurgi-
cal process,” Advanced in material science and engineering, vol. 2013, article ID 857196.
Available: https://cyberleninka.org/article/n/299910/viewer
18. T. Kemmotsu, T. Nagai, and M. Maeda, “Removal Rate of Phosphorous form Melting
Silicon,” High Temperature Materials and Processes, vol. 30, no. 1–2, pp. 17–22,
2011. Available: https://www.degruyter.com/journal/key/htmp/30/1-2/html
19. J.C.S. Pires, A.F.B. Barga, and P.R. May, “The purification of metallurgically grade
silicon by electron beam melting,” Journal of Materials Processing Technology, vol.
169, no. 1, pp. 347–355, 2005. Available: https://www.academia.edu/9442020/
The_purification_of_metallurgical_grade_silicon_by_electron_beam_melting
20. D. Luo, N. Liu, Y. Lu, G. Zhang, and T. Li, “Removal of impurities from metallur-
gically grade silicon by electron beam melting,” Journal of Semiconductors, vol. 32,
no. 3, Article ID 033003, 2011. Available: http://www.jos.ac.cn/en/article/
doi/10.1088/1674-4926/32/3/033003
21. A.E. Davis et all., “Tailoring equiaxed β-grain structures in Ti-6Al-4V coaxial elec-
tron beam wire additive manufacturing,” Materialia, vol. 20, December 2021, 101202.
Available: https://www.sciencedirect.com/science/article/abs/pii/S2589152921002052
22. I.V. Melnik, “Simulation of geometry of high voltage glow discharge electrodes’
systems, formed profile electron beams,” Proceedings of SPIE (2006), Volume 6278,
Seventh Seminar on Problems of Theoretical and applied Electron and Ion Optics,
pp. 627809-1–627809-13. Available: https://www.spiedigitallibrary.org/conference-
proceedings-of-spie/6278/627809/Simulation-of-geometry-of-high-voltage-glow-
discharge-electrodes-systems/10.1117/12.693202.short
23. I.V. Melnyk and A.V. Pochynok, “Modeling of electron sources for high voltage
glow discharge forming profiled electron beams,” Radioelectronic and Commu-
nication Systems, vol. 62, no. 6 (684), pp. 311–323, 2019. Available:
http://radioelektronika.org/issue/view/2019-06
24. I. Melnyk, V. Melnyk, B. Tugai, S. Tuhai, N. Mieshkova, and A. Pochynok, “Sim-
plified Universal Analytical Model for Defining of Plasma Boundary Position in the
Glow Discharge Electron Guns for Forming Conic Hollow Electron Beam,” 2019
IEEE 39th International Conference on Electronics and Nanotechnology
(ELNANO). Conference proceedings. April 16-18, 2019, Kyiv, Ukraine, pp. 548–
552. Available: https://ieeexplore.ieee.org/xpl/conhome/8767103/proceeding?isnum-
ber=8783212&refinementName=Author&refinements=Author:I.V.%20Melnyk
25. J.I. Etcheverry, N. Mingolo, J.J. Rocca, and O.E. Martınez, “A Simple Model of a
Glow Discharge Electron Beam for Materials Processing,” IEEE Transactions on
Plasma Science, vol. 25, no. 3, pp. 427–432, 1997.
26. I.V. Melnyk, “Numerical simulation of distribution of electric field and particle tra-
jectories in electron sources based on high-voltage glow discharge,” Radioelectronic
and Communication Systems, vol. 48, no. 6, pp. 61–71, 2005. Available:
http://radioelektronika.org/article/view/S0735272705060087
27. S.V. Denbnovetsky, J. Felba, V.I. Melnik, and I.V. Melnik, “Model of Beam Forma-
tion in A Glow Discharge Electron Gun With a Cold Cathode,” Applied Surface Sci-
ence, 111, pp. 288–294, 1997. Available: https://www.sciencedirect.com/science/ ar-
ticle/pii/S0169433296007611?via%3Dihub
28. I. Melnyk, S. Tuhai, M. Surzhykov, I. Shved, V. Melnyk, and D. Kovalchuk, “Dif-
ferent Approaches for Analytic and Numerical Estimation of Operation Temperature
I.V. Melnyk, S.B. Tuhai, D.V. Kovalchuk, M.S. Surzhikov, I.S. Shved, M.Yu. Skrypka, O.M. Kovalenko
ISSN 1681–6048 System Research & Information Technologies, 2024, № 1 120
of Cooled Cathode Surface in High Voltage Glow Discharge Electron Guns,” in Il-
chenko M., Uryvsky L., Globa L.: editors. Progress in Advanced Information and
Communication Technology and Systems. MCiT 2021. Lecture Notes in orks and
Systems, vol. 548. Springer, 2023, Cham, pp. 575–595. Available:
https://link.springer.com/book/10.1007/978-3-031-16368-5;
29. A.F. Tseluyko, V.T. Lazurik, D.L. Ryabchikov, V.I. Maslov, and I.N. Sereda,
“Experimental study of radiation in the wavelength range 12.2-15.8 nm from a
pulsed high-current plasma diode,” Plasma Physics Reports, 34(11), pp. 963–968,
2008. Available: https://link.springer.com/article/10.1134/S1063780X0811010X
30. V.G. Rudychev, V.T. Lazurik, and Y.V. Rudychev, “Influence of the electron beams
incidence angles on the depth-dose distribution of the irradiated object,” Radiation
Physics and Chemistry, 186, 109527, 2021. Available: https://www.sciencedirect.
com/science/article/abs/pii/S0969806X21001778
31. V.M. Lazurik, V.T. Lazurik, G.Popov, and Z. Zimek, “Two-parametric model of
electron beam in computational dosimetry for radiation processing,” Radiation Phys-
ics and Chemistry, 124, pp. 230–234, 2016. Available: https://www.sciencedirect.
com/science/article/abs/pii/S0969806X1530133X
32. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, and David
P. DeWitt, Fundamentals of Heat and Mass Transfer; 8th Edition. Wiley, 2020,
992 p. Available: https://www.amazon.com/Fundamentals-Heat-Transfer-Theodore-
Bergman/dp/1119722489/ref=zg_bs_14587_sccl_6/144-8112897-9282521?psc=1
33. P. Atkins, The Laws of Thermodynamics: A Very Short Introduction. Oxford Univer-
sity Press, 2010, 103 р.
34. H. Kuchling, Taschenbuch der Physik (in German); 21 Edition. Hanser Verlag, 2014.
35. W. Espe, Materials of High Vacuum Technology. Pergamon Press, 1966.
36. I. Melnyk and A. Luntovskyy, “Estimation of Energy Efficiency and Quality of Ser-
vice in Cloud Realizations of Parallel Computing Algorithms for IBN,” Future In-
tent-Based Networking. On the QoS Robust and Energy Efficient Heterogeneous Soft-
ware Defined Networks. Lecture Notes in Electrical Engineering, vol. 831, pp. 339–379.
Springer, 2022. Available: https://link.springer.com/chapter/10.1007/978-3-030-
92435-5_20
37. E. Wolf, Practical Guide to Continuous Delivery. Addison-Wesley Professional,
2017, 288 p.
38. J.F. Epperson, An Introduction to Numerical Methods and Analysis; Revised Edition.
Wiley-Interscience, 2007, 590 p.
39. I. Melnyk and A. Luntovskyy, “Networked Simulation with Compact Visualization
of Complex Graphics and Interpolation Results,” in Klymash M., Luntovskyy A.,
Beshley M., Melnyk I., Schill A. (Editors) Emerging Networking in the Digital
Transformation Age. TCSET 2022. Lecture Notes in Electrical Engineering, vol.
965, pp. 175–196. Springer, Cham. Available: https://doi.org/10.1007/978-3-031-
24963-1_10
40. J.H. Mathews and K.D. Fink, Numerical Methods. Using MATLAB. Amazon, 1998.
Available: https://www.amazon.com/Numerical-Methods-Engineers-Steven-Chapra/
dp/007339792X
41. Handbook on Mathematical Functions with Formulas, Graphs and Mathematical
Tables. Edited by Milton Abramovich and Irene Stegun, National Bureau of Stan-
dards, Applied Mathmatic Series, 55, Washington, 1964, 1046 p.
42. I.N. Bronshtein, K.A. Semendyayev, G. Musiol, and H. Mühlig, Handbook of Mathemat-
ics; 5th Edition. Springer, 2007, 1164 p.
43. M.K. Jain, S.R.K. Iengar, and R.K. Jain, Numerical Methods for Scientific & Engi-
neering Computation. New Age International Pvt. Ltd., 2010, 733 p. Available:
https://www.google.com.ua/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2a
hUKEwippcuT7rX8AhUhlYsKHRfBCG0QFnoE-
CEsQAQ&url=https%3A%2F%2Fwww.researchgate.net%2Fprofile%2FAbiodun_O
panuga%2Fpost%2Fhow_can_solve_a_non_linear_PDE_using_numerical_method
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%25401444899200343%2Fdownload%2FNumerical%2BMethods.pdf&usg=AOvV
aw0MjNl3K877lVWUWw-FPwmV
44. S.C. Chapra and R.P. Canale, Numerical Methods for Engineers; 7th Edition.
McGraw Hill, 2014, 992 p.
45. K.H. Chang, Machining Simulation Using Solidworks CAM 2021.
46. P.J. Schilling and R.H. Shih, Parametric Modeling with Solidworks 2021.
Received 01.06.2023
INFORMATION ON THE ARTICLE
Igor V. Melnyk, ORCID: 0000-0003-0220-0615, National Technical University of Ukraine
“Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: imelnik@phbme.kpi.ua
Serhii B. Tuhai, ORCID: 0000-0001-7646-1979, National Technical University of
Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: sbtuhai@gmail.com
Dmytro V. Kovalchuk, ORCID: 0000-0001-9016-097X, the enterprise “Chervona
Khvyla” Open Joint Stock Company, e-mail: dv_kovalchuk@yahoo.com
Mykola S. Surzhykov, National Technical University of Ukraine “Igor Sikorsky Kyiv
Polytechnic Institute”, Ukraine, e-mail: nikolajsurzikov@gmail.com
Iryna S. Shved, ORCID: 0009-0008-6603-586X, National Technical University of
Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: shvettd@gmail.com
Mykhailo Yu. Skrypka, ORCID: 0009-0006-7142-5569, National Technical University
of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: scien-
tetik@gmail.com
Oleksandr M. Kovalenko, National Technical University of Ukraine “Igor Sikorsky
Kyiv Polytechnic Institute”, Ukraine, e-mail: sashakovalenko51640@gmail.com
ОЦІНЮВАННЯ ТЕПЛОВОГО РЕЖИМУ РОБОТИ КАТОДА ЕЛЕКТРОННИХ
ГАРМАТ ВИСОКОВОЛЬТНОГО ТЛІЮЧОГО РОЗРЯДУ, ЯКІ ФОРМУЮТЬ
СТРІЧКОВИЙ ЕЛЕКТРОННИЙ ПУЧОК / І.В. Мельник, С.Б. Тугай, Д.В. Ковальчук,
М.С. Суржиков, І.С. Швед, М.Ю. Скрипка, О.М. Коваленко
Анотація. Розглянуто різні способи оцінювання температури поверхні катода
електронної гармати високовольтного тліючого розряду (ВТР), яка формує
стрічковий електронний пучок з лінійним фокусом. Оцінювання виконано для
конструкції катодного вузла гармати промислового призначення. Показано, що
найбільш ефективним для проведення наближених оцінок температури повер-
хні катода в гарматах ВТР різного технологічного призначення є використання
арифметико-логічних співвідношень для моделювання геометрії катодного ву-
зла та локусів для оцінювання розподілу темпеsратури. Точність оцінювання,
проведеного з використанням рівняння теплового балансу, складала 5–10%,
що є достатнім на початковому етапі проектування електронної гармати. Пока-
зано, що використання для проектування електронних гармат ВТР програмно-
го комплексу CAD SolidWorks є ефективним лише для вирішення завдань
комплексного інженерного проектування гармат ВТР та оформлення відповід-
ної технічної документації. Результати теоретичних досліджень є цікавими
для широкого кола фахівців, які займаються розробленням електронно-
променевого обладнання та його впровадженням у промислове виробництво.
Ключові слова: електронна гармата, високовольтний тліючий розряд, автома-
тизоване проектування, рівняння теплопровідності, рівняння теплового балан-
су, арифметико-логічне співвідношення, функції Рвачова.
|
| id | journaliasakpiua-article-304504 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:28:31Z |
| publishDate | 2024 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/44/cbe11aa253fd98f6afce8431b920e244.pdf |
| spelling | journaliasakpiua-article-3045042024-05-23T07:09:36Z Evaluation of the thermal regime of the cathode operation of a high-voltage glow discharge electron gun, which forms a ribbon electron beam Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок Melnyk, Igor Tuhai, Serhii Kovalchuk, Dmytro Surzhykov, Mykola Shved, Iryna Skrypka, Mykhailo Kovalenko, Oleksandr electron gun high-voltage glow discharge CAD-systems thermodynamic equation heat balance equation arithmetic-logical relation locus електронна гармата високовольтний тліючий розряд автоматизоване проектування рівняння теплопровідності рівняння теплового балансу арифметико-логічне співвідношення функції Рвачова The article discusses the various methods of estimating the surface cathode temperature of the high-voltage glow discharge electron gun, which forms a ribbon electron beam with a linear focus. Numerical estimations have been made to design the cathode assembly of an industrial gun. It is shown that the most effective way to make approximate estimates of the temperature of the cathode surface in high-voltage glow discharge electron guns for various technological purposes is to use arithmetic-logical ratios for modeling the geometry of the cathode assembly and locus functions for estimating the temperature distribution. The accuracy of such estimates, made using the heat balance equation, was 5–10%, sufficient at the initial stage of designing an electron gun. It is shown that using the SolidWorks CAD software complex for designing high-voltage glow discharge electron guns is effective only for solving the complex engineering design tasks and preparing the corresponding technical documentation. The results of the theoretical research published in the article are of interest to a wide range of specialists engaged in developing electron beam equipment and its implementation in industrial production. Розглянуто різні способи оцінювання температури поверхні катода електронної гармати високовольтного тліючого розряду (ВТР), яка формує стрічковий електронний пучок з лінійним фокусом. Оцінювання виконано для конструкції катодного вузла гармати промислового призначення. Показано, що найбільш ефективним для проведення наближених оцінок температури поверхні катода в гарматах ВТР різного технологічного призначення є використання арифметико-логічних співвідношень для моделювання геометрії катодного вузла та локусів для оцінювання розподілу темпеsратури. Точність оцінювання, проведеного з використанням рівняння теплового балансу, складала 5–10%, що є достатнім на початковому етапі проектування електронної гармати. Показано, що використання для проектування електронних гармат ВТР програмного комплексу CAD SolidWorks є ефективним лише для вирішення завдань комплексного інженерного проектування гармат ВТР та оформлення відповідної технічної документації. Результати теоретичних досліджень є цікавими для широкого кола фахівців, які займаються розробленням електронно-променевого обладнання та його впровадженням у промислове виробництво. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2024-03-29 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/304504 10.20535/SRIT.2308-8893.2024.1.08 System research and information technologies; No. 1 (2024); 99-121 Системные исследования и информационные технологии; № 1 (2024); 99-121 Системні дослідження та інформаційні технології; № 1 (2024); 99-121 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/304504/296374 |
| spellingShingle | електронна гармата високовольтний тліючий розряд автоматизоване проектування рівняння теплопровідності рівняння теплового балансу арифметико-логічне співвідношення функції Рвачова Melnyk, Igor Tuhai, Serhii Kovalchuk, Dmytro Surzhykov, Mykola Shved, Iryna Skrypka, Mykhailo Kovalenko, Oleksandr Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| title | Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| title_alt | Evaluation of the thermal regime of the cathode operation of a high-voltage glow discharge electron gun, which forms a ribbon electron beam |
| title_full | Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| title_fullStr | Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| title_full_unstemmed | Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| title_short | Оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| title_sort | оцінювання теплового режиму роботи катода електронних гармат високовольтного тліючого розряду, які формують стрічковий електронний пучок |
| topic | електронна гармата високовольтний тліючий розряд автоматизоване проектування рівняння теплопровідності рівняння теплового балансу арифметико-логічне співвідношення функції Рвачова |
| topic_facet | electron gun high-voltage glow discharge CAD-systems thermodynamic equation heat balance equation arithmetic-logical relation locus електронна гармата високовольтний тліючий розряд автоматизоване проектування рівняння теплопровідності рівняння теплового балансу арифметико-логічне співвідношення функції Рвачова |
| url | https://journal.iasa.kpi.ua/article/view/304504 |
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