Positively charged microparticles in plasma
The processes of recharging and changing the temperature of a positively charged microparticle (MP) introduced into plasma are considered. It is assumed that the MP is charged to a positive charge outside the plasma, and then enters the plasma due to the accelerating field. For various values of pla...
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Chibisov, D.V. Chibisov, O.D. Zhernovnykova, O.A. Deynychenko, G.V. Masych, V.V. 2023-12-08T14:44:17Z 2023-12-08T14:44:17Z 2023 Positively charged microparticles in plasma / D.V. Chibisov, O.D. Chibisov, O.A. Zhernovnykova, G.V. Deynychenko, V.V. Masych // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 17-20. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.40.Hf DOI: https://doi.org/10.46813/2023-143-017 https://nasplib.isofts.kiev.ua/handle/123456789/195959 The processes of recharging and changing the temperature of a positively charged microparticle (MP) introduced into plasma are considered. It is assumed that the MP is charged to a positive charge outside the plasma, and then enters the plasma due to the accelerating field. For various values of plasma density and temperature, a numerical solution of the energy and current balance equations of a MP is obtained. The equation that determines the evapora-tion of particles is solved numerically. The time dependence of the radius of a MP during evaporation has been ob-tained. Розглянуто процеси перезарядки та зміни температури позитивно зарядженої мікрочастинки (МЧ), введеної в плазму. Передбачається, що МЧ заряджається до позитивного заряду поза плазмою, а потім потрапляє в плазму в результаті прискорювального поля. Для різних значень густини та температури плазми отримано чисельний розв’язок рівнянь балансу енергії та струму МЧ. Чисельно розв’язано рівняння, яке визначає можливість випаровування таких частинок. Отримано часову залежність радіусу МЧ при випаровуванні. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology Basic plasma physics Positively charged microparticles in plasma Позитивно заряджені мікрочастинки в плазмі Article published earlier |
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Positively charged microparticles in plasma |
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Positively charged microparticles in plasma Chibisov, D.V. Chibisov, O.D. Zhernovnykova, O.A. Deynychenko, G.V. Masych, V.V. Basic plasma physics |
| title_short |
Positively charged microparticles in plasma |
| title_full |
Positively charged microparticles in plasma |
| title_fullStr |
Positively charged microparticles in plasma |
| title_full_unstemmed |
Positively charged microparticles in plasma |
| title_sort |
positively charged microparticles in plasma |
| author |
Chibisov, D.V. Chibisov, O.D. Zhernovnykova, O.A. Deynychenko, G.V. Masych, V.V. |
| author_facet |
Chibisov, D.V. Chibisov, O.D. Zhernovnykova, O.A. Deynychenko, G.V. Masych, V.V. |
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Basic plasma physics |
| topic_facet |
Basic plasma physics |
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2023 |
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English |
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Problems of Atomic Science and Technology |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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| title_alt |
Позитивно заряджені мікрочастинки в плазмі |
| description |
The processes of recharging and changing the temperature of a positively charged microparticle (MP) introduced into plasma are considered. It is assumed that the MP is charged to a positive charge outside the plasma, and then enters the plasma due to the accelerating field. For various values of plasma density and temperature, a numerical solution of the energy and current balance equations of a MP is obtained. The equation that determines the evapora-tion of particles is solved numerically. The time dependence of the radius of a MP during evaporation has been ob-tained.
Розглянуто процеси перезарядки та зміни температури позитивно зарядженої мікрочастинки (МЧ), введеної в плазму. Передбачається, що МЧ заряджається до позитивного заряду поза плазмою, а потім потрапляє в плазму в результаті прискорювального поля. Для різних значень густини та температури плазми отримано чисельний розв’язок рівнянь балансу енергії та струму МЧ. Чисельно розв’язано рівняння, яке визначає можливість випаровування таких частинок. Отримано часову залежність радіусу МЧ при випаровуванні.
|
| issn |
1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/195959 |
| citation_txt |
Positively charged microparticles in plasma / D.V. Chibisov, O.D. Chibisov, O.A. Zhernovnykova, G.V. Deynychenko, V.V. Masych // Problems of Atomic Science and Technology. — 2023. — № 1. — С. 17-20. — Бібліогр.: 7 назв. — англ. |
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2025-11-26T13:43:17Z |
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BASIC PLASMA PHYSICS
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143).
Series: Plasma Physics (29), p. 17-20. 17
https://doi.org/10.46813/2023-143-017
POSITIVELY CHARGED MICROPARTICLES IN PLASMA
D.V. Chibisov1, O.D. Chibisov2, O.A. Zhernovnykova2, G.V. Deynychenko2, V.V. Masych2
1V.N. Karazin Kharkiv National University, Kharkiv, Ukraine;
2H.S. Skovoroda Kharkiv National Pedagogical University, Kharkiv, Ukraine
E-mail: dmitriychibisov@karazin.ua
The processes of recharging and changing the temperature of a positively charged microparticle (MP) introduced
into plasma are considered. It is assumed that the MP is charged to a positive charge outside the plasma, and then
enters the plasma due to the accelerating field. For various values of plasma density and temperature, a numerical
solution of the energy and current balance equations of a MP is obtained. The equation that determines the evapora-
tion of particles is solved numerically. The time dependence of the radius of a MP during evaporation has been ob-
tained.
PACS: 52.40.Hf
INTRODUCTION
The usual way to obtain plasma from a substance
that is in a solid state under normal conditions is to
evaporate it in a crucible, followed by ionization of the
previously created plasma. This method of obtaining
vapors of a substance is not economical, and in some
cases, for example, for a radioactive substance, it is
dangerous. An alternative to this method of obtaining
plasma from a given substance can be the introduction
of MP of a given substance into the previously obtained
plasma, followed by their evaporation and ionization.
Such a scheme, for example, is implemented in devices
for controlled thermonuclear fusion, in which fuel is
introduced in the form of solid hydrogen pellets using a
high-velocity injection system to achieve and maintain
ignited plasma [1, 2]. Once in the plasma, the granules
evaporate, and the resulting gas is ionized.
A similar scheme was proposed for devices with
technological plasma used to create coatings on a sub-
strate and created by a vacuum arc discharge. Here there
is a problem of microdroplets that fly out from the cath-
ode and, falling on the substrate, worsen the properties
of the coatings. To eliminate this problem, it was pro-
posed to evaporate microdroplets with a high-energy
electron beam [3, 4], which is additionally introduced
into the plasma, since the energy of the plasma itself is
not enough to evaporate microdroplets. The created
negative potential of the particles leads to a strong flow
of plasma ions onto them and, as a result, to heating and
evaporation of these MP. This not only eliminates the
problem of interfering microdroplets, but also increases
the flux of neutral atoms and ions onto the substrate due
to their evaporation.
Thus, there are certain achievements in increasing
the plasma density using solid-state or liquid MP that
evaporate and ionize in pre-prepared plasma.
In [5], to obtain plasma of this substance, it was pro-
posed to introduce into the plasma MP charged to a high
positive potential. The high positive potential plays a
dual role. On the one hand, a high potential makes it
possible to introduce MP not mechanically, but electro-
statically, accelerating them in an electric field. On the
other hand, a particle with a high potential leads to a
significant influx of electrons to the MP, heating them.
Thus, an additional source of energy is created, that
contributes to the evaporation of the MP. Interest in
positively charged particles is due to the absence of
thermionic emission during particle heating, as well as
the field emission of electrons. In addition, MP intro-
duced at a given rate, which are then evaporated and
ionized, make it possible to obtain plasma with a given
distribution function, for example, to create a plasma
flow rotating in a magnetic field with axis-encircling
ions, and also to obtain helical ion beams in a magnetic
field without the use of additional methods. To intro-
duce particles with a large positive charge into the
plasma, one can use the method developed in [6, 7].
Here, positively charged particles of micron and submi-
cron sizes are used to simulate the flow of micrometeor-
ites in the laboratory. These particles are accelerated by
high voltages up to 2 MV. The speed and charge of such
particles reach 80 km/s and 107 proton charges, respec-
tively [6, 7].
In this paper, which is a development of [5], the
equations describing the processes of recharge and heat-
ing of MP charged to a significant positive potential are
solved numerically at various values of plasma density,
and temperature, as well as various parameters of MP,
their size and potential. The equation that determines
the conditions for the evaporation of a charged MP due
to the flow of electron energy from the plasma is solved.
The time of evaporation of MP is calculated depending
on the plasma density.
1. HEATING OF MICROPARTICLES
On a MP placed in plasma, flows of plasma ions and
electrons occur. The absorption of plasma ions and elec-
trons is accompanied by the transfer of energy from the
plasma to the MP surface. In addition, due to these
flows, secondary electron emission, as well as with
strong heating of the MF, thermionic emission occurs.
In the case of strongly positively charged MPs, plasma
18 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
ions are scattered in the MP electric field, and the charg-
ing and heating of the MP is determined only by the
flow of accelerated plasma electrons. In the OML ap-
proximation, the electron and energy fluxes on the MP
are described by the system of equations
;
,
=
− =
pl
e mp
pl
e r
I dQ dt
P P mc d T dt
(1)
where Ie
pl = eΓe is the electron current on MP,
Pe
pl = Γe(2kTe+eφa), is the electron power flux on MP,
2
0
| |
8 1 a
e Te
e
e
a n v
kT
= +
, φa is the potential of MP,
n0 is the plasma number density, Pr = σT 4 is the power
flux of thermal radiation from the MP, T is the MP tem-
perature, c is the heat capacity of a substance MP, m is
the mass of MP.
We assume that the value of the initial potential φ0
of MP is sufficiently high, so that the potential energy
of the charged MP significantly exceeds the average
thermal energy of plasma ions and electrons
eφ0 >> Te > Ti.
The system of equations (1) was solved numerically
for a copper MP. The dependences of the temperature of
MP on time were obtained for various values of its ini-
tial potential, as well as for various values of the plasma
density and electron temperature. The initial tempera-
ture of the MP is 300 K, its radius is 1 μm.
Fig. 1 shows the dependences of the temperature of
a copper particle on time for various values of its initial
potential φ0 with a radius of 1 μm.
Fig. 1. The temperature of MP versus time at different
values of φ0: 1 – φ0 = 0; 2 – φ0 = 10kV; 3 – φ0 = 20 kV;
4 – φ0 = 30 kV; n0 = 10 10 cm-3, Te = 50 eV
Curve 1 in Fig. 1 shows the dependence T(t) at
φ0 = 0. The particle temperature begins to increase due
to the plasma electron flow approximately 10-3 s after
the appearance of the particle in plasma and reaches an
equilibrium value due to the equality of the incoming
and outgoing energy flows. Curve 2 shows dependence
T(t) at φ0 = 10 kV. At the first stage, heating occurs due
to the influx of electrons during the recharge of the par-
ticle. A further increase in temperature occurs due to the
flow of thermal electrons. Curves 3 and 4 show this
dependence at φ0 = 20 kV and φ0 = 30 kV, respectively.
At φ0 = 30 kV, the temperature of the particle reaches
the boiling point of the material and after some time
decreases, reaching the equilibrium value. At φ0 = 20 kV
(curve 3), the potential energy of the charged MP turns
out to be insufficient to heat it up to the boiling point.
Note that in all cases the final temperature of the parti-
cle turns out to be equal to the same value, which is
determined by the equality of the incoming and out-
going energy from the particle.
The results of studying the effect of plasma number
density on the MP temperature are shown in Fig. 2.
Fig. 2. The temperature of MP versus time at different
values of n0: 1 – n0 = 109 cm-3; 2 – n0 = 1010 cm-3;
3 – n0 =1011 cm-3; 4 – n0 = 1012 cm-3; Te = 50 eV,
φ0 = 30 kV
For all considered values of number density, the
temperature of the MP reaches the boiling point. It can
be seen that the denser the plasma, the shorter the time
to reach the temperature of boiling, and the longer the
time spent at this temperature. This effect is explained
by a larger flux of plasma electrons on the MP and, as a
result, a larger flux of energy from the plasma. This can
also explain the greater value of the equilibrium temper-
ature at the final stage of the process, which is deter-
mined by the equality of the incoming and outgoing
energy flows.
Fig. 3 shows the dependence T(t) for various elec-
tron temperatures.
Fig. 3. The temperature of MP versus time at different
values of Te: 1 – Te = 10 eV; 2 – Te = 50 eV;
3 – Te = 100 eV; 4 – Te = 200 eV; φ0 = 30 kV
As can be seen from the Fig. 3, the time during
which the MP temperature reaches the boiling point is
somewhat longer for plasma with hot electrons than for
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143) 19
plasma with cold ones. This effect can be explained by
the fact that in the model under consideration, hotter
electrons fly past the particle to a greater extent than
colder ones. The time during which the temperature of
the particle remains equal to the boiling point also does
not differ much. However, the equilibrium temperature
at the final stage for plasma with hotter electrons is
higher, which is explained by a larger energy flux on
particle.
Let us estimate the speed of MP assuming that it is
accelerated by the same potential to which it is charged.
Equating the kinetic energy of the particle and the elec-
trostatic energy of the charged sphere, we obtain
0 03
=v
a
, (2)
where ε0 is the electric constant, is the particle matter
density. For a copper particle with a radius a =1 µm and
an initial potential φ0 = 30 kV we get from (2)
v = 1.6·10 3 m/s, and thus, during the time when the
particle stays in the heated to the boiling point, the par-
ticle moves over a distance of about 2 cm.
2. EVAPORATION OF MICROPARTICLES
The additional energy flow from the plasma onto the
MP surface due to the initial positive charge of the MP
causes heating and vaporization of the MP substance.
The quantity of the evaporated substance that associated
with the initial potential is determined by Δm = ε / Hv,
where ε is the energy related with the initial charge of
the MP, Hv is the heat of vaporization. In the general
case, the MP in plasma evaporates partially, that is, the
spherical shell evaporates, and the final radius of MP is
3
3
3
4
f
v
r a
H
= −
. (3)
Assuming fr (3) to be equal to zero, we obtain a re-
lation for the energy ε (4) and size a of MP, which can
be completely evaporated
34
3
va H = . (4)
In order to find the time of complete evaporation of
the MP we calculate the energy that transferred from the
plasma to the MP taken into account the initial MP
charge. When the MP entered into the plasma the pro-
cess of heating starts immediately, as the heating is be-
ing, the power flux is getting smaller. The vaporization
of the MP is possible when the power influx on the MP
surface greater than power radiated from the MP.
The time interval τv when vaporization of the MP is
possible can be found from the condition of equality
energy flows on the MP surface Pe
pl(τv )−Pr (τv ) = 0:
2
0
4
1
ln
2 4
v
ba T
, (5)
where α = 4πe2n0vTe/Te. We neglect the cooling asso-
ciated with evaporation of the MP substance, since the
energy that has spent on evaporation leads to losses of
the mass and it will be further taken into account.
The energy transferred to the MP in the time interval
τv (5) has been spent on vaporization, can be evaluated
as:
( ) ( )( )
0
v
pl
e r bP t P T dt= − =
2 4 2
0 0
4
2
1 ln .
2 4
b
b
a T
a
T
= − +
(6)
The energy required for the complete evaporation of the
MP radius is determined by (4). Equating this value to
(6), we obtain the condition for the evaporation of the
MP of initial radius a in the case of a positively charged
MP
2 4 2
20 0
4
2 4
1 ln
2 4 3
b
b
T
a H
T
− + =
. (7)
Equation (7) determines the relationship between
characteristic properties of MP substance such as heat of
vaporization, boiling point as well as initial magnitude
of MP potential and its radius. Defined such way rela-
tion between the parameters determines which MP can
be vaporized. The numerical solution of the equation (7)
was performed for copper and tungsten MPs (Fig. 4).
Obtained curves represent critical values of electric po-
tential and MP radius and define regions of the parame-
ters (MP size and its electric potential) where MP can be
vaporized completely and where is not.
Fig. 4. The critical MP radius versus the initial MP
potential: 1 ‒ copper, 2 – tungsten; n0 = 1010 cm-3,
Te = 50 eV, Ti = 1 eV
The MP which sizes and initial electric potential are
in the region of the parameters that is under the curve
can be vaporized completely. This graph shows the en-
ergy possibility of vaporization, but the time needed for
complete vaporization of MPs is differ. For MPs which
parameters are closer to the curve the time needed to
vaporization is greater than for those ones which param-
eters are further from the curve. The MPs from the up-
per region depending on their size and initial potential
can be vaporized partially and their final size is deter-
mined by (3).
The change in the MP radius during evaporation is
governed by the equation
20 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №1(143)
2 2 4
0 4 4rt
b
dr
e T H
dt
− − = . (8)
To study the vaporization process the initial parame-
ters of the MP in (8) was taken close to curve 1 in
Fig. 4. The results of numerical solution of equation (8)
for a copper MP are shown in Fig. 5.
Fig. 5. The radius of MP versus time at different n0:
1 – n0 = 109 cm-3; 2 – n0 = 1010 cm-3;
3 – n0 = 1011 cm-3; 4 – n0 = 1012 cm-3; Te = 50 eV,
Ti = 1 eV; φ0 = 30 kV; a = 0.5 μm
As can be seen from the Fig. 5 the cooper MP with
the radius 0.5 m evaporates completely, moreover, the
denser the plasma, the faster the evaporation. However,
calculations show that MPs with an initial size 1 m
evaporate only partially. This is consistent with the
graph in Fig. 1. Thus we conclude that the introducing
positively charged MP to high enough potential can lead
to it partially or complete vaporization.
CONCLUSIONS
Positively charged to a potential of 30 kV a copper
MP with a size of 1μm, entering the plasma, can be
heated to the boiling point and partially evaporate due to
the energy influx by the plasma electrons during re-
charging, while a particle 0.5 μm in size evaporates
completely.
It is shown that an increase in the plasma density
leads to a decrease in MP recharging time, which leads
to an increase in the residence time of the particle at the
boiling temperature. An increase in the temperature of
plasma electrons does not lead to an increase in the resi-
dence time of MP at the boiling temperature; however,
to enhance the subsequent ionization of the evaporated
substance of the MP, the electron temperature should be
increased.
The speed of a charged particle in plasma is estimat-
ed under the assumption that it is accelerated by the
same potential to which it is charged. It is shown that
the time during which the particle is at the boiling tem-
perature, it moves over a distance of about 2 cm.
The equation relating the initial potential and the
critical radius of MP, when it can be completely evapo-
rated, is derived and solved numerically. Diagram criti-
cal radius – initial potential for copper and tungsten is
drawn (Fig.4).
The equation for changing the MP radius during va-
porization is derived and numerically solved. It is
shown that at an initial MP potential of 30 kV and vari-
ous number densities of plasma, partial evaporation of
particles 1 m in size occurs, while particles 0.5 m in
size evaporate completely.
REFERENCES
1. C.A. Foster, R.J. Colchin, S.L. Milora, et al. Solid
hydrogen pellet injection into the Ormak tokamak //
Nuclear Fusion. 1977, v. 17, p. 1067.
2. M.J. Gouge, St. Onge, S.L. Milora, et al. Pellet fuel-
ing system for ITER // Fusion Engineering and Design.
1992, v. 19, p. 53-72.
3. A.A. Bizyukov, K.N. Sereda, A.D. Chibisov. Charg-
ing processes of metal macroparticles in the low-
temperature plasma at presence of high-energy electron
beam // Problems of Atomic Science and Technology.
Series “Plasma Physics” (17). 2011, № 1, p. 107-109.
4. A.A. Bizyukov, A.D. Chibisov, E.V. Romashchenko,
Yu.E. Kolyada. Decay of liquid metallic macroparticles
in plasma-beam systems due to Rayleigh instability //
Problems of Atomic Science and Technology. Series
“Plasma Physics” (23). 2017, № 1, p. 163-166.
5. A.A. Bizyukov, A.D. Chibisov, D.V. Chibisov,
O.A. Zhernovnykova, T.I. Deуnichenko, N.N. Yunakov.
Positively charged macroparticles in low-temperature
plasma // East European Journal of Physics. 2022, № 1,
p. 110-115.
6. A. Mocker, S. Bugiel, et al. A 2 mV Van de Graaff
accelerator as a tool for planetary and impact physics
research // Rev. Sci. Instrum. 2011, v. 82, p. 095111.
7. J.D. Kerby, R.T. Daly, D.E. Austin. A novel particle
source based on electrospray charging for dust accelera-
tors and its significance for cosmic dust studies // Earth
Planets Space. 2013, v. 65, p. 157-165.
Article received 02.12.2022
ПОЗИТИВНО ЗАРЯДЖЕНІ МІКРОЧАСТИНКИ В ПЛАЗМІ
Д.В. Чібісов, О.Д. Чібісов, О.А. Жерновникова, Г.В. Дейниченко, В.В. Масич
Розглянуто процеси перезарядки та зміни температури позитивно зарядженої мікрочастинки (МЧ), вве-
деної в плазму. Передбачається, що МЧ заряджається до позитивного заряду поза плазмою, а потім потрап-
ляє в плазму в результаті прискорювального поля. Для різних значень густини та температури плазми отри-
мано чисельний розв’язок рівнянь балансу енергії та струму МЧ. Чисельно розв'язано рівняння, яке визначає
можливість випаровування таких частинок. Отримано часову залежність радіусу МЧ при випаровуванні.
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