22P005-O
Numerical simulation of a direct current glow discharge with gas flow atatmosphere pressure
微細希ガス流を用いた大気圧グロー放電の数値シミュレーション
T. Yoshida, N. Shirai, S. Uchida, F. Tochikubo
吉田 拓真, 白井 直樹, 内田 諭, 杤久保 文嘉,
Department of Electrical and Electronic Engineering, Tokyo Metropolitan University,
1-1, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan
首都大学東京〒192-0397 八王子市南大沢1-1
We carried out two-dimensional numerical simulation of atmospheric pressure dc glow discharge between
nozzle and plate electrodes. Since helium is injected from the nozzle into atmospheric pressure nitrogen,the discharge is generated along the helium flow. That is, the spatial distribution of helium is very
important for determining the discharge property. The purpose of this work is to clarify the relationshipbetween the glow discharge property and helium mole fraction distribution. We found that the discharge is
generated in the region with helium mole fraction larger than 99 %.

1. Introduction
In recent years, non-equilibrium plasmas at
atmospheric pressure attract much attention because
they can be irradiated easily to liquids [1-2], fineparticles [3] at relatively low temperature andwithout vacuum unit. Yokoyama et al. developed amethod to generate an atmospheric pressure dc
glow discharge with a miniature helium flow in air
between nozzle and plane electrodes [4]. In thesedischarges, the spatial distribution of helium is very
important for determining the shape of thedischarge because swarm parameters of charged
species are strongly influenced by the local gas
composition.
In this work, we carried out two-dimensional
numerical simulation of atmospheric pressure dc
glow discharge between nozzle and plate electrodes
with miniature helium flow in nitrogen, following
our previous report [5]. Discussion is focused on
the relation between the discharge shape and thehelium mole fraction distribution.
2. Simulation method
Simulation model in this work is shown in Fig. 1.
The dc glow discharge is generated between nozzle
and plate electrodes with gap distance of 1 mm. The
inner diameter of the nozzle is 250 μm. Helium gas
is injected from the nozzle with flow velocity of 10
m/s into atmospheric pressure nitrogen. Positive dc
voltage of 500 V is applied to the nozzle or plateelectrode while the counter electrode is grounded.
We used the axisymmetric two-dimensional modelin cylindrical coordinates. The calculation region is
1 mm in a longitudinal direction and 5 mm in aradial direction.

Fig.1 Simulation model

The simulation is divided into two parts, the gas
flow simulation and the gas discharge simulation.
The gas flow simulation provides the spatial
distributions of helium and nitrogen densities basedon a two-component compressible fluid model. The
calculation was carried out by commercial softwareCFD2000 by Adaptive Research. The gas discharge
simulation was carried out by a two-dimensional
fluid approximation model. The densities ofcharged and neutral species are calculated bysolving continuity equations for all species andconservation equation of electron energy coupledwith Poisson’s equation. In the present simulation,
we considered electron, He+, He2+, N2+, N4+,He(21S) and He(23S). We considered 26 chemical
reactions. The rate coefficient for helium-nitrogenmixed reactions was taken from ref. [6]. Electron’sswarm parameters were prepared by solvingBoltzmann equation using Bolsig+ [7]. The
mobility of each ion in helium and in nitrogen was
taken from the ref. [8].
3. Results and discussion
3.1. Gas flow simulation
Figure 2 shows the calculated mole fraction ofhelium at steady state in helium-nitrogen mixtures.
The helium mole fraction is very high within radial
distance of 250 μm from the central axis. After thehelium flow along the central axis reaches theplate electrode, it flows radially over the plateelectrode. Therefore, the mole fraction of nitrogenis about 1% or less near the plate electrode near
the central axis.

Fig. 2 Helium mole fraction in calculation region.

3.2. Gas discharge simulation
Figure.3
showsthecalculated
spatialdistributions of electron density and ionization rate
at steady state under the nozzle anode condition.
Solid and dashed lines in figures are the contour
lines indicating the helium mole fraction of 0.99
and 0.999, respectively. Electron density is high inthe region within approximately 250 μm from
central axis where the helium mole fraction ishigher than 99%. Therefore, it is found that thedischarge plasma is formed along the helium flow.
He+ is mainly generated by the electron impact
ionization of He in the cathode fall region because
high electron energy is required. Penning ionizationof N2 is active in the cathode fall region and also at
the side surface of positive column along thecontour line indicating the helium mole fraction of99.9%, where helium metastable atoms aregenerated a lot and moderate amount of N2 exits.
The highest electron density is located in the region
with helium mole fraction of 99-99.9%, wherePenning ionization of N2 is active. These resultsindicate that the spatial distribution of helium isquite important in determining the discharge
characteristics.
Next, calculated results under the nozzle cathodecondition are shown in Fig. 4. The cathode fallregion in nozzle cathode case is limited by thenozzle diameter while the cathode fall region in
front of plate electrode is wider in nozzle anodecase. Penning ionization of N2 in the cathode fallregion is also limited in nozzle cathode casebecause nitrogen density just beneath the nozzle isalmost zero. As a result, the plasma density in thepositive column becomes lower in comparison tothe nozzle anode case.
4. Conclusion

In this work, we investigated the fundamental
property of atmospheric pressure dc glow discharge
along a miniature helium flow in nitrogen. In thesedischarge He spatial distribution of helium mole
fraction plays a significant role in determining thecharacteristics of glow discharge.

Fig. 3 Spatial distributions of (a) electron density, (b)electron impact ionization of He+, (c) Penning ionizationof N2+, respectively. Positive voltage of 500 V is applied
to the nozzle electrode.

Fig. 4 Spatial distributions of (a) electron density, (b)electron impact ionization of He+, (c) Penning ionizationof N2+, respectively. Positive voltage of 500 V is applied
to the plate electrode.

Acknowledgement
This work was partly supported by Grant-in-Aidfor Scientific Research (No 21110007) from the
Ministry of Education, Culture, Sports, Science andTechnology, Japan.
References[1] P. Bruggeman, C. Leys: J. Phys. D 42 (2009) 053001.
[2] N. Shirai, K. Ichinose, S. Uchida, F. Tochikubo,
Plasma Sources Sci. Technol. 20 (2011) 034013.
[3] T. Nakajima, K. Tanaka, T. Inomata, M. Kogoma,Thin Solid Films 386 (2001) 208.
[4] T. Yokoyama, S. Hamada, S. Ibuka, K. Yasuoka, S.
Ishii, J. Phys. D 38 (2005) 1684.
[5] F. Tochikubo, N. Shirai, S. Uchida, Appl. Phys.
Express 4 (2011) 056001.
[6] G. M. Petrov, J. P. Matte, I. P´er`es, J. Margot, T.
Sadi, J. Hubert, K. C. Tran, L. L. Alves, J. Loureiro, C.
M. Ferreira,V. Guerra, and G. Gousset: Plasma Chem.
Plasma Proc. 20(2000) 183.
[7] G. J. M. Hagelaar, L. C. Pitchford, Plasma Sources
Sci. Technol. 14 (2005) 722.
[8] L. A. Viehland, E. A. Mason, Atom. Data Nucl. Data
Tab. 60 (1995) 37.