Child-Langmuir law for cathode sheath of glow discharge in CO₂
This work is devoted to the determination of the law that may be applicable to the description of the cathode sheath in CO₂. To this end three versions of the Child-Langmuir law have been considered – a collision free one (for the ions moving through a cathode sheath without collisions with gas mole...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1221562017-06-29T03:02:52Z Child-Langmuir law for cathode sheath of glow discharge in CO₂ Lisovskiy, V.A. Krol, H.H. Osmayev, R.O. Yegorenkov, V.D. Низкотемпературная плазма и плазменные технологии This work is devoted to the determination of the law that may be applicable to the description of the cathode sheath in CO₂. To this end three versions of the Child-Langmuir law have been considered – a collision free one (for the ions moving through a cathode sheath without collisions with gas molecules) as well as two collision- related versions– one for a constant mean free path of positive ions and one for a constant mobility of positive ions. The current-voltage characteristics and the cathode sheath thickness of the glow discharge in СО₂ have been simultaneously measured in the pressure range from 0.05 to 1 Torr and with the discharge current values up to 80 mA. In the whole range of the discharge conditions we have studied the cathode sheath characteristics are found to obey correctly only to the Child-Langmuir law version with a constant ion mobility. Данная работа посвящена определению закона, который может применяться для описания катодного слоя в CO₂. Выполнен анализ трёх законов Чайльда-Ленгмюра – бесстолкновительного (для движения ионов через катодный слой без столкновений с молекулами газа), а также двух столкновительных – с постоянными длиной свободного пробега и подвижностью положительных ионов. Для этого были одновременно измерены вольт-амперные характеристики и толщина катодного слоя тлеющего разряда в СО₂ в диапазоне давлений от 0,05 до 1 Торр и разрядных токов до 80 мА. В результате получено, что во всём исследованном нами диапазоне разрядных условий характеристики катодного слоя корректно описываются только законом Чайльда-Ленгмюра с постоянной подвижностью ионов. Ця робота присвячена визначенню закону, який може застосовуватися для опису катодного шару в CO₂. Виконано аналіз трьох законів Чайльда-Ленгмюра – для руху іонів крізь катодний шар без зіткнень з молекулами газу, а також законів з постійними довжиною вільного пробігу і рухливістю позитивних іонів. Для цього були одночасно виміряні вольт-амперні характеристики і товщина катодного шару тліючого розряду в СО₂ в діапазоні тиску від 0,05 до 1 Торр і розрядних струмів до 80 мА. У результаті отримано, що в усьому дослідженому нами діапазоні розрядних умов характеристики катодного шару коректно описуються тільки законом Чайльда-Ленгмюра з постійною рухливістю іонів. 2017 Article Child-Langmuir law for cathode sheath of glow discharge in CO₂ / V.A. Lisovskiy, H.H. Krol, R.O. Osmayev, V.D. Yegorenkov // Вопросы атомной науки и техники. — 2017. — № 1. — С. 140-143. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 52.80.Hc http://dspace.nbuv.gov.ua/handle/123456789/122156 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| topic |
Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
| spellingShingle |
Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Lisovskiy, V.A. Krol, H.H. Osmayev, R.O. Yegorenkov, V.D. Child-Langmuir law for cathode sheath of glow discharge in CO₂ Вопросы атомной науки и техники |
| description |
This work is devoted to the determination of the law that may be applicable to the description of the cathode sheath in CO₂. To this end three versions of the Child-Langmuir law have been considered – a collision free one (for the ions moving through a cathode sheath without collisions with gas molecules) as well as two collision- related versions– one for a constant mean free path of positive ions and one for a constant mobility of positive ions. The current-voltage characteristics and the cathode sheath thickness of the glow discharge in СО₂ have been simultaneously measured in the pressure range from 0.05 to 1 Torr and with the discharge current values up to 80 mA. In the whole range of the discharge conditions we have studied the cathode sheath characteristics are found to obey correctly only to the Child-Langmuir law version with a constant ion mobility. |
| format |
Article |
| author |
Lisovskiy, V.A. Krol, H.H. Osmayev, R.O. Yegorenkov, V.D. |
| author_facet |
Lisovskiy, V.A. Krol, H.H. Osmayev, R.O. Yegorenkov, V.D. |
| author_sort |
Lisovskiy, V.A. |
| title |
Child-Langmuir law for cathode sheath of glow discharge in CO₂ |
| title_short |
Child-Langmuir law for cathode sheath of glow discharge in CO₂ |
| title_full |
Child-Langmuir law for cathode sheath of glow discharge in CO₂ |
| title_fullStr |
Child-Langmuir law for cathode sheath of glow discharge in CO₂ |
| title_full_unstemmed |
Child-Langmuir law for cathode sheath of glow discharge in CO₂ |
| title_sort |
child-langmuir law for cathode sheath of glow discharge in co₂ |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2017 |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/122156 |
| citation_txt |
Child-Langmuir law for cathode sheath of glow discharge in CO₂ / V.A. Lisovskiy, H.H. Krol, R.O. Osmayev, V.D. Yegorenkov // Вопросы атомной науки и техники. — 2017. — № 1. — С. 140-143. — Бібліогр.: 18 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| first_indexed |
2025-07-08T21:15:44Z |
| last_indexed |
2025-07-08T21:15:44Z |
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1837114954009804800 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2017. №1(107)
140 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 140-143.
CHILD-LANGMUIR LAW FOR CATHODE SHEATH OF GLOW
DISCHARGE IN CO2
V.A. Lisovskiy
1, 2
, H.H. Krol
1
, R.O. Osmayev
1
, V.D. Yegorenkov
1
1
V.N. Karazin Kharkiv National University, Kharkov, Ukraine;
2
Scientific Center of Physical Technologies, Kharkov, Ukraine
E-mail: lisovskiy@yahoo.com
This work is devoted to the determination of the law that may be applicable to the description of the cathode
sheath in CO2. To this end three versions of the Child-Langmuir law have been considered – a collision free one (for
the ions moving through a cathode sheath without collisions with gas molecules) as well as two collision- related
versions– one for a constant mean free path of positive ions and one for a constant mobility of positive ions. The
current-voltage characteristics and the cathode sheath thickness of the glow discharge in СО2 have been
simultaneously measured in the pressure range from 0.05 to 1 Torr and with the discharge current values up to
80 mA. In the whole range of the discharge conditions we have studied the cathode sheath characteristics are found
to obey correctly only to the Child-Langmuir law version with a constant ion mobility.
PACS: 52.80.Hc
INTRODUCTION
A direct current glow discharge in СО2 is widely
applied for pumping carbon dioxide gas discharge
lasers [1]. Recently there has been observed the
growing interest to the plasma conversion of
greenhouse gases the carbon dioxide being the
principal one (its presence in the Earth atmosphere is
of fundamental importance in the ambient medium) to
the species which are of interest for chemical industry
or which may be used as a fuel for internal
combustion engines [2, 3]. Besides, СО2 is a
component of different atmospheres enveloping the
planets of the solar system as well as their satellites.
The studies of СО2 plasmas are also necessary
because of their applications in plasma reactors of
various types.
As the cathode sheath is the most important part of
the direct current glow discharge [4-7], the
optimization of plasma technologies and respective
devices demands studying its characteristics in СО2
and revealing which Child-Langmuir law version it
obeys.
Child [8] and Langmuir [9] have presented the
analytical models of a dc discharge in a flat gap
between the anode and the cathode. The paper [8] has
considered the motion of positive ions form the anode,
whereas the paper [9] has dealt with the problem what
secondary electrons leave the surface of the heated
cathode due to thermoelectric emission and travel to
the anode. The effect of the space charge on the
charged particle motion has been taken into account.
As a result both Child [8] and Langmuir [9] have
established the law of the identical mathematical form:
2
2321
0
2
d
U
M
e
KJ i
(1)
where Ki = 200/243=0.82, 0 is the vacuum dielectric
permittivity, е is the elementary charge, М is the
charged particle mass.
Thus the models [8, 9] have dealt only with a
collision-free case when charged particles cross the
sheath experiencing no collisions with gas molecules.
However in many research and technological devices the
gas pressure is sufficiently high for the charged particles
to participate in frequent collisions with molecules.
Therefore the papers of other researchers have reported
the following two law versions (they are similarly also
called the Child-Langmuir laws), one of which has
assumed the ion motion with a constant mean free path i
[10, 11]
25
2321
0
2
68.1
d
U
M
e
J i ,
(2)
and another one has been obtained for the ion motion with
a constant ion mobility i (not depending on velocity)
[12, 13]:
3
2
0
8
9
d
U
J i .
(3)
Because of the strong electric field present in the
cathode sheath one may assume that the law version (2)
with the constant ion mean free path i is the most
appropriate for the description of the cathode sheath
characteristics. The authors of paper [14] have claimed
that in the glow discharge in argon the cathode sheath
characteristics obey to the law version (2). But in
molecular gases one may observe various situations. For
example in N2O [15] at the pressure below 0.3 Torr one
observes the law version (3), at the pressure p 0.75 Torr
already the law version (2) is observed, but in the range
from 0.3 to 0.75 Torr none of the law versions (1)-(3)
cannot be employed for the description of the cathode
sheath. In nitrogen [16, 17] at the pressure values
p < 1 Torr and p > 1.5 Torr the law version (3) for the
constant ion mobility i is met whereas within the range
from 1 до 1.5 Torr none of the law versions (1)-(3)
describe the cathode sheath. At the same time in hydrogen
in the total range of pressure values from 0.05 to 2 Torr
studied by the authors of paper [18] there holds only the
law version (3) with the constant ion mobility i.
This paper reports the current-voltage characteristics
and cathode sheath thickness measured in СО2. It has
been obtained that in the total range of gas pressure and
,
ISSN 1562-6016. ВАНТ. 2017. №1(107) 141
discharge current values studied one has to employ the
law version (3) for the constant mobility i.
1. EXPERIMENTAL
We have employed the discharge chamber with the
design show in Fig. 1. The glass discharge tube
possessed the inner diameter of 56 mm. The CO2
pressure has been measured with the capacitive
manometer (Baratron) having the maximum measured
pressure of 10 Torr. The experiments have been
performed within the gas pressure range from 0.05 to
1 Torr.
The movable anode could be displaced along the
discharge tube axis, its diameter comprising 55 mm.
The discharge current studied did not exceed 80 mA.
Experiments have been performed in short tubes
with the discharge consisting of only the cathode
sheath and a small part of the negative glow.
Therefore the voltage drop over the cathode sheath
was approximately equal to the potential difference
across the electrodes.
2. EXPERIMENTAL RESULTS
All three Child-Langmuir law versions (1)-(3) may
be cast in the general form:
m
n
U
I C
d
(4)
where I = J S is the discharge current, S is the cathode
area. Note that the exponents m and n in these law
versions vary. In the collision free law version (1) they
are m = 1.5, n = 2; in the law version with the constant
mean free path (2) we have m = 1.5, n = 2.5, and in the
version with the constant ion mobility (3) the
exponents are equal to m = 2, n = 3. In this paper the
discharge current I, the voltage drop across the sheath
U and the cathode sheath thickness d have been
measured simultaneously for different fixed values of
the carbon dioxide pressure. With these data the
dependence of the current I on the U
m
/d
n
ratio has
been plotted. Note that the values of the U
m
/d
n
ratio
differ strongly for each of the m, n pairs thus
complicating the treatment of the (1)-(3) law versions.
Therefore the U
m
/d
n
values have been normalized over
their average value for a given m, n pair at the gas
pressure fixed. If for one of the m, n pairs the I(U
m
/d
n
)
dependence will be well described with a straight lined
drawn through the origin of coordinates then the Child-
Langmuir version which corresponds to this pair is
applicable for the description of the cathode sheath.
In Fig. 2 the dependences of the discharge current and
cathode sheath thickness on the voltage across the
electrodes are presented at the gas pressure of 0.05 Torr.
As is clear from the figure, the increase in the voltage
leads to the current growth, the CVC possesses a positive
tilt and the discharge is burning only in the abnormal
mode covering the total cathode surface. The maximum
cathode sheath thickness is observed at the lowest current
values. With the growth of the voltage across the
electrodes and the current the cathode sheath thickness
decreases and then becomes actually constant.
Fig. 2 also presents the dependence of the discharge
current on the normalized values of the U
m
/d
n
ratio. It is
clear from the figure that in a broad range of discharge
current values only the results for the m = 2, n = 3 pair fit
a straight line drawn through the origin of coordinates,
this pair corresponding to the law version (3) associated
with the constant ion mobility in the cathode sheath. For
two other m, n pairs corresponding to the ion motion
without collisions with gas molecules (1) as well as to the
motion with constant ion mean free path (2) the results
demonstrate poor agreement with a linear dependence
especially in the range of high discharge current values.
One may clearly observe a normal mode at the
discharge CVC (Fig. 3) at the CO2 pressure of 1 Torr and
the current below 11 mA what indicates a part of the
negative (falling) CVC when the discharge occupied only
a part of the cathode surface. After the discharge
Gas
supply
Pumping
V
AnodeCathode
U
R
A
Fig. 1. Design of the discharge setup
0 1 2 3 4
0
10
20
30
p = 0.05 Torr
m = 1.5, n = 2.0
m = 1.5, n = 2.5
m = 2.0, n = 3.0
I,
m
A
U
m
/d
n
500 1000 1500 2000
0
10
20
30
I,
m
A
U, V
d I
12
14
16
18
d
,
m
m
Fig. 2. The discharge current I and the cathode sheath
thickness d versus the voltage across the electrodes as
well as the discharge current versus the U
m
/d
n
ratio
for the carbon dioxide pressure of 0.05 Torr
,
142 ISSN 1562-6016. ВАНТ. 2017. №1(107)
transition to the abnormal mode when the discharge
has covered the cathode completely, the current grows
with the voltage across the electrodes increasing.
0,0 0,5 1,0 1,5 2,0 2,5 3,0
0
20
40
60
80
p = 1 Torr
m = 1.5, n = 2.0
m = 1.5, n = 2.5
m = 2.0, n = 3.0
I,
m
A
U
m
/d
n
350 400 450 500 550
0
20
40
60
80
I,
m
A
U, V
d
I
1,0
1,5
2,0
2,5
3,0
d
,
m
m
Fig. 3. The discharge current I and the cathode sheath
thickness d versus the voltage across the electrodes as
well as the discharge current versus the U
m
/d
n
ratio
for the carbon dioxide pressure of 1 Torr
400 500 600 700 800 900
0,000
0,005
0,010
0,015
412.4 nm
451.1 nm
483.5 nm
519 nm
561 nm
662 nm
844.6 nm
O
In
te
n
si
ty
,
n
W
/n
m
, nm
777.1 nm
O
608 nm
CO
Fig. 4. The emission spectrum of the cathode glow
(2 mm from the cathode surface) at the CO2 pressure
of 0.5 Torr and the discharge current of 5 mA
In this case the expansion of the discharge over the
cathode is accompanied, first, by a decrease of the
voltage across the electrodes (from 390 V before the
discharge extinction at 374 V when it experiences a
transition from the normal mode to the abnormal one).
Second, the cathode sheath thickness does not remain
constant but also decreases. Despite the falling pattern
of the I(U) and d(U) dependences the normal mode is
depicted on the I(U
m
/d
n
) graph by practically vertical
sections of the curves for different m, n pairs. After
the discharge transition to the abnormal mode the
increase of the voltage across the electrodes is
accompanied by the current increase and the cathode
sheath thickness decrease. Only the results for the m = 2,
n = 3 pair fit well the straight line drawn through the
origin of coordinates indicating the applicability of the
law version (3) with the constant ion mobility for the
description of the cathode sheath characteristics.
It has been obtained as a result that in the total range
of discharge the cathode sheath characteristics obey only
the Child-Langmuir law version with the constant ion
mobility (3).
This phenomenon may be associated with a
considerable conversion of СО2 molecules in the cathode
sheath and the negative glow. This is supported by the
optical spectra of radiation (Fig. 4). It has been
demonstrated that near the cathode surface the radiation
line of atomic oxygen OI 777 nm is the most intense one
(in the range from 400 to 1000 nm). Its intensity exceeds
ten times the line intensities of CO, CO2 and their ions but
on moving away from the cathode it decreases fast. In the
negative glow the line intensities of different atoms,
molecules and ions are comparable in magnitude (Fig. 5).
Probably the O
+
ion is a dominant positive ion in the
cathode sheath rather than the CO2
+
one, and the charge
exchange between O
+
ions and CO2 and CO molecules
may be impeded. In such a case O
+
ions will move
through the cathode sheath with a constant mobility (but
not with a constant mean free path as it might be when the
resonant charge exchange exerts a substantial influence
on ion motion).
0 10 20 30 40 50
10
-3
10
-2
10
-1
Cathode
In
te
n
si
ty
,
n
W
/n
m
z, mm
O 777.19 nm
O
2
437.26 nm
O
+
464.91 nm
O
2
+
559.75 nm
CO 483.53 nm
CO
2
+
369.32 nm
CO
+
360.08 nm
Cathode
sheath
Negative glow
Anode
Fig. 5. The axial distribution of emission line intensities
at the CO2 pressure of 0.05 Torr,
the discharge current of 10 mA and the distance between
the electrodes of 50 mm
CONCLUSIONS
In this paper the CVC and cathode sheath thickness of
the glow discharge in СО2 have been measured
simultaneously in a wide range of pressure and discharge
current values. The paper has been aimed to find out
which of the Child-Langmuir law versions may be
applied for the description of the cathode sheath in CO2. It
has been obtained that in the wide range of discharge
conditions studied the characteristics of the cathode
sheath obey only the Child-Langmuir law version
associated with the constant ion mobility (3). This
phenomenon may be caused by a substantial conversion
of carbon dioxide molecules.
ISSN 1562-6016. ВАНТ. 2017. №1(107) 143
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Article received 23.10.2016
ЗАКОН ЧАЙЛЬДА-ЛЕНГМЮРА ДЛЯ КАТОДНОГО СЛОЯ ТЛЕЮЩЕГО РАЗРЯДА В СО2
В.А. Лисовский, Г.Г. Кроль, Р.О. Осмаев, В.Д. Егоренков
Данная работа посвящена определению закона, который может применяться для описания катодного
слоя в CO2. Выполнен анализ трёх законов Чайльда-Ленгмюра – бесстолкновительного (для движения ионов
через катодный слой без столкновений с молекулами газа), а также двух столкновительных – с постоянными
длиной свободного пробега и подвижностью положительных ионов. Для этого были одновременно
измерены вольт-амперные характеристики и толщина катодного слоя тлеющего разряда в СО2 в диапазоне
давлений от 0,05 до 1 Торр и разрядных токов до 80 мА. В результате получено, что во всём исследованном
нами диапазоне разрядных условий характеристики катодного слоя корректно описываются только законом
Чайльда-Ленгмюра с постоянной подвижностью ионов.
ЗАКОН ЧАЙЛЬДА-ЛЕНГМЮРА ДЛЯ КАТОДНОГО ШАРУ ТЛІЮЧОГО РОЗРЯДУ В СО2
В.О. Лісовський, Г.Г. Кроль, Р.О. Осмаєв, В.Д. Єгоренков
Ця робота присвячена визначенню закону, який може застосовуватися для опису катодного шару в CO2.
Виконано аналіз трьох законів Чайльда-Ленгмюра – для руху іонів крізь катодний шар без зіткнень з
молекулами газу, а також законів з постійними довжиною вільного пробігу і рухливістю позитивних іонів.
Для цього були одночасно виміряні вольт-амперні характеристики і товщина катодного шару тліючого
розряду в СО2 в діапазоні тиску від 0,05 до 1 Торр і розрядних струмів до 80 мА. У результаті отримано, що
в усьому дослідженому нами діапазоні розрядних умов характеристики катодного шару коректно
описуються тільки законом Чайльда-Ленгмюра з постійною рухливістю іонів.
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