Effect of electron emission processes on macroparticle charging in plasma systems with electron beam
The effect of different electron emission processes on macropraticle (MP) charging in a plasma at the presence of electron beam is investigated. A complete model of the MP charging in the beam-plasma systems, which includes possible electron emission processes from the MP surface, such as secondary...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Effect of electron emission processes on macroparticle charging in plasma systems with electron beam / E.V. Romashchenko, I.О. Girka, A.A. Bizyukov, A.D. Chibisov //Problems of atomic science and tecnology. — 2020. — № 6. — С. 150-153. — Бібліогр.: 11 назв. — англ. |
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Romashchenko, E.V. Girka, I.О. Bizyukov, A.A. Chibisov, A.D. 2023-11-28T13:42:20Z 2023-11-28T13:42:20Z 2020 Effect of electron emission processes on macroparticle charging in plasma systems with electron beam / E.V. Romashchenko, I.О. Girka, A.A. Bizyukov, A.D. Chibisov //Problems of atomic science and tecnology. — 2020. — № 6. — С. 150-153. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 52.40.Hf https://nasplib.isofts.kiev.ua/handle/123456789/194664 The effect of different electron emission processes on macropraticle (MP) charging in a plasma at the presence of electron beam is investigated. A complete model of the MP charging in the beam-plasma systems, which includes possible electron emission processes from the MP surface, such as secondary electron emission, the thermionic electron emission, the field electron emission and thermal-field electron emission, is presented. Досліджено вплив різних процесів електронної емісії на зарядження макрочастинки (МЧ) у плазмі у присутності електронного пучка. Подано повну модель зарядження МЧ у пучково-плазмових системах, до складу якої входять можливі процеси електронної емісії з поверхні МЧ, такі як вторинна електронелектронна емісія, термоелектронна, автоелектронна та термоавтоелектронна емісії. Исследовано влияние различных процессов электронной эмиссии на зарядку макрочастицы (МЧ) в плазме в присутствии электронного пучка. Представлена полная модель зарядки МЧ в пучково-плазменных системах, которая включает в себя возможные процессы электронной эмиссии с поверхности МЧ, такие как вторичная электрон-электронная эмиссия, термоэлектронная, автоэлектронная, термоавтоэлектронная эмиссии. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies Effect of electron emission processes on macroparticle charging in plasma systems with electron beam Вплив процесів електронної емісії на зарядження макрочастинки у плазмових системах з електронним пучком Влияние процессов електронной емиссии на зарядку макрочастицы в плазменных системах с электронным пучком Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam |
| spellingShingle |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam Romashchenko, E.V. Girka, I.О. Bizyukov, A.A. Chibisov, A.D. Low temperature plasma and plasma technologies |
| title_short |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam |
| title_full |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam |
| title_fullStr |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam |
| title_full_unstemmed |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam |
| title_sort |
effect of electron emission processes on macroparticle charging in plasma systems with electron beam |
| author |
Romashchenko, E.V. Girka, I.О. Bizyukov, A.A. Chibisov, A.D. |
| author_facet |
Romashchenko, E.V. Girka, I.О. Bizyukov, A.A. Chibisov, A.D. |
| topic |
Low temperature plasma and plasma technologies |
| topic_facet |
Low temperature plasma and plasma technologies |
| publishDate |
2020 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Вплив процесів електронної емісії на зарядження макрочастинки у плазмових системах з електронним пучком Влияние процессов електронной емиссии на зарядку макрочастицы в плазменных системах с электронным пучком |
| description |
The effect of different electron emission processes on macropraticle (MP) charging in a plasma at the presence of electron beam is investigated. A complete model of the MP charging in the beam-plasma systems, which includes possible electron emission processes from the MP surface, such as secondary electron emission, the thermionic electron emission, the field electron emission and thermal-field electron emission, is presented.
Досліджено вплив різних процесів електронної емісії на зарядження макрочастинки (МЧ) у плазмі у присутності електронного пучка. Подано повну модель зарядження МЧ у пучково-плазмових системах, до складу якої входять можливі процеси електронної емісії з поверхні МЧ, такі як вторинна електронелектронна емісія, термоелектронна, автоелектронна та термоавтоелектронна емісії.
Исследовано влияние различных процессов электронной эмиссии на зарядку макрочастицы (МЧ) в плазме в присутствии электронного пучка. Представлена полная модель зарядки МЧ в пучково-плазменных системах, которая включает в себя возможные процессы электронной эмиссии с поверхности МЧ, такие как вторичная электрон-электронная эмиссия, термоэлектронная, автоэлектронная, термоавтоэлектронная эмиссии.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/194664 |
| citation_txt |
Effect of electron emission processes on macroparticle charging in plasma systems with electron beam / E.V. Romashchenko, I.О. Girka, A.A. Bizyukov, A.D. Chibisov //Problems of atomic science and tecnology. — 2020. — № 6. — С. 150-153. — Бібліогр.: 11 назв. — англ. |
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| first_indexed |
2025-11-25T08:08:43Z |
| last_indexed |
2025-11-25T08:08:43Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2020. №6(130)
150 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2020, № 6. Series: Plasma Physics (26), p. 150-153.
https://doi.org/10.46813/2020-130-150
EFFECT OF ELECTRON EMISSION PROCESSES
ON MACROPARTICLE CHARGING IN PLASMA SYSTEMS
WITH ELECTRON BEAM
E.V. Romashchenko, I.О. Girka, A.A. Bizyukov, A.D. Chibisov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: ev.romashchenko@gmail.com
The effect of different electron emission processes on macropraticle (MP) charging in a plasma at the presence of
electron beam is investigated. A complete model of the MP charging in the beam-plasma systems, which includes
possible electron emission processes from the MP surface, such as secondary electron emission, the thermionic elec-
tron emission, the field electron emission and thermal-field electron emission, is presented.
PACS: 52.40.Hf
INTRODUCTION
Charging of a MP in beam-plasma systems is one of
the basic problems in studies of interaction between the
MP and the plasma. In the presence of electron beam
there are several electron emission processes from the
MP surface. First, the electron beam directly causes
secondary electron-electron emission from the MP sur-
face. The thermionic and field electron emissions are
consequences of the MP bombardment by the electron
beam due to the increasing of temperature and absolute
value of negative potential of the MP, respectively. MP
has a negative potential in the “usual” two-component
low-temperature plasma due to higher mobility of elec-
trons. The MP charging due to electron beam impact and
MP recharging due to electron emission are competitive
processes. Moreover, under certain conditions, effect of
electron emission can even be more pronounced. As a
result, MP can become positively charged.
In previous studies, MP charging in the electron-
beam systems with account for the secondary electron
emission has been investigated in the framework of the
orbit motion limited (OML) approach [1] and on the
basis of the discrete charging model [2]. The influence
of field electron emission and secondary electron emis-
sion on MP potential has been studied in [3]. The effect
of thermionic electron emission and secondary electron
emission on MP potential has been investigated in [4].
In the present work, the studies of MP charging are
developed. A complete model of the MP charging,
which includes a possible electron emission processes
from the MP surface in the presence of electron beam in
the plasma, is presented. Obtained results are of im-
portance for better understanding of the MP charging
mechanisms in the beam-plasma systems.
1. MP FLOATING POTENTIAL WITH
ACCOUNT FOR EMISSION PROCESSES
The steady-state potential φ, to which a MP is
charged, is determined from the balance of particle fluxes
which are collected by the MP surface and emitted from
it:
0, TEeeebei IIIII . (1)
Неre, Ii is the ion current, Ie is the current of plasma
electrons , Ib is the current of electron beam, Ie-e is the
current of secondary electrons emitted from the MP
surface due to bombardment of electron beam, and Ie,TE
is the current of relevant electron emission (thermionic
electron emission, field electron emission, thermal-field
electron emission).
The currents Ii , Ie, and Ib to the MP surface are cal-
culated by using the OML theory [5]. The OML ap-
proach is applicable for MP radius a much less than the
Debye length λD=(ε0Te /n0e
2
)
1/2
: a<< λD. In the case of
negatively charged MP
,exp8 2
eВ
Тееe
Tk
e
enaI
(2)
iВ
Tiii
Tk
e
enaI
18 2 , (3)
е
ebb
e
uenaI
12 . (4)
In the case of positively charged MP
,18 2
eВ
Тееe
Tk
e
enaI
(5)
,exp8 2
iВ
Тiii
Tk
e
enaI
(6)
е
ebb
e
uenaI
12 . (7)
In (2)-(7) ne, ni, and nb are the particle density of
plasma electrons, plasma ions and beam electrons, re-
spectively; Te (Ti) is the electron (ion) temperature,
υTe=(kBTe /me)
1/2
(υTi= (kBTi /mi)
1/2
) is the electron (ion)
thermal velocity, ue is the velocity of beam electrons, εe
is the energy of beam electrons.
The secondary electron current Ie-e caused by elec-
tron impact is [6]
,bее II 0 . (8)
The secondary electron yield δ is described by
Sterng-lass’s universal curve [6]
m
е
m
е
m
е
2exp4.7 , (9)
ISSN 1562-6016. ВАНТ. 2020. №6(130) 151
where εem is the energy for which the secondary yield δm
is maximum.
In the case of positively charged MP, the vast major-
ity of the secondary electrons returns to the MP surface
and only the most energetic ones leave the surface.
Thus, secondary electron current Ie-e is given by:
sBsB
bее
Tk
e
Tk
e
II
1exp , 0 , (10)
where Ts is the thermal temperature of emitted second-
ary electrons, which is quite small (1...5 eV).
The secondary electron emission results in the suffi-
cient increasing of absolute value of MP negative poten-
tial in the energy range of beam electrons, within which
the secondary electron yield δ>1. Moreover, in the case
of the equality of plasma and electron beam densities,
the MP floating potential can even become positive [1].
Another important emission process is the thermionic
electron emission. The current density of thermionic elec-
tron emission is given by Richardson-Dushman equation
[7]:
mpB
mpРDReТEe
Tk
e
TAjj exp2
,, , (11)
where Tmp is the MP temperature, eΦ is the work func-
tion, AR is the Richardson constant. For most metals
АР = (4...7)∙10
5
А/(m
2
∙K
2
)[8].
The thermionic electron emission occurs if MP is
heated to a temperature above some threshold. One can
find this critical temperature by equating the plasma
electron current density and current density of thermion-
ic electron emission
Tee jj , , (12)
where current density of electrons is expressed as:
4/0 ee еnj . (13)
Here, n0 is the plasma particle density, υTe= (kBTe
/me )
1/2 is the average thermal velocity of electrons.
MP critical temperature Tcr (K)
еФ,
еV
Te =10 еV
n0 =10
15
m
3
n0 =10
16
m
3
Al 4.2 2023 2218
Ti 4.3 2068 2267
Сu,W 4.5 2156 2363
The results of calculations of critical temperature Tcr
for MP with different work function material such as
aluminium, titanium, copper and tungsten in the plasma
with electron temperature Te =10 еV and plasma density
n0=10
15
...10
16
m
3
are presented in the Table. For all the
materials, except tungsten, the critical temperature is
higher than the boiling temperature. The value of critical
temperature of MP turns out to be higher in the plasma
with density 10
16
m
3
than that in the plasma with the
smaller density 10
15
m
3
.
In the case of negatively charged MP, the repulsive
potential accelerates thermionic electrons from the MP
surface. The electric field causes the increase in the
work function due to the electrostatic barrier. Richard-
son-Dushman equation with Schottky correction for the
work function is
mpB
mpРShReТEe
Tk
Ebe
TAjj exp2
,, , (14)
where E is the electric field. This equation is also called
as Richardson-Schottky equation.
The electric field on the MP surface is related to the
electric potential by
E=/a, (15)
and Schottky correction can be rewritten as
еEb
а
e
0
3
4
. (16)
When the MP is positively charged, the electrons
have to overcome the floating potential and the surface
barrier. In this case, the current density of the thermion-
ic emission is given by [9]
mpBmpB
MЧРТЕe
Tk
еe
Tk
е
TAj exp12
,
. (17)
In the case of very strong electric field, when
eΔΦ>eΦ, there is the field electron emission from MP
surface. In this case the emission current density should
be calculated according to Fowler-Nordheim formula [7]:
y
еhE
еm
yth
Ee
j
e
НФe
3
)(28
exp
)(8
3
2
22
, , (18)
with
е
Ее
y
1
4 0
3
. (19)
In (18), t(y) and ν(y) are the elliptical functions [7].
Field electron emission from a MP occurs when its
surface electric field is about 2∙10
7
V/cm. In the follow-
ing, the plasma conditions and MP size, under which MP
has such electric field on its surface, are evaluated. The
field emission from MP surface is absent in the case of
low-temperature plasma, which consists of electrons and
ions. For example, in nitrogen plasma with Te /Ti =10
normalized potential z=eφ/kBTe = 10 [8]. The corre-
sponding electric field on the surface of the MP with
radius 1 µm equals 3∙10
5
and 3∙10
6
V/cm for MP with
radius 0.1 µm. However, the field emission from MP
surface is possible in the case of plasma with electron
beam. The MP can acquire the high negative charge due
to bombardment of electron beam. The floating poten-
tial of MP reaches -200 V for beam electron energy of
the order of a few keV [1]. If electric potential of MP
with radius 0.1 µm equals -200 V, the corresponding
electric field on its surface is 2∙10
7
V/cm. Thus, the field
emission becomes important for MP with radius of
about 0.1 µm.
We have emission formulas (14) and (18) for two
cases: thermionic electron emission with taking into
account the Schottky effect, and field electron emission,
respectively. The relevant temperature and electric field
ranges are determined by [10]:
mpB
mp
e
Tck
TkЕe
em
Еe
e
144
B
43
0
3
0
3
, (20)
152 ISSN 1562-6016. ВАНТ. 2020. №6(130)
mpBmpB TkfTck 21 . (21)
Here,
)(
2
2
2
yt
eE
em
c e
, (22)
ħ is the Plank constant, and
1
2
0
2 4
1
)(2
2
1
eE
еeE
ym
f e
. (23)
The electric field-temperature curves calculated
from (20) and (21) divide the diagram in the Fig. 1 into
three regions: first one marked as TE, which corre-
sponds to the thermionic electron emission; second one
marked as FE, which corresponds to the field electron
emission, and a large region TFE between them. Both
temperature and electric field are high in the latter. Such
a case is possible in the vacuum arc discharge. Electron
emission in TFE range of temperatures and electric
fields belongs to so-called thermal-field emission. The
current density of thermal-field emission is given by
Murphy-Good formula [7]:
mpB
mpBe
GMe
Tk
Ebe
h
hTkem
j exp
sin2 0
0
32
2
,
,
(24)
were
mpBe
Tk
Eb
em
E
h
41
52
4
0
. (25)
Murphy-Good theory is the more general approach.
The formula (24) in the limiting cases transforms to the
Richardson-Schottky thermionic emission formula (14)
and Fowler-Nordheim field emission formula (18):
.,
;1,
,
0,
,
eej
hj
j
NFe
ShRe
TEe
(26)
Besides, the thermo-field (thermionic) emission cur-
rent Ie,TE from the MP surface is limited by the space
charge. The maximum current is determined by Lang-
muir-Blodgett formula [11]:
Fig. 1. Thermionic emission (TE), field emission (FE)
and thermal-field emission (TFE) regions of
temperature and electric field for 4.5 eV work function
,
9
2
2
2/3
0
2/3
U
m
e
I
e
(27)
where α is the tabulated function [11].
Thus, the thermal-field (thermionic) emission cur-
rent Ie,TE from the MP surface is determined by the fol-
lowing conditions:
.,
;,
2/3
,,
2/3
,
2/3
,
eTEeTEe
eTEee
TEe
III
III
I (28)
One can conclude that the solution of current bal-
ance equation (1) requires careful choice of the appro-
priate expression for emission current. At the same time,
one must keep in mind that electron emission is a limit-
ing process.
2. RESULTS AND DISCUSSION
The current balance equation (1) is numerically
solved in the two limiting cases: for MP with high tem-
perature and weak surface electric field, and for MP
with low temperature and strong surface electric field.
The numerical calculations are carried out for a colli-
sionless nitrogen plasma with the density of
n0=10
16
m
3
, electron temperature of Te = 10 eV, ion
temperature of Ti =1 eV, electron beam density of
n0 = 10
15
m
3
, and electron beam energies of
εe = 0.01...5 keV.
Fig. 2. The floating potential of MP with radius 1 µm
versus the electron beam energy for different MP
temperatures: “cold” MP (solid line), Tmp=2363 K
(dashed line); Tmp=2500 K (dotted line)
To begin with, the tungsten MP with radius a = 1 μm
is considered at fixed temperatures: Tmp = 2363 K (criti-
cal temperature) and Tmp=2500 K in the energy range of
beam electrons εe = 0.01...5 keV. This case corresponds
to the thermionic electron emission. The emission current
is calculated according to the Richardson-Dushman equa-
tion (3) with taking into account the Schottky effect. If
MP is positively charged, emission current density is cal-
culated according to (9). The floating potential of MP as a
function of the electron beam energy is shown in Fig. 2.
The potential of “cold” MP turns out to be negative in the
whole energy range of beam electrons. The secondary
electron emission cannot lead to positive potential in the
plasma with density larger than density of electron
beam. At the temperature Tmp=2363 K, the MP potential
increases, but it remains negative. At the higher temper-
ature Tmp= 2500 K, the MP potential becomes positive.
TE
TFE
FE
ISSN 1562-6016. ВАНТ. 2020. №6(130) 153
The other example is shown in Fig. 3. The tungsten
MP with radius 0.1 µm yields a high electric field at
electron beam energy more than 2 keV. The Fig. 3
shows the comparison of MP potential without taking
into account the field emission, and with it. One can see
that in the first case, the MP potential φ = -400 V for the
electron beam energy εe = 4 keV, and in the second case,
φ = -300V. Thus, the field electron emission sufficiently
decreases the absolute value of negative MP potential.
Fig. 3. The floating potential of MP with radius 0.1 µm
versus the electron beam energy. MP potential is
calculated without taking into account the field emission
(solid line). MP potential is calculated with taking into
account the field emission (dashed line)
CONCLUSIONS
The present paper describes the mechanisms of
different kind of electron emission from MP in plasma
system in the presence of electron beam. Both field elec-
tron emission and thermionic electron emissions result in
the increasing of absolute value of MP negative potential.
However, the field electron emission does not change the
sign of the MP potential. This is explained by the differ-
ence of the energy range of beam electrons, at which the
thermionic and field electron emissions take place.
REFERENCES
1. A.A. Bizyukov, E.V. Romashchenko, K.N. Sereda,
and A.D. Chibisov. Electric potential of a macro-
particle in beam-plasma systems // Plasma Physics Re-
ports. 2009, v. 35, № 6, p. 499-501.
2. A.A. Bizyukov, E.V. Romashchenko, K.N. Sereda,
and S.N. Abolmasov. Particle charging in beam-plasma
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Article received 03.10.2020
ВЛИЯНИЕ ПРОЦЕССОВ ЕЛЕКТРОННОЙ ЕМИССИИ НА ЗАРЯДКУ МАКРОЧАСТИЦЫ
В ПЛАЗМЕННЫХ СИСТЕМАХ С ЭЛЕКТРОННЫМ ПУЧКОМ
Е.В. Ромащенко, И.А. Гирка, А.А. Бизюков, А.Д. Чибисов
Исследовано влияние различных процессов электронной эмиссии на зарядку макрочастицы (МЧ) в
плазме в присутствии электронного пучка. Представлена полная модель зарядки МЧ в пучково-плазменных
системах, которая включает в себя возможные процессы электронной эмиссии с поверхности МЧ, такие как
вторичная электрон-электронная эмиссия, термоэлектронная, автоэлектронная, термоавтоэлектронная эмис-
сии.
ВПЛИВ ПРОЦЕСІВ ЕЛЕКТРОННОЇ ЕМІСІЇ НА ЗАРЯДЖЕННЯ МАКРОЧАСТИНКИ
У ПЛАЗМОВИХ СИСТЕМАХ З ЕЛЕКТРОННИМ ПУЧКОМ
О.В. Ромащенко, I.О. Гірка, О.А. Бізюков, О.Д. Чібісов
Досліджено вплив різних процесів електронної емісії на зарядження макрочастинки (МЧ) у плазмі у
присутності електронного пучка. Подано повну модель зарядження МЧ у пучково-плазмових системах, до
складу якої входять можливі процеси електронної емісії з поверхні МЧ, такі як вторинна електрон-
електронна емісія, термоелектронна, автоелектронна та термоавтоелектронна емісії.
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