Honeycomb-like superlattice pattern in dielectric barrier discharge

LI Yaohua; YAN Zhaohe; YAN Zhihao; LI Cheng; PAN Yuyang; DONG Lifang

doi:10.7498/aps.74.20250952

Abstract

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 D_6h symmetry to a quasi honeycomb superlattice pattern with D_2h 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.

Keywords:

Authors and contacts

1.
College of Physics Science and Technology, Hebei University, Baoding 071002, China
2.
College of Quality and Technical Supervision, Engineering Research Center of Zero-carbon Energy Buildings and Measurement Techniques, Ministry of Education, Hebei University, Baoding 071002, China

Corresponding author: DONG Lifang, donglfhbu@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12075075), the Central Government Guiding Local Science and Technology Development Fund (Grant No. 246Z7607G), the Foundation of President of Hebei University, China (Grant No. XZJJ202317), and the Excellent Youth Research Innovation Team of Hebei University, China (Grant No. QNTD202402).

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References

[1]	Bánsági T, Vanag V K, Epstein I R 2011 Science 331 1309 Google Scholar
[2]	Kameke A V, Huhn F, Muñuzuri A P, Pérez-Muñuzuri 2013 Phys. Rev. Lett. 110 088302 Google Scholar
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[33]	Li Y H, Wang Y, Pan Y Y, Tian M, Zhang J H, Dong L F 2024 Phys. Plasmas 31 033502 Google Scholar

Cited By

图 1 实验装置图

Figure 1. Schematic diagram of the experimental setup.

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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.

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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).

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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).

DownLoad: Full-Size Img PowerPoint

图 6 (a1), (b1) 蜂窝超点阵斑图及其电压电流波形图; (a2), (b2) 类蜂窝超点阵斑图及其电压电流波形图

Figure 6. (a1), (b1) Honeycomb superlattice pattern and its voltage and current waveforms diagram; (a2), (b2) quasi honeycomb superlattice pattern and its voltage and current waveforms diagram.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

map

[1]	Bánsági T, Vanag V K, Epstein I R 2011 Science 331 1309 Google Scholar
[2]	Kameke A V, Huhn F, Muñuzuri A P, Pérez-Muñuzuri 2013 Phys. Rev. Lett. 110 088302 Google Scholar
[3]	Rogers J L, Schatz M F, Brausch, Pesch W 2000 Phys. Rev. Lett. 85 4281 Google Scholar
[4]	Perkins A C, Grigoriev R O, Schatz M F 2011 Phys. Rev. Lett. 107 064501 Google Scholar
[5]	Cominotti R, Berti A, Farolfi A, Zenesini A, Lamporesi G, Carusotto I, Recati A, Ferrari G 2022 Phys. Rev. Lett. 128 210410 Google Scholar
[6]	Frumkin V, Gokhale S 2023 Phys. Rev. E 108 012601 Google Scholar
[7]	Bernecker B, Callegari T, Boeuf J P 2011 J. Phys. D: Appl. Phys. 44 262002 Google Scholar
[8]	Shi H, Wang Y H, Wang D Z 2008 Phys. Plasmas 15 122306 Google Scholar
[9]	McKay K, Donaghy D, He F, Bradley J W 2017 Plasma Sources Sci. Technol. 27 015002 Google Scholar
[10]	Fan W L, Deng T K, Liu S, Liu R Q, He Y F, Liu Y H, Liu Y N, Liu F C 2025 Phys. Rev. E 111 024210 Google Scholar
[11]	Kogelschatz U 2003 Plasma Chem. Plasma Process. 23 1 Google Scholar
[12]	Callegari T, Bernecker B, Boeuf J P 2014 Plasma Sources Sci. Technol. 23 054003 Google Scholar
[13]	Boeuf J P 2003 J. Phys. D: Appl. Phys. 36 R53 Google Scholar
[14]	Polonskyi O, Hartig T, Uzarski J R, Gordon M J 2021 Appl. Phys. Lett. 119 211601 Google Scholar
[15]	Peng B F, Li J, Jiang N, Jiang Y, Chen Z Q, Lei Z P, Song J C 2024 Phys. Fluids 36 037144 Google Scholar
[16]	Brauer I, Bode M, Ammelt E, Purwins H G 2000 Phys. Rev. Lett. 84 4104 Google Scholar
[17]	Breazeal W, Flynn K M, Gwinn E G 1995 Phys. Rev. E 52 1503 Google Scholar
[18]	Guikema J, Miller N, Niehof J, Klein M, Walhout M 2000 Phys. Rev. Lett. 85 3817 Google Scholar
[19]	Bernecker B, Callegari T, Blanco S, Fournier R, Boeuf J P 2009 Eur. Phys. J. Appl. Phys. 47 22808 Google Scholar
[20]	Nie Q Y, Ren C S, Wang D Z, Li S Z, Zhang J L, Kong M G 2007 Appl. Phys. Lett. 90 221504 Google Scholar
[21]	Dong L F, Mao Z G, Ran J X 2005 Chin. Phys. 14 1618 Google Scholar
[22]	Dong L F, Li Y H, Qi X X, Fan W L, Li R, Liu S, Pan Y Y 2025 Opt. Express 33 37246 Google Scholar
[23]	Dong L F, Zhang L J, He Y N, Wei T, Li Y H, Li C, Pan Y Y 2024 Appl. Phys. Lett. 125 104101 Google Scholar
[24]	Liu F C, Liu Y N, Liu Q, Wu Z C, Liu Y H, Gao K Y, He Y F, Fan W L, Dong L F 2022 Plasma Sources Sci. Technol. 31 025015 Google Scholar
[25]	Fan W L, Wang Q H, Li R, Deng T K, Wang S, Li Y H, He Y F, Chu L Z, Liu F C 2024 Appl. Phys. Lett. 124 121703 Google Scholar
[26]	Duan X X, Ouyang J T, Zhao X F, He F 2009 Phys. Rev. E 80 016202 Google Scholar
[27]	Feng J Y, Dong L F, Wei L Y, Fan W L, Li C X, Pan Y Y 2016 Phys. Plasmas 23 093502 Google Scholar
[28]	卫婷, 董丽芳, 张立佳, 贺玉楠, 李耀华, 李骋, 潘宇扬 2024 中国科学: 物理学力学天文学 54 105211 Google Scholar Wei T, Dong L F, Zhang L J, He Y N, Li Y H, Li C, Pan Y Y 2024 Sci. Sin. Phys. Mech. Astron. 54 105211 Google Scholar
[29]	Dong L F, Fan W L, He Y F, Liu F C, Li S, Gao R L, Wang L 2006 Phys. Rev. E 73 066206 Google Scholar
[30]	Dong L F, Liu W L, Wang H F, He Y F, Fan W L, Gao R L 2007 Phys. Rev. E 76 046210 Google Scholar
[31]	Zhu P, Dong L F, Yang J, Gao Y N, Wang Y J, Li B 2015 Phys. Plasmas 22 023507 Google Scholar
[32]	于广林, 董丽芳, 窦亚亚, 孙浩洋, 米彦霖 2018 发光学报 39 1527 Google Scholar Yu G L, Dong L F, Dou Y Y, Sun H Y, Mi Y L 2018 Chin. J. Lumin. 39 1527 Google Scholar
[33]	Li Y H, Wang Y, Pan Y Y, Tian M, Zhang J H, Dong L F 2024 Phys. Plasmas 31 033502 Google Scholar

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Vol. 74, Issue 22 - 2025-11-20

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