22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Computational study of a dielectric barrier discharge in argon
Y. Peng1, Y. Zhang2, W. Jiang1 and A. Bogaerts2
1
2
School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
Research group PLASMANT, Department of Chemistry, University of Antwerp, 2610 Antwerpen-Wilrijk, Belgium
Abstract: The behaviour of a dielectric barrier discharge in argon at atmospheric pressure
has been investigated numerically. In this simulation we considered secondary electron
emission from the electrodes, which has a vital importance for maintaining the discharge.
The electron and ion density and temperature profiles, the electron energy distribution
function (EEDF) and the electric field are calculated for a driving voltage of 500 V. In our
simulation, the electron and ion densities are in the glow discharge limit, as the ionization
degree is lower than 1%. We also find that in the bulk region the electron temperature is
higher than the ion temperature, and the EEDF shows one group distribution, which is
consistent with a Druyvesteyn distribution.
Keywords:
dielectric barrier discharge, particle in cell, Monte Carlo
1. Introduction
Dielectric barrier discharges (DBDs) [1], also called
silent discharges, can occurs when an alternating high
voltage is applied to conductive electrodes, at least one of
which is covered with a dielectric layer. A prominent
feature of DBDs is the simple scalability from small
laboratory reactors to large industrial installations. The
first experimental investigations were reported by
Siemens [2]. It has been developed more than a century
since then and its applications have covered many areas,
including ozone generation [1, 3], the treatment of
polymers [1, 4-6], thin film deposition [1, 7-8], pollution
control [1, 9], high power CO 2 lasers [1, 10], ultraviolet
excimer lamps [1, 11], and large area flat plasma displays
[1, 12]. As far as industrial applications are concerned,
except for the surface discharge CO 2 laser, DBDs are
operated in the filamentary mode [13].
In recent years, significant research efforts have been
devoted to study atmospheric pressure non-equilibrium
plasmas in DBDs. A self-consistent two-dimensional
model was presented in [14].
The discharge
development was divided into four phases, a Townsend
phase, an ionization wave or streamer phase, a cathode
layer formation phase, and a decay phase. A DBD
generated by flowing helium between two parallel-plate
electrodes in an open reactor has been characterized in
[15]. The authors found that it is possible to observe a
transition from the filamentary mode to an apparently
uniform and repeatable discharge mode by adjusting the
operation conditions with flowing helium. Surface
discharges created in DBD configurations and proposed
as actuators for flow control have also been investigated,
based on a two-dimensional fluid model [16]. Unfer et
al. [17] also developed a two–dimensional self-consistent
numerical model in which nanosecond voltage pulses
were applied between electrodes in a DBD configuration.
However, there is only limited work [18] discussing
DBDs using an implicit PIC-MC method and the involved
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physics is still not completely clear, partially due to the
time-consuming numerical simulation process. The aim
of the present work is to study the discharge
characteristics in DBDs with various operation parameters,
such as the MD gap size and the pulse voltage. We want
to understand the basic phenomena that determine the
behaviour of atmospheric pressure DBDs.
2. Description of the model
In this work, we have employed a direct implicit
PIC-MCC code [19-20]. Our method has been described
in detail and tested a number of times before. In this
PIC-MCC code scheme, the field equations are obtained
from direct summation and extrapolation of the equations
of particle motion. After the particle pushing procedure
and solving the electric field, a standard MCC procedure
is executed to account for elastic, excitation and
ionization electron-neutral collisions and for elastic
scattering and charge exchange ion-neutral collisions.
Coulomb collisions are negligible as the ionization degree
is less than 1%. The cross sections used for these
reactions are adopted from [21-23].
In this simulation we have considered secondary
electron emission (SEE) which is self–consistently
coupled in the code. SEE is an Auger electron emission
process [24], and Zhang et al. [24] have elucidated that
the secondary electrons play an essential role in
maintaining the discharge. Here we assume a constant
ion impact SEE coefficient of 0.1, which is the same as
the one typically used in fluid models [25]. As the
electron and ion densities increase rapidly duo to SEE, a
particle merging algorithm is used when the particle
number exceeds a certain value. This PIC-MC method
is stable over a very broad range of physical and
numerical parameters.
A voltage source with amplitude of 500 V is used to
drive the discharge. Argon gas is at a temperature of
300 K. The simulation time-step is fixed at 4x10-12 s
1
and the gap size is divided into 128 cells. The discharge
is sustained between two parallel plate electrodes covered
with two dielectric layers. All the simulation results,
such as the electron temperature, electron and ion
densities and current, the electric field and the EEDFs,
will be averaged by several thousand time steps at steady
state.
3. Results and discussion
Fig. 1 shows the electron and ion density profiles for an
rf voltage of 500 V. The electron and ion densities are
more or less equal to each other, except in the sheaths
where the ion density is slightly higher. The electron
and ion density profiles show two symmetric peaks near
the sheath boundary, which is similar to experimental
observations [26] in a SEE sustaining MD and to a
computational study [24] in a radio frequency MD. It is
clear from the density profiles that the discharge is local
(i.e., steep density peak at the sheath boundaries and low
density in the bulk). It is because the mean free path of
electrons is smaller than the width of the bulk region
between the sheath boundaries, so the electrons cannot
reach or pass through the bulk region and generate
ionization.
Fig. 2. Electric field as a function of position, for an
rf voltage of 500 V.
In order to examine the corresponding electron kinetics,
we present the electron and ion temperatures and the
electron energy distribution functions (EEDFs) in Figs. 3
and 4, respectively. From figure 3 we can see that the
electron temperature is much higher than the ion
temperature in the bulk region, which demonstrates that
the electrons are effectively heated by the electric field
and the energetic electrons produce more electron impact
ionization. There are also two little peaks in the sheaths,
which is consistent with the peaks of the electric field in
Fig. 2. In the sheaths the electrons are accelerated due to
the potential drop, which is in agreement with [27]. The
EEDFs manifest a Druyvesteyn distribution, which is
different from [24]. In that paper, the EEDFs show a
three-temperature profile (hybrid mode) and a
two-temperature distribution (α mode). Shi et al. [28]
have elucidated that secondary electron emission strongly
affects the gas ionization in the γ mode, but is of little
importance in the α mode, and our calculated EEDFs
confirm this.
Fig. 1. Electron and ion densities as a function of
position, for an rf voltage of 500 V.
Fig. 2 presents the time-averaged electric field
distributions. It is clear that in the dielectric layers the
electric field is almost constant, whereas in the two
sheaths there is a peak. This is because the deposition of
the electrons on the left dielectric sheet results in a
negative field just near the dielectric surface, which will
lead to the accumulation of the electrons in the gas gap,
and more ion deposition on the right dielectric sheet. In
the bulk region the electric field is nearly zero, which can
be explained from Fig. 1, where the electron and ion
densities are nearly equal to each other.
Fig. 3. Electron and ion temperature profiles, for an
rf voltage of 500 V.
2
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[6]
[7]
[8]
[9]
[10]
[11]
Fig. 4. Space-time-averaged electron energy
distribution function, for an rf voltage of 500 V.
4. Conclusion
A direct implicit PIC-MC method is applied to
investigate an argon discharge operating in a dielectric
barrier configuration. This implicit method allows us to
employ much larger space and time steps, therefore it
reduces the computational cost and self-heating.
The evolutions of the electron and ion densities and
temperatures, the time-averaged electric field, and the
space-time-averaged EEDF have been presented. In our
simulation, the electron and ion densities are in the glow
discharge limit, as the ionization degree is lower
than 1%. We also find that in the bulk region the
electron temperature is higher than the ion temperature,
and the EEDF shows a Druyvesteyn distribution. Our
work is a step forward toward a better understanding of
DBDs, and in the next step, we will study a pulsed driving
micro-discharge, which has received much more attention
in recent years due to its technical simplicity and
appealing possibilities to influence and control the
discharge process.
5. Acknowledgments
This work was partially supported by the NSFC
(11405067, 11105057, 11275007) and China Postdoctoral
Science Foundation, as well as by the Belgian Federal
Science Policy Office (BELSPO).
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