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本文基于PASSKEy(PArallel streamer solver with KinEtics)构建了一个多层介质球的二氧化碳填充式介质阻挡放电二维模型, 并对此模型的流注传播演化动态过程进行了深入系统的仿真研究. 研究指出第1层和第2层介质球的内侧不是二氧化碳解离等反应发生的主要区域, 主要区域为流注传播路径以及第1层介质球的外侧. 同时, 本文还对此模型的电子密度与电场的演化进行深入解析, 并给出了相应的物理机理和对应特征点的局部电场演化. 此外, 还分别研究了空间电荷和表面电荷的时空演化, 指出整体上空间中的负电荷随着流注的形成和传播, 不断收缩于流注内部和介质表面, 而正电荷主导放电空间的电荷分布. 并且通过展开特定介质球的表面, 给出了具体的分布角度范围和演变趋势. 最后研究了一氧化碳粒子和二氧化碳离子和氧气离子的时空演化机理, 并且对放电空间中所有的电子和二氧化碳离子的空间能量沉积进行积分, 数据表明在此模型中的总能量沉积值约为1.428 mJ/m, 二氧化碳离子的沉积能量约为0.1251 mJ/m, 占比达8.8%.The streamer propagation and electric field distribution in a two-dimensional fluid model of a packed bed reactor (PBR) filled with carbon dioxide are comprehensively studied by utilizing the PASSKEy simulation platform in this work. The spatiotemporal evolution of electron density, electric fields and key plasma species in the discharge process are studied in depth. The PBR with layered dielectric spheres is simulated by using the model, indicating that the inner sides of the first layer and the second layer of dielectric spheres are not the main regions for reactions such as CO2 dissociation; instead, the main regions are along the streamer propagation path and the outer side of the first layer of dielectric sphere. In this work, the propagation of streamers in an electric field is investigated, highlighting the influence of anode voltage rise and dielectric polarization on local electric field enhancement. This enhancement leads the electron density and temperature to increase, which facilitats streamer propagation and the formation of filamentary microdischarges and surface ionization waves. This work provides a detailed analysis of the local electric field evolution at specific points within the PBR, and a further investigation of the spatiotemporal dynamics of spatial and surface charges, revealing that negative charges concentrate in the streamer and on the dielectric surface, with density being significantly higher than that of positive charges. The positive charge distribution is closely related to the streamer path, and with time going by, the charge distribution becomes dominated in the discharge space. This work also explores the surface charge deposition on the dielectric spheres, and discusses the evolution trend of the distribution. Additionally, this work discusses the temporal and spatial evolution of key plasma species, including ions and radicals, and their contributions to the overall discharge characteristics. The production mechanisms of carbon monoxide particles, carbon dioxide ions, and oxygen ions are analyzed, with a focus on their spatial distribution and correlation with electron density. Finally, the energy deposition within the PBR is examined by integrating the spatial energy deposition of electrons and major positive ions. The results indicate a total energy deposition value of approximately 1.428 mJ/m, with carbon dioxide ions accounting for 8.8% of this value.
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Keywords:
- packed-bed dielectric barrier discharge /
- dissociation of carbon dioxide /
- numerical simulation of plasma /
- reaction mechanism
[1] Bogaerts A, Tu X, Whitehead J C, Centi G, Lefferts L, Guaitella O, Azzolina-Jury F, Kim H, Murphy A B, Schneider W F 2020 J. Phys. D: Appl. Phys. 53 443001
Google Scholar
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Google Scholar
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Google Scholar
[4] Sun S R, Wang H X, Bogaerts A 2020 Plasma Sources Sci. Technol. 29 025012
Google Scholar
[5] 张泰恒, 王绪成, 张远涛 2021 物理学报 70 215201
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Zhang T H, Wang X C, Zhang Y T 2021 Acta Phys. Sin. 70 215201
Google Scholar
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Google Scholar
[7] McClean J B, Hoffman J A, Hecht M H, Aboobaker A M, Araghi K R, Elangovan S, Graves C R, Hartvigsen J J, Hinterman E D, Liu A M, Meyen F E, Nasr M, Ponce A, Rapp D, SooHoo J G, Swobada J, Voecks G E 2022 Acta Astronaut. 192 301
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[8] Wang W Z, Kim H H, Laer K V, Bogaerts A 2018 Chem. Eng. J. 334 2467
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[9] Kruszelnicki J, Engeling K W, Foster J E, Xiong Z M, Kushner M J 2017 J. Phys. D: Appl. Phys. 50 025203
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[10] Engeling K W, Kruszelnicki J, Kushner M J, Foster J E 2018 Plasma Sources Sci. Technol. 27 085002
Google Scholar
[11] Ren C H, Huang B D, Luo Y, Zhang C, Shao T 2023 Plasma Chem. Plasma Process 43 1613
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[12] Wang W Z, Butterworth T, Bogaerts A 2021 J. Phys. D: Appl. Phys. 54 214004
Google Scholar
[13] Cheng H, Ma M Y, Zhang Y Z, Liu D W, Lu X P 2020 J. Phys. D: Appl. Phys. 53 144001
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[14] Lu N, Liu N, Zhang C K, Su Y, Shang K F, Jiang N, Li J, Wu Y 2021 Chem. Eng. J. 417 129283
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[15] Zhu M, Hu S Y, Wu F F, Ma H, Xie S Y, Zhang C H 2022 J. Phys. D: Appl. Phys. 55 225207
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[16] Kaliyappan P, Paulus A, Haen J D, Pieter S, Uytdenhouwen Y, Hafezkhiabani N, Bogaerts A, Meynen V, Elen K, Hardy A, Bael M V 2021 J. CO2 Util. 46 101468
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[17] Uytdenhouwen Y, Meynen V, Cool P, Bogaerts A 2020 Catalysts 10 530
Google Scholar
[18] Uytdenhouwen Y, Alphen S V, Michielsen I, Meynen V, Cool P, Bogaerts A 2018 Chem. Eng. J. 348 557
Google Scholar
[19] Li X R, Dijcks S, Sun A B, Nijdam S, Teunissen J 2024 Plasma Sources Sci. Technol. 33 095009
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[20] Marskar R 2024 Plasma Sources Sci. Technol. 33 025023
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[21] Zhou C, Yuan C X, Kudryavtsev A, Katircioglu T Y, Rafatov I, Yao J F 2023 Plasma Sources Sci. Technol. 32 015010
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[22] 付强, 王聪, 王语菲, 常正实 2022 物理学报 71 115204
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Fu Q, Wang C, Wang Y F, Chang Z S 2022 Acta Phys. Sin. 71 115204
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Google Scholar
Li Y, Mu H B, Deng J B, Zhang G J, Wang S H 2013 Acta Phys. Sin. 62 124703
Google Scholar
[25] 肖江平, 戴栋, Victor F. Tarasenko, 邵涛 2023 物理学报 72 105201
Google Scholar
Xiao J P, Dai D, Tarasenko V F, Shao T 2023 Acta Phys. Sin. 72 105201
Google Scholar
[26] Zhu Y F, Chen X C, Wu Y, Starikovskaia S 2021 PASSKEy code [software]. Available from http://www.plasma-tech.net/parser/passkey/, Science and Technology of Plasma Dynamics Laboratory, Xi’an, China and Laboratoire de Physique des Plasmas, Paris, France
[27] Zhu Y F, Chen X C, Wu Y, Hao J B, Ma X G, Lu P F, Tardiveau P 2021 Plasma Sources Sci. Technol. 30 075025
Google Scholar
[28] Pancheshnyi S 2014 Plasma Sources Sci. Technol. 24 015023
Google Scholar
[29] Zhu Y F, Wu Y, Li J 2020 arXiv. 2005.10021
[30] Guo Y L, Li Y R, Zhu Y F, Sun A B 2023 Plasma Sources Sci. Technol. 32 025003
Google Scholar
[31] Bourdon A, Pasko V P, Liu N Y, Célestin S, Ségur P, Marode E 2007 Plasma Sources Sci. Technol. 16 656
Google Scholar
[32] Teich T H 1967 Z. Phys. 199 378
Google Scholar
[33] Przybylski A 1962 Z. Phys. 168 504
Google Scholar
[34] Sroka W 1970 Zeitschrift für Naturforschung A 25 1437
[35] Bagheri B, Teunissen J, Ebert U 2020 Plasma Sources Sci. Technol. 29 125021
Google Scholar
[36] Levko D, Pachuilo M, Raja L L 2017 J. Phys. D: Appl. Phys. 50 354004
Google Scholar
[37] Zhu Y F, Starikovskaia S 2018 Plasma Sources Sci. Technol. 27 124007
Google Scholar
[38] Peng B F, Jiang N, Zhu Y F, Wu Y 2024 Plasma Sources Sci. Technol. 33 045018
Google Scholar
[39] Itikawa database, www. lxcat. net [2024-05-19]
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[41] Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722
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[42] Bogaerts A, Wang W Z, Berthelot A, Guerra V 2016 Plasma Sources Sci. Technol. 25 055016
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[43] Qian M Y, Zhong W S, Kang J S, Liu S Q, Ren C S, Zhang J L, Wang D Z 2020 Jpn. J. Appl. Phys. 59 066003
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图 2 模型结构图 (a)几何结构; (b)电压波形; (c)网格剖分示意图
Fig. 2. Model structure: (a) Geometry; (b) voltage; (c) mesh.
图 5 局部电场的时间演化 (a) 6个节点的空间位置, 背景图为5 ns时的约化电场; (b) 6个节点处的约化电场强度随时间的变化
Fig. 5. Time evolution of the local electric field: (a) The location of the six points, with the reduced electric field at 5 ns in the background image; (b) the variation of the reduced electric field amplitude with time at the six points.
图 7 介质表面电荷的时空演化 (a), (f) D2; (b) (e) D1; (c) (d) D0
Fig. 7. Time evolution of the dielectric surface charge: (a), (f) D2; (b) (e) D1; (c) (d) D0.
图 12 电子和二氧化碳离子的空间能量沉积
Fig. 12. Total energy deposition of electrons and carbon dioxide ions.
表 1 三项亥姆霍兹方程系数An与λn
Table 1. Coefficients of the three terms Helmholtz equation An and λn.
n An/(cm–2·torr–1) λn /(cm–1·torr–1) 1 3.74×10–5 2.31 2 4.35×10–6 0.837 3 1.55×10–4 7.79 
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表 2 模型中包含的粒子概述
Table 2. Overview of particles included in the model.
分子 CO2, CO, O2 离子 ${\mathrm{CO}}_2^+ $, CO+, C+, O+, ${\mathrm{O}}_2^+ $, O–, ${\mathrm{O}}_2^- $ 自由基 O, C
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表 3 模型中包含的电子碰撞反应
Table 3. Electron collision reactions included in the model.
类型 反应 焓变/eV 反应速率 电离 e + CO2$ \Rightarrow$${\mathrm{CO}}_2^+ $ + e + e –13.80 BOLSIG+ 电离 e + CO2$ \Rightarrow$CO + O+ + e + e –19.1 BOLSIG+ 电离 e + CO2$ \Rightarrow$O + CO+ + e + e –19.5 BOLSIG+ 电离 e + CO2$ \Rightarrow$O2+C+ + e + e –27.8 BOLSIG+ 电离 e + CO$ \Rightarrow$CO+ + e + e –14.01 BOLSIG+ 电离 e + CO$ \Rightarrow$C++O + e + e –22.0 BOLSIG+ 电离 e + CO$ \Rightarrow$C + O+ + e + e –25.0 BOLSIG+ 电离 e + O2$ \Rightarrow$${\mathrm{O}}_2^+ $ + e + e –12.06 BOLSIG+ 解离 e + O2$ \Rightarrow$e + O + O 0.8 BOLSIG+ 解离 e + CO2$ \Rightarrow$e + CO + O –7.0 BOLSIG+ 吸附 e + O2 + O2$ \Rightarrow$${\mathrm{O}}_2^- $+O2 0 6.0 × 10–39$ T_{\text{e}}^{{{ - 1}}} $b* 吸附 e + O2 + CO2$ \Rightarrow$CO2 + ${\mathrm{O}}_2^- $ 1.60 3.0 × 10–42 b* 吸附 e + O + CO2$ \Rightarrow$CO2 + O– 1.60 1.0 × 10–43 b* 解离+吸附 e + CO2$ \Rightarrow$CO + O– 0 BOLSIG+ 解离+吸附 e + CO$ \Rightarrow$C + O– 0 BOLSIG+ 解离+吸附 e + O2$ \Rightarrow$O–+O 0 BOLSIG+ e-i 复合 e + ${\mathrm{CO}}_2^+ $$ \Rightarrow$CO + O 1.60 $2.0 \times 10^{-11} T_{\text{e}}^{{{ - 0}}{.5}} \cdot T_{\text{g}}^{ - 1} $a* e-i 复合 e + ${\mathrm{CO}}_2^+ $$ \Rightarrow$C + O 1.60 $3.68 \times 10^{-14} T_{\text{e}}^{-0.55} $a* e-i 复合 e + ${\mathrm{CO}}_2^+ $$ \Rightarrow$C + O2 1.60 $3.94 \times 10^{-13} T_{\text{e}}^{-0.4} $a* e-i 复合 e + ${\mathrm{O}}_2^+ $$ \Rightarrow$O + O 1.60 $6.0 \times 10^{-13} T_{\text{e}}^{{{ - 0}}{.5}} \cdot T_{\text{g}}^{ - 0.5} $a* e-i 复合 e + O2+ + CO2$ \Rightarrow$O2 + CO2 1.60 1.0 × 10–38 b* e-i 复合 e + O+ + CO2$ \Rightarrow$O + CO2 1.60 1.0 × 10–38 b* 注: a*代表单位为m3/(mol·s), b*代表单位为m6/(mol2·s).
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表 4 模型中包含的重粒子反应
Table 4. Heavy particle reactions included in the model.
类型 反应 焓变/eV 反应速率 电子分离 O– + O$ \Rightarrow$O2+e 0 1.4 × 10–16 a* 电子分离 ${\mathrm{O}}_2^- $ + O$ \Rightarrow$O2 + O + e 0 1.5 × 10–16 a* i-i复合 ${\mathrm{O}}_2^- $+${\mathrm{O}}_2^+ $ + O2$ \Rightarrow$O2 + O2 + O2 7.0 2.0 × 10–37 b* 电荷转移 O+ + CO2$ \Rightarrow$${\mathrm{O}}_2^+ $ + CO 0 9.4 × 10–16 a* 电荷转移 O+ + CO2$ \Rightarrow$${\mathrm{CO}}_2^+ $ + O 0 4.5 × 10–16 a* 电荷转移 CO+ + CO2$ \Rightarrow$${\mathrm{CO}}_2^+ $ + CO 0 1.0 × 10–15 a* 电荷转移 C+ + CO$ \Rightarrow$CO+ + C 0 5.0 × 10–19 a* 电荷转移 ${\mathrm{O}}_2^+ $ + C$ \Rightarrow$CO+ + O 0 5.2 × 10–17 a* 电荷转移 ${\mathrm{CO}}_2^+ $ + O2$ \Rightarrow$CO2 + ${\mathrm{O}}_2^+ $ 0 5.3 × 10–17 a* 电荷转移 ${\mathrm{CO}}_2^+ $ + O$ \Rightarrow$CO+${\mathrm{O}}_2^+ $ 0 1.64 × 10–16 a* 电荷转移 ${\mathrm{CO}}_2^+ $ + O$ \Rightarrow$CO2 + O+ 0 9.62 × 10–17 a* 电荷转移 CO+ + O$ \Rightarrow$CO + O+ 0 1.4 × 10–16 a* 电荷转移 CO+ + O2$ \Rightarrow$CO + ${\mathrm{O}}_2^+ $ 0 1.2 × 10–16 a* 中性反应 CO2 + CO2$ \Rightarrow$CO + O + CO2 0.60 $3.91 \times 10^{-16} \exp [-(49430/T_{\rm g})]$ a* 中性反应 CO2 + O$ \Rightarrow$CO + O2 0 $2.8 \times 10^{-17} \exp [-(26500/T_{\rm g})] $ a* 中性反应 CO2 + C$ \Rightarrow$CO + CO 0 $1.0 \times 10^{-21}$ a* 中性反应 CO + O + CO2$ \Rightarrow$CO2 + CO2 0 $8.2 \times 10^{-46} \exp [-(1510/T_{\rm g})] $ b* 中性反应 O2 + CO$ \Rightarrow$CO2 + O 0 $4.2 \times 10^{-18} \exp [-(24000/T_{\rm g})] $ a* 中性反应 O2 + C$ \Rightarrow$CO + O 0 $3.0 \times 10^{-17} $ a* 中性反应 O + C + CO2$ \Rightarrow$CO + CO2 0 $9.12 \times 10^{-37}T_{\rm g}^{-3.08} \exp [-(2114/T_{\rm g})] $ b* 中性反应 O + O + CO2$ \Rightarrow$O2 + CO2 0 $3.81 \times 10^{-42}T_{\rm g}^{-1} \exp [-(170/T_{\rm g})] $ b* 注: a*代表单位为m3/(mol·s), b*代表单位为m6/(mol2·s).
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[1] Bogaerts A, Tu X, Whitehead J C, Centi G, Lefferts L, Guaitella O, Azzolina-Jury F, Kim H, Murphy A B, Schneider W F 2020 J. Phys. D: Appl. Phys. 53 443001
Google Scholar
[2] George A, Shen B X, Craven M, Wang Y L, Kang D R, Wu C F, Tu X 2021 Renew. Sust. Energ. Rev. 135 109702
Google Scholar
[3] Bogaerts A, Neyts E C, Guaitella O, Murphy A B 2022 Plasma Sources Sci. Technol. 31 053002
Google Scholar
[4] Sun S R, Wang H X, Bogaerts A 2020 Plasma Sources Sci. Technol. 29 025012
Google Scholar
[5] 张泰恒, 王绪成, 张远涛 2021 物理学报 70 215201
Google Scholar
Zhang T H, Wang X C, Zhang Y T 2021 Acta Phys. Sin. 70 215201
Google Scholar
[6] Hinterman E, Hoffman J A 2020 Acta Astronaut. 170 678
Google Scholar
[7] McClean J B, Hoffman J A, Hecht M H, Aboobaker A M, Araghi K R, Elangovan S, Graves C R, Hartvigsen J J, Hinterman E D, Liu A M, Meyen F E, Nasr M, Ponce A, Rapp D, SooHoo J G, Swobada J, Voecks G E 2022 Acta Astronaut. 192 301
Google Scholar
[8] Wang W Z, Kim H H, Laer K V, Bogaerts A 2018 Chem. Eng. J. 334 2467
Google Scholar
[9] Kruszelnicki J, Engeling K W, Foster J E, Xiong Z M, Kushner M J 2017 J. Phys. D: Appl. Phys. 50 025203
Google Scholar
[10] Engeling K W, Kruszelnicki J, Kushner M J, Foster J E 2018 Plasma Sources Sci. Technol. 27 085002
Google Scholar
[11] Ren C H, Huang B D, Luo Y, Zhang C, Shao T 2023 Plasma Chem. Plasma Process 43 1613
Google Scholar
[12] Wang W Z, Butterworth T, Bogaerts A 2021 J. Phys. D: Appl. Phys. 54 214004
Google Scholar
[13] Cheng H, Ma M Y, Zhang Y Z, Liu D W, Lu X P 2020 J. Phys. D: Appl. Phys. 53 144001
Google Scholar
[14] Lu N, Liu N, Zhang C K, Su Y, Shang K F, Jiang N, Li J, Wu Y 2021 Chem. Eng. J. 417 129283
Google Scholar
[15] Zhu M, Hu S Y, Wu F F, Ma H, Xie S Y, Zhang C H 2022 J. Phys. D: Appl. Phys. 55 225207
Google Scholar
[16] Kaliyappan P, Paulus A, Haen J D, Pieter S, Uytdenhouwen Y, Hafezkhiabani N, Bogaerts A, Meynen V, Elen K, Hardy A, Bael M V 2021 J. CO2 Util. 46 101468
Google Scholar
[17] Uytdenhouwen Y, Meynen V, Cool P, Bogaerts A 2020 Catalysts 10 530
Google Scholar
[18] Uytdenhouwen Y, Alphen S V, Michielsen I, Meynen V, Cool P, Bogaerts A 2018 Chem. Eng. J. 348 557
Google Scholar
[19] Li X R, Dijcks S, Sun A B, Nijdam S, Teunissen J 2024 Plasma Sources Sci. Technol. 33 095009
Google Scholar
[20] Marskar R 2024 Plasma Sources Sci. Technol. 33 025023
Google Scholar
[21] Zhou C, Yuan C X, Kudryavtsev A, Katircioglu T Y, Rafatov I, Yao J F 2023 Plasma Sources Sci. Technol. 32 015010
Google Scholar
[22] 付强, 王聪, 王语菲, 常正实 2022 物理学报 71 115204
Google Scholar
Fu Q, Wang C, Wang Y F, Chang Z S 2022 Acta Phys. Sin. 71 115204
Google Scholar
[23] 张增辉, 张冠军, 邵先军, 常正实, 彭兆裕, 许昊 2012 物理学报 61 245205
Google Scholar
Zhang Z H, Zhang G J, Shao X J, Chang Z S, Peng Z Y, Xu H 2012 Acta Phys. Sin. 61 245205
Google Scholar
[24] 李元, 穆海宝, 邓军波, 张冠军, 王曙鸿 2013 物理学报 62 124703
Google Scholar
Li Y, Mu H B, Deng J B, Zhang G J, Wang S H 2013 Acta Phys. Sin. 62 124703
Google Scholar
[25] 肖江平, 戴栋, Victor F. Tarasenko, 邵涛 2023 物理学报 72 105201
Google Scholar
Xiao J P, Dai D, Tarasenko V F, Shao T 2023 Acta Phys. Sin. 72 105201
Google Scholar
[26] Zhu Y F, Chen X C, Wu Y, Starikovskaia S 2021 PASSKEy code [software]. Available from http://www.plasma-tech.net/parser/passkey/, Science and Technology of Plasma Dynamics Laboratory, Xi’an, China and Laboratoire de Physique des Plasmas, Paris, France
[27] Zhu Y F, Chen X C, Wu Y, Hao J B, Ma X G, Lu P F, Tardiveau P 2021 Plasma Sources Sci. Technol. 30 075025
Google Scholar
[28] Pancheshnyi S 2014 Plasma Sources Sci. Technol. 24 015023
Google Scholar
[29] Zhu Y F, Wu Y, Li J 2020 arXiv. 2005.10021
[30] Guo Y L, Li Y R, Zhu Y F, Sun A B 2023 Plasma Sources Sci. Technol. 32 025003
Google Scholar
[31] Bourdon A, Pasko V P, Liu N Y, Célestin S, Ségur P, Marode E 2007 Plasma Sources Sci. Technol. 16 656
Google Scholar
[32] Teich T H 1967 Z. Phys. 199 378
Google Scholar
[33] Przybylski A 1962 Z. Phys. 168 504
Google Scholar
[34] Sroka W 1970 Zeitschrift für Naturforschung A 25 1437
[35] Bagheri B, Teunissen J, Ebert U 2020 Plasma Sources Sci. Technol. 29 125021
Google Scholar
[36] Levko D, Pachuilo M, Raja L L 2017 J. Phys. D: Appl. Phys. 50 354004
Google Scholar
[37] Zhu Y F, Starikovskaia S 2018 Plasma Sources Sci. Technol. 27 124007
Google Scholar
[38] Peng B F, Jiang N, Zhu Y F, Wu Y 2024 Plasma Sources Sci. Technol. 33 045018
Google Scholar
[39] Itikawa database, www. lxcat. net [2024-05-19]
[40] IST-Lisbon database, www. lxcat. net [2024-05-19]
[41] Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722
Google Scholar
[42] Bogaerts A, Wang W Z, Berthelot A, Guerra V 2016 Plasma Sources Sci. Technol. 25 055016
Google Scholar
[43] Qian M Y, Zhong W S, Kang J S, Liu S Q, Ren C S, Zhang J L, Wang D Z 2020 Jpn. J. Appl. Phys. 59 066003
Google Scholar
[44] Chen Y L, Peng Y, Qian M Y, Liu S Q, Zhang J L, Wang D Z 2022 Jpn. J. Appl. Phys. 61 086001
Google Scholar
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