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Patterns formed in dielectric barrier discharge is a typical nonlinear self-organization phenomenon. Research on the patterns helps elucidate the formation and evolution mechanisms of spatiotemporal structures in non-equilibrium systems, while also holding potential application value in fields such as material processing and plasma chemical engineering. A honeycomb superlattice pattern with an alternately-stretched honeycomb frame is observed in dielectric barrier discharge with a rectangular modulated gas gap for the first time and is studied both experimentally and theoretically. As the applied voltage increases, the pattern evolves from a hexagonal superlattice pattern with D6h symmetry to a quasi honeycomb superlattice pattern with D2h symmetry. Experimentally, the spatiotemporal structures of these two patterns are measured using an intensified charge coupled device (ICCD) and two photomultiplier tubes (PMTs). It is found that the hexagonal sublattice in the honeycomb superlattice pattern is divided into two sublattices, including a large stripe sublattice and a small stripe lattice. Additionally, the honeycomb frame sublattice is alternately-stretched. Discharges occur during both the rising and falling edges of the applied voltage. Through the estimation of the wall charge quantities of the two types of honeycomb frames and the analysis of the influence of boundaries on pattern formation, it is found that the quasi honeycomb superlattice pattern emerges as a self-organized structure under the influence of gas gap symmetry. Theoretically, the Poisson equation is numerically solved using COMSOL Multiphysics to simulate the electric field of the alternately-stretched honeycomb frame before and after discharge during the rising phase of the applied voltage. The result well explains the experimental phenomenon and provides the formation mechanism of the alternately-stretched honeycomb frame.
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Keywords:
- dielectric barrier discharge /
- pattern /
- spatiotemporal dynamics
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图 1 实验装置图
Figure 1. Schematic diagram of the experimental setup.
图 2 随着外加电压的增加斑图的演化序列 (a) 随机放电丝, U = 4.0 kV; (b) 蜂窝超点阵斑图, U = 4.9 kV; (c) 蜂窝框架加厚的蜂窝超点阵斑图, U = 5.3 kV; (d) 类蜂窝超点阵斑图, U = 5.6 kV; (e) 不稳定的蜂窝超点阵斑图, U = 5.8 kV; (f) 模糊条纹状, U = 6.4 kV; (g) 不同蜂窝斑图中蜂窝框架子点阵的示意图; (h) 斑图(a)—(f)的电压U与氩气含量φ的相图; (i) 类蜂窝超点阵斑图的气压p与氩气含量φ的相图
Figure 2. Transition of the pattern with the applied voltage increasing: (a) Random discharge filament, U = 4.0 kV; (b) honeycomb superlattice pattern, U = 4.9 kV; (c) honeycomb superlattice pattern with thicker honeycomb frame, U = 5.3 kV; (d) quasi honeycomb superlattice pattern, U = 5.6 kV; (e) unstable honeycomb superlattice pattern, U = 5.8 kV; (f) vague stripe, U = 6.4 kV; (g) schematic diagram of the sublattice of the honeycomb frame in different honeycomb patterns; (h) the phase diagram of the patterns in evolution sequence as a function of the voltage U and argon concentration φ shown in panel (a)—(f); (i) the phase diagram of quasi honeycomb superlattice pattern as a function of the gas pressure p and argon concentration φ.
图 3 类蜂窝超点阵斑图的瞬时照片 (a) 斑图的电压电流波形图(Δt1 = 1440 ns, Δt2 = 640 ns); (b), (c) 分别对应曝光时间为Δt1和Δt2的染色叠加100个电压周期的瞬时照片; (d) 图(b)和图(c)的叠加图
Figure 3. Instantaneous images of the quasi honeycomb superlattice pattern: (a) Waveforms of the voltage and the current. (Δt1 = 1440 ns, Δt2 = 640 ns); (b), (c) images exposed corresponding to the current pulse phases denoted by Δt1 and Δt2 in panel (a), respectively, and the images are integrated for 100 voltage cycles; (d) superposition of panels (b), (c).
图 4 类蜂窝超点阵斑图中不同子结构的时空相关性测量 (a) 类蜂窝超点阵斑图; (b), (c) F和S、B和S的时间相关性测量; (d) 斑图时空结构示意图
Figure 4. Spatiotemporal correlation measurement of different substructures in a quasi honeycomb superlattice pattern: (a) Quasi honeycomb superlattice pattern; (b), (c) measurement of the temporal correlation between F and S, B and S; (d) schematic diagram of the spatial and temporal structure of the pattern.
图 5 蜂窝超点阵斑图的瞬时照片 (a) 斑图的电压电流波形图(Δt1 = 560 ns, Δt2 = 2000 ns); (b), (c) 分别对应曝光时间为Δt1和Δt2的染色叠加100个电压周期的瞬时照片; (d) 图(b)和(c)的叠加图
Figure 5. Instantaneous images of the honeycomb superlattice pattern: (a) Waveforms of the voltage and the current. (Δt1 = 560 ns, Δt2 = 2000 ns); (b), (c) images exposed corresponding to the current pulse phases denoted by ∆t1 and ∆t2 in (a), respectively, and the images are integrated for 100 voltage cycles; (d) superposition of panels (b), (c).
图 6 两种蜂窝超点阵斑图的电压电流波形图 (a1) 蜂窝超点阵斑图及其电压电流波形图(b1); (a2) 类蜂窝超点阵斑图及其电压电流波形图(b2)
Figure 6. Waveform diagram of voltage and current of two kinds of honeycomb superlattice patterns: (a1) Honeycomb superlattice pattern and its voltage and current waveforms diagram (b1); (a2) quasi honeycomb superlattice pattern and its voltage and current waveforms diagram (b2).
图 7 隔列拉伸的蜂窝框架放电前后的电场分布 (a) 放电前; (b) 放电后
Figure 7. Electric field distribution of the alternately-stretched honeycomb frame before and after discharge: (a) Before discharging; (b) after discharging.
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