The features of the electron distribution function in the hollow cathode glow discharge in nitrogen
In the present paper experimental and theoretical studies of the electron energy distribution function in a stationary glow discharge with a hollow cathode in nitrogen are performed. It is shown that in such discharge in nitrogen in the energy range ε = 2 ÷ 4 eV a significant gap and respective inve...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Cite this: | The features of the electron distribution function in the hollow cathode glow discharge in nitrogen / V.Yu. Bazhenov, A.V. Ryabtsev, I.A. Soloshenko, A.G. Terentyeva, V.V. Tsiolko, A.I. Shchedrin // Вопросы атомной науки и техники. — 2001. — № 3. — С. 191-193. — Бібліогр.: 5 назв. — англ. |
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Bazhenov, V.Yu. Ryabtsev, A.V. Soloshenko, I.A. Terentyeva, A.G. Tsiolko, V.V. Shchedrin, A.I. 2015-03-30T08:53:44Z 2015-03-30T08:53:44Z 2001 The features of the electron distribution function in the hollow cathode glow discharge in nitrogen / V.Yu. Bazhenov, A.V. Ryabtsev, I.A. Soloshenko, A.G. Terentyeva, V.V. Tsiolko, A.I. Shchedrin // Вопросы атомной науки и техники. — 2001. — № 3. — С. 191-193. — Бібліогр.: 5 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/79273 PACS numbers: 52.80.Hc In the present paper experimental and theoretical studies of the electron energy distribution function in a stationary glow discharge with a hollow cathode in nitrogen are performed. It is shown that in such discharge in nitrogen in the energy range ε = 2 ÷ 4 eV a significant gap and respective inverse region appear on the EDF, which is due to vibrational excitation of N₂ molecules. This work was supported in part by Grant #57 of Science and Technology Center in Ukraine. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники The features of the electron distribution function in the hollow cathode glow discharge in nitrogen Свойства функции распределения электронов в тлеющем разряде полого катода в азоте Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
The features of the electron distribution function in the hollow cathode glow discharge in nitrogen |
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The features of the electron distribution function in the hollow cathode glow discharge in nitrogen Bazhenov, V.Yu. Ryabtsev, A.V. Soloshenko, I.A. Terentyeva, A.G. Tsiolko, V.V. Shchedrin, A.I. |
| title_short |
The features of the electron distribution function in the hollow cathode glow discharge in nitrogen |
| title_full |
The features of the electron distribution function in the hollow cathode glow discharge in nitrogen |
| title_fullStr |
The features of the electron distribution function in the hollow cathode glow discharge in nitrogen |
| title_full_unstemmed |
The features of the electron distribution function in the hollow cathode glow discharge in nitrogen |
| title_sort |
features of the electron distribution function in the hollow cathode glow discharge in nitrogen |
| author |
Bazhenov, V.Yu. Ryabtsev, A.V. Soloshenko, I.A. Terentyeva, A.G. Tsiolko, V.V. Shchedrin, A.I. |
| author_facet |
Bazhenov, V.Yu. Ryabtsev, A.V. Soloshenko, I.A. Terentyeva, A.G. Tsiolko, V.V. Shchedrin, A.I. |
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2001 |
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English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Article |
| title_alt |
Свойства функции распределения электронов в тлеющем разряде полого катода в азоте |
| description |
In the present paper experimental and theoretical studies of the electron energy distribution function in a stationary glow discharge with a hollow cathode in nitrogen are performed. It is shown that in such discharge in nitrogen in the energy range ε = 2 ÷ 4 eV a significant gap and respective inverse region appear on the EDF, which is due to vibrational excitation of N₂ molecules.
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1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/79273 |
| citation_txt |
The features of the electron distribution function in the hollow cathode glow discharge in nitrogen / V.Yu. Bazhenov, A.V. Ryabtsev, I.A. Soloshenko, A.G. Terentyeva, V.V. Tsiolko, A.I. Shchedrin // Вопросы атомной науки и техники. — 2001. — № 3. — С. 191-193. — Бібліогр.: 5 назв. — англ. |
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2025-11-26T20:09:14Z |
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| fulltext |
THE FEATURES OF THE ELECTRON DISTRIBUTION FUNCTION IN
THE HOLLOW CATHODE GLOW DISCHARGE IN NITROGEN
V.Yu. Bazhenov, A.V. Ryabtsev, I.A. Soloshenko, A.G. Terentyeva,
V.V. Tsiolko, A.I. Shchedrin
Institute of Physics of NAS of Ukraine
Pr. Nauki 46, Kiev, 03022, Ukraine
E-mail: tsiolko@iop.kiev.ua
In the present paper experimental and theoretical studies of the electron energy distribution function in a stationary
glow discharge with a hollow cathode in nitrogen are performed. It is shown that in such discharge in nitrogen in the
energy range ε = 2 ÷ 4 eV a significant gap and respective inverse region appear on the EDF, which is due to vibra-
tional excitation of N2 molecules.
PACS numbers: 52.80.Hc
1 INTRODUCTION
Due to wide use of technologies with the plasma of
low-pressure gas discharges in nitrogen and its mix-
tures, in the last years a great attention is paid to experi-
mental and theoretical investigations of the electron en-
ergy distribution function (EDF) with an aim of clearer
understanding of the essence of plasma-chemical pro-
cesses occurring in various plasma devices. It should be
noted at once that EDF appearance depends essentially
on the discharge kind and parameters even for the same
gas mixtures. In the present work the experimental and
theoretical investigations of the electron energy distribu-
tion function are performed for the system which is
completely different from those studied both in [1, 2]
and in [3], particularly, for the stationary glow discharge
with a hollow cathode in nitrogen. As it is shown by the
measurements, the electric field in the main region of
such discharge is less than 0.1 V/cm at pressure
∼ 0.1 Torr, that is, at field value being one order of mag-
nitude less than that in [1, 2]. Ionization and electron
heating is provided in this case by the flow of fast elec-
trons with an energy of ∼ 400 eV which are emitted
from the near-cathode region.
2 EXPERIMENTAL SET-UP AND METH-
ODS
The experiments were accomplished with a hollow
cathode having a cylindrical shape with 280 mm diame-
ter and 400 mm length. The vacuum chamber was evac-
uated by forevacuum pump down to a residual pressure
of 5⋅10-3 Torr, after that working gas was supplied to the
chamber up to a pressure of 3⋅10-2 - 1⋅10-1 Torr. The dis-
charge current was varied in the range 0.5 – 0.9 A; the
voltage – in range 400 - 600 V. Measurements of the
plasma density, electric fields and EDF were performed
by means of two single Langmuire probes. The EDF
was determined by numerical double differentiation of
VAC by means of mathematical processing routines
(with preliminary interpolation of the data, if required).
For improvement precision of VAC measurements the
technique based on the use of a specially developed
software-hardware complex controlled by a personal
computer [4] was implemented. The potential of the
probe, at which the second derivative of its current on
voltage crossed zero level, was taken as a plasma poten-
tial. The plasma density was calculated from the satura-
tion current of electrons onto the probe.
3 EXPERIMENTAL RESULTS
In Fig. 1 the radial distributions of plasma density
for various pressures of nitrogen are given. One can see
that dependence behavior strongly depends on the work-
ing gas pressure. At p = 0.1 Torr plasma density has
minimum at cathode axis, and it grows up slowly along
the radius reaching its maximum at R ≈ 11 cm. At lower
pressures (p = 0.03 Torr, p = 0.06 Torr) the plasma den-
sity distribution along the cathode radius possesses in-
verse behavior – ne reaches its maximum at a system
axis and decreases monotonously with R growth. Such
peculiarity of the distribution is due to specifics of the
discharge with hollow cathode. At a pressure of 0.1 Torr
fast primary electrons emitted by the cathode spend al-
most all their energy for excitation and ionization of
working gas already at a distance of several centimeters
from the cathode, that is why the plasma at the system
axis appears mostly due to diffusion from the region of
its formation. Thus, maximum of plasma concentration
is observed in the region of maximum energy losses of
fast electrons (that is, maximum of plasma formation),
rather than at the cathode axis. As the gas pressure de-
creases the length of the fast primary electron energy re-
laxation increases, and due to that maximum of the plas-
ma density initially shifts to smaller radius values, and
at p ≈ 0.05 Torr the plasma density distribution appears
as bell-shaped curve.
Experimentally measured radial distributions of Er
electric field component at various pressures of nitrogen
are presented in Fig. 2. One can see from the figure that
the behavior of Er dependence on the radius corresponds
to the character of the radial plasma density depen-
dence. At low nitrogen pressure the field has a positive
sign and increases monotonously along the radius. At
p = 0.1 Torr in the near-axis region of the cathode (plas-
ma density minimum) Er field has a negative sign, and
then after crossing zero level also increases
monotonously along the radius. The longitudinal elec-
tric field component (Ez) in a whole range of used nitro-
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №3.
Серия: Ядерно-физические исследования (38), с. 191-193.
191
gen pressure does not exceed 1-2⋅10-2 V/cm. Figures 3,
4 exhibit typical EDF on energies at nitrogen pressures
0.03 and 0.1 Torr for various values of the system ra-
dius. One can see that EDF possess clearly exhibited
non-maxwellian behavior with significant gap in the en-
ergy range 2÷4 eV. At the lower pressure (Fig. 3) two
minima are being observed in this energy range. It has
been also determined that at low pressures the EDF
shape is practically independent on the radius, whereas
at p = 0.1 Torr EDF shape changes significantly along
the radius, and the gap depth is smaller in the center of
the chamber, where E/N has its minimum value. Such
behavior of an EDF radial dependence is not connected
with the presence of an electric field, since its action
would result in an inverse behavior of EDF dependen-
cies on the radius (i.e., a minimum gap depth on the
EDF would appear at the discharge periphery, where the
field has its maximum value). Decrease of the gap in
EDF near the hollow cathode axis at high pressures ob-
served (Fig. 4) may be due to the decrease of the
amount of high-energy electrons which represent the
main energy source in the plasma and, consequently,
due to contribution enhancement for the processes
which are responsible for EDF maxwellization.
Fig. 1. Plasma density versus R for various pres-
sures of nitrogen:
1 – p = 0.10 Torr, Id = 0.63 A, Ud = 470 V;
2 – p = 0.06 Torr, Id = 0.73 A, Ud = 580 V;
3 −р = 0.03 Torr, Id = 0.77 A, Ud = 615 V.
Fig. 2. Distributions of the electric field radial com-
ponent for various pressures of nitrogen.
1 - p = 0.10 Torr, Id = 0.63 A, Ud = 470 V;
2 - p = 0.06 Torr, Id = 0.73 A, Ud = 580 V;
3 - p = 0.03 Torr, Id = 0.77 A, Ud = 615 V.
4 RESULTS OF THE COMPUTER SIMULA-
TION AND DISCUSSION
Calculation of the electron energy distribution func-
tion was accomplished following the Boltzman equation
in the two-term approximation [5]:
( )
)(2
3
1
2
1
0
0
2
0
2
02/1
2/1
ε
ε
ε
ε
ε
ε
ε
ε
ASSfTfQ
M
m
f
QN
E
t
fn
e
m
Nn
eeeNT
T
e
e
++=
∂
∂+
∂
∂−
−
∂
∂
∂
∂
−
∂
∂
(1)
where f0(ε) is the symmetric part of the electron energy
distribution function; T is the gas temperature (eV);
e = 1,602⋅10-12 erg/eV; M, N, QT are the molecule mass,
gas concentration and transport scattering cross section,
respectively; m, ne are the electron mass and concentra-
tion; SeN is the integral of non-elastic collisions; See is the
integral of electron-electron scattering; A(ε) is the ion-
ization term including the source of primary electrons.
Expressions for terms SeN, See, A(ε) are given in [4].
The function f0(e) was normalized by condition:
∫
∞
=εεε
0
0
2/1 1)( df . (2)
When solving equation (1) for nitrogen the electron pro-
cesses presented in Table 1 [4] were taken into consid-
eration. Hyperelastic scattering with vibrationally excit-
ed molecules was not taken into account in the calcula-
tions, because in our case the specific power introduced
into the discharge and, respectively, vibrational temper-
ature Tv was essentially less than that in [2, 3]. Cross
sections of elastic and non-elastic scattering on N2
molecules were taken as in [4]. The electric field
strength and electron concentration in various regions of
the discharge chamber were measured experimentally,
and these values were used in the calculations. It was
assumed that the energy of the primary electron beam εп
comprised value of the order of cathode potential fall (ε
п ≈ 400 eV). Equation (1) was solved by numeric tech-
nique analogously to [5].
Fig. 3. Set of EDF on energies in nitrogen at
p = 0.03 Torr for various R.
192
Fig. 4. Set of EDF on energies in nitrogen at
p = 0.1 Torr for various R.
Fig. 5 exhibits theoretical electron distribution func-
tions in the discharge with a hollow cathode in nitrogen.
The range of EDF calculation parameters (ne, E) corre-
sponds to the range of ne, E variations along the radius
of the discharge chamber. At all discharge parameters
two minima in the energy range ε = 2÷4 eV are clearly
observed on EDF which are determined by a distinct
maxima in the cross section of vibrational excitation of
N2 molecules in the above mentioned energy ranges. In
case of excluding the process of N2 vibrational excita-
tion from the calculation EDF becomes monotonous.
The gap in the electron distribution function also disap-
pears at artificial increase of E/N value by the order up
to values used in [1-4] due to maxwellizing action of
electric field.
Fig. 5. Calculated EDF for nitrogen.
1 - p=0.03 Torr, ne=1⋅1010 cm- 3, E=0.01 V/cm;
2 - p=0.03 Torr, ne=1⋅1010 cm-3, E=0.10 V/cm;
3 - p=0.10 Torr, ne=1⋅1010 cm-3, E=0.01 V/cm;
4 - p=0.10 Torr, ne=2⋅1010 cm-3, E=0.06 V/cm.
Comparison of measured (Fig. 3) and calculated
(Fig. 5) electron distribution functions in nitrogen plas-
ma at low pressure demonstrates not just qualitative, but
quantitative agreement. Positions of experimental and
theoretical minima in EDF in the energy range ε = 2÷
4 eV coincide with 10-20% precision. Value of the gap
depth in the measured electron distribution function
(with respect to the right-side maximum) coincides with
the calculation with a precision of measurement error. It
should be noted that the experimental technique used
does not allow correct EDF measurements in the energy
range ≤ 1 eV. For this reason the measured value of f(ε)
decrease at ε < 1 eV is significantly less than calculated
one. However, comparison of f(ε) decrease with respect
to the EDF value at 1 eV also demonstrates a good
agreement between the theory and the experiment.
Somewhat worse relation of calculated and experi-
mental electron distribution functions at higher pres-
sures (Fig. 4) may be due to strong inhomogeneity in
the energy distribution along the radius for a fast elec-
tron beam emitted from the cathode, as it was already
mentioned. The calculations assumed complete spatial
homogeneity of all parameters determining the electron
distribution function.
5 CONCLUSIONS
Thus, investigations of EDF in the discharge with a
hollow cathode, in which main source of plasma heating
is represented by fast electrons formed at the cathode
and accelerated by the field of near-cathode space dis-
charge layer, have demonstrated that in nitrogen on
EDF in the energy range ε = 2÷4 eV a significant gap is
observed which is due to vibrational excitation of N2
molecules.
Results of theoretical calculations are in agreement
with the experiment.
6 ACKNOWLEDGEMENTS
This work was supported in part by Grant #57 of
Science and Technology Center in Ukraine.
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