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^{1,2}, B. Bernecker

^{1}, Th. Callegari

^{1}, S. Blanco

^{1}and R. Fournier

^{1}

### Abstract

Dielectric barrier discharges (DBDs) operating in a glow regime exhibit a variety of complex self-organized static or dynamical structures of filaments. Using a fluid model combined with fast camera diagnostics, we propose a clear physical description and explanation of the mechanisms responsible for the generation, annihilation, motion and self-organization of discharge filaments in DBDs in a glow regime. We show that low current “side discharges” generated during the same half-cycle in the vicinity of an isolated filament beyond the inhibition zone associated with charge spreading along the dielectricsurface play an essential role in the triggering of these mechanisms.

### Key Topics

- Glow discharges
- 15.0
- Dielectrics
- 13.0
- Surface charge
- 11.0
- Pattern formation
- 10.0
- Double layers
- 7.0

##### H05H1/24

## Figures

Quasi-1D dielectric barrier discharge arrangement.

Quasi-1D dielectric barrier discharge arrangement.

Contour plot showing the time evolution over 5 cycles of the transverse distribution of the ion density (averaged along the discharge axis and over a time step of 1 *μ*s) as predicted by the fluid model. Neon, 100 torr, 2 mm gas gap, 2 mm dielectric layer thickness, 2 cm transverse dimension, and voltage amplitude and frequency 600 V and 20 kHz, respectively. The initial electron and ion density is a centered Gaussian along the transverse direction, uniform in the discharge direction, with a maximum of 10^{8} cm^{−3} and a standard deviation of 1 mm. The applied voltage and calculated current are plotted as a function of time on top of the figure. Same color bar as Fig.4, unit 4 × 10^{9} cm^{−3} (density is averaged along x).

Contour plot showing the time evolution over 5 cycles of the transverse distribution of the ion density (averaged along the discharge axis and over a time step of 1 *μ*s) as predicted by the fluid model. Neon, 100 torr, 2 mm gas gap, 2 mm dielectric layer thickness, 2 cm transverse dimension, and voltage amplitude and frequency 600 V and 20 kHz, respectively. The initial electron and ion density is a centered Gaussian along the transverse direction, uniform in the discharge direction, with a maximum of 10^{8} cm^{−3} and a standard deviation of 1 mm. The applied voltage and calculated current are plotted as a function of time on top of the figure. Same color bar as Fig.4, unit 4 × 10^{9} cm^{−3} (density is averaged along x).

Space (x and y) distribution of the ion density (colors), and electric potential contours in the gap (lines) at three times (indicated t_{1}, t_{2}, t_{3}—see Fig. 2) in the conditions of Fig. 2. The dielectric layers are in grey. Same color bar as Fig. 4, units t_{1}:2.4 × 10^{11} cm^{−3}, t_{2}: 2.3 × 10^{10} cm^{−3}, t_{3}: 8 × 10^{9} cm^{−3}.

Space (x and y) distribution of the ion density (colors), and electric potential contours in the gap (lines) at three times (indicated t_{1}, t_{2}, t_{3}—see Fig. 2) in the conditions of Fig. 2. The dielectric layers are in grey. Same color bar as Fig. 4, units t_{1}:2.4 × 10^{11} cm^{−3}, t_{2}: 2.3 × 10^{10} cm^{−3}, t_{3}: 8 × 10^{9} cm^{−3}.

Contour plot showing the time evolution of the transverse distribution of the ion density in the same conditions as in Fig. 2 but on a much longer time scale (the plotted density is averaged over time steps of 1 cycle instead of 1 *μ*s in the case of Fig. 2, and along x). Unit 10^{9} cm^{−3}.

Contour plot showing the time evolution of the transverse distribution of the ion density in the same conditions as in Fig. 2 but on a much longer time scale (the plotted density is averaged over time steps of 1 cycle instead of 1 *μ*s in the case of Fig. 2, and along x). Unit 10^{9} cm^{−3}.

Contour plot showing the time evolution of transverse distribution of the ion density (averaged along x and on time intervals of 1 cycle) in conditions similar to Fig. 2 except for the voltage amplitude which is close to the minimum sustaining voltage amplitude, i.e., (a) 500 V, (b) 500 V, and (c) 504 V. Voltage frequency is 20 kHz. The initial electron and ion density consist of two filaments with Gaussian density distributions of maximum 10^{8} cm^{−3}, standard deviations of 1 mm and separated by (a) 4 mm, and (b), (c) 2 mm. Unit is 6** ×** 10^{8} cm^{−3}, color bar as in Fig. 4.

Contour plot showing the time evolution of transverse distribution of the ion density (averaged along x and on time intervals of 1 cycle) in conditions similar to Fig. 2 except for the voltage amplitude which is close to the minimum sustaining voltage amplitude, i.e., (a) 500 V, (b) 500 V, and (c) 504 V. Voltage frequency is 20 kHz. The initial electron and ion density consist of two filaments with Gaussian density distributions of maximum 10^{8} cm^{−3}, standard deviations of 1 mm and separated by (a) 4 mm, and (b), (c) 2 mm. Unit is 6** ×** 10^{8} cm^{−3}, color bar as in Fig. 4.

Images of the quasi-1D DBD of Fig. 1 over successive cycles showing the generation and annihilation of filaments (argon, 50 torr, 3 mm gap, 1 kV, and 1 kHz).

Images of the quasi-1D DBD of Fig. 1 over successive cycles showing the generation and annihilation of filaments (argon, 50 torr, 3 mm gap, 1 kV, and 1 kHz).

Examples of filament motion over several half-cycles, within a self-organized structure, (a) experiments^{12} (1, 1 + 2, 1 + 2 + 3,… mean that the corresponding images are integrated in time over, 1, 2, 3,… successive half-cycles) and (b) simulations (images integrated over successive half-cycles).

Examples of filament motion over several half-cycles, within a self-organized structure, (a) experiments^{12} (1, 1 + 2, 1 + 2 + 3,… mean that the corresponding images are integrated in time over, 1, 2, 3,… successive half-cycles) and (b) simulations (images integrated over successive half-cycles).

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