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In this paper, the effect of pre-ionization on the small-gap and large-gap direct-current glow discharge at atmospheric pressure are investigated based on a two-dimensional self-consistent fluid model. For both the discharges, the results show that with the enhancement of pre-ionization, the charged particle distribution gradually shifts toward the cathode along the discharge direction, making the cathode fall zone shrink continuously. The width of the positive column region, negative glow space, and cathode fall zone continuously extend along the vertical discharge direction, and the distribution of electron density and ion density are more uniform. For the electric field, with the enhancement of pre-ionization, the longitudinalal component distribution of the electric field in the cathode fall zone gradually contracts toward the cathode, and the overall electric field near the cathode decreases and becomes more uniformly distributed. The transverse component distribution of the electric field gradually decreases and shrinks toward the wall. The overall electron temperature in the discharge space decreases with the enhancement of the pre-ionization level, and the electron temperature distribution in the cathode fall zone gradually shrinks toward the cathode. In addition, the overall potential of the discharge space also decreases. The introduction of pre-ionization significantly reduces the maintaining voltage and discharge power of the direct-current glow discharge. Furthermore, the potential drop in the small-gap discharge is always concentrated in the cathode fall zone as the pre-ionization increases, while the potential drop in the large-gap discharge is gradually shifted from the cathode fall zone to the positive column region. This simulation shows that the pre-ionization not only effectively enhances the discharge uniformity, but also largely reduces the maintaining voltage and energy consumption of the direct-current glow discharge. This work is an important guideline for further optimizing the electrode configuration and the operating parameters of the plasma source.
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Keywords:
- pre-ionization /
- fluid model /
- direct-current glow discharge
[1] Hansen L, Kohlmann N, Kienle L, Kersten H 2023 Thin Solid Films 765 139633
Google Scholar
[2] Marcus R K, Hoegg E D, Hall K A, Williams T J, Koppenaal D W 2021 Mass Spec. Rev. 42 652
Google Scholar
[3] Zheng P C, Luo Y J, Wang J M, Yang Y, Hu Q, Mao X F, Lai C H 2022 Microchem. J. 172 106883
Google Scholar
[4] Ibrahim J, Al-Bataineh S A, Michelmore A, Whittle J D 2021 Plasma Chem. Plasma P. 41 47
Google Scholar
[5] Schoenbach K H, Becker K 2016 Eur. Phys. J. D 70 29
Google Scholar
[6] Wanten B, Maerivoet S, Vantomme C, Slaets J, Trenchev G, Bogaerts A 2022 J. CO2 Util. 56 101869
Google Scholar
[7] Stolárik T, Henselová M, Martinka M, Novák O, Zahoranová A, Černák M 2015 Plasma Chem. Plasma P. 35 659
Google Scholar
[8] 刘定新, 何桐桐, 张浩 2019 高电压技术 45 14
Google Scholar
Liu D X, He T T, Zhang H 2019 High Voltage Engineering 45 14
Google Scholar
[9] Lei B Y, Xu B P, Wang J, Mao X L, Li J, Wang Y S, Zhao W, Duan Y X, Zorba V, Tang J 2023 Cell Rep. Phys. Sci. 4 101267
Google Scholar
[10] 朱海龙, 师玉军, 王嘉伟, 张志凌, 高一宁, 张丰博 2022 物理学报 71 145201
Google Scholar
Zhu H L, Shi Y J, Wang J W, Zhang Z L, Gao Y N, Zhang F B 2022 Acta Phys. Sin. 71 145201
Google Scholar
[11] 李成榕, 王新新, 詹花茂, 张贵新 2003 高压电器 39 4
Google Scholar
Li C R, Wang X X, Zhan H M, Zhang G X 2003 High Voltage Apparatus 39 4
Google Scholar
[12] Staack D, Farouk B, Gutsol A, Fridman A 2005 Plasma Sources Sci. Technol. 14 700
Google Scholar
[13] 王艳辉, 王德真 2003 物理学报 52 1694
Google Scholar
Wang Y H, Wang D Z 2003 Acta Phys. Sin. 52 1694
Google Scholar
[14] 齐兵, 田晓, 王静, 王屹山, 司金海, 汤洁 2022 物理学报 71 245202
Google Scholar
Qi B, Tian X, Wang J, Wang Y S, Si J H, Tang J 2022 Acta Phys. Sin. 71 245202
Google Scholar
[15] Massines F, Gherardi N, Naude N, Segur P 2009 Eur. Phys. J. Appl. Phys. 47 22805
Google Scholar
[16] Sremački I, Gromov M, Leys C, Morent R, Snyders R, Nikiforov A 2020 Plasma Process. Polym. 17 1900191
Google Scholar
[17] Mohamed A A H, Kolb J F, Schoenbach K H 2010 Eur. Phys. J. D 60 517
Google Scholar
[18] Rathore K, Wakim D, Chitre A, Staack D 2020 Plasma Sources Sci. Technol. 29 055011
Google Scholar
[19] Hansen L, Kohlmann N, Schürmann U, Kienle L, Kersten H 2022 Plasma Sources Sci. Technol. 31 035013
Google Scholar
[20] Bieniek M S, Hasan M I 2022 Phys. Plasmas 29 034503
Google Scholar
[21] Tochikubo F, Shirai N, Uchida S 2011 Appl. Phys. Express 4 056001
Google Scholar
[22] Saifutdinov A I 2021 J. Appl. Phys. 129 093302
Google Scholar
[23] Wang Q, Economou D J, Donnelly V M 2006 J. Appl. Phys. 100 023301
Google Scholar
[24] 齐冰, 任春生, 马腾才, 王友年, 王德真 2006 物理学报 55 331
Google Scholar
Qi B, Ren C S, Ma T C, Wang Y N, Wang D Z 2006 Acta Phys. Sin. 55 331
Google Scholar
[25] Tang J, Li S B, Zhao W, Wang Y S, Duan Y X 2012 Appl. Phys. Lett. 100 253505
Google Scholar
[26] Li X M, Tang J, Zhan X F, Yuan X, Zhao Z J, Yan Y Y, Duan Y X 2013 Appl. Phys. Lett. 103 033519
Google Scholar
[27] Jiang W M, Tang J, Wang Y S, Zhao W, Duan Y X 2014 Appl. Phys. Lett. 104 013505
Google Scholar
[28] Li J, Wang J, Lei B Y, Zhang T Y, Tang J, Wang Y S, Zhao W, Duan Y X 2020 Adv. Sci. 7 1902616
Google Scholar
[29] Sasaki K, Hosoda R, Shirai N 2020 Plasma Sources Sci. Technol. 29 085012
Google Scholar
[30] 王晓臣, 王宁会, 李国峰 2007 高电压技术 33 2
Google Scholar
Wang X C, Wang N H, Li G F 2007 High Voltage Engineering 33 2
Google Scholar
[31] Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722
Google Scholar
[32] Laca M, Kaňka A, Schmiedt L, Hrachová V, Morávek M J 2019 Contrib. Plasma Phys. 59 e201800190
Google Scholar
[33] Park G, Lee H, Kim G, Lee J K 2008 Plasma Process Polym. 5 569
Google Scholar
[34] Wang Y H, Wang D Z 2004 Chin. Phys. Lett. 21 2234
Google Scholar
[35] Kong M G, Xu T D 2003 IEEE Trans. Plasma Sci. 31 7
Google Scholar
[36] Yuan X, Raja L L 2003 IEEE Trans. Plasma Sci. 31 495
Google Scholar
[37] 张百灵, 王宇天, 李益文, 樊昊, 高岭, 段成铎 2016 高电压技术 42 7
Google Scholar
Zhang B L, Wang Y T, Li Y W, Fan H, Gao L, Duan C D 2016 High Voltage Engineering 42 7
Google Scholar
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图 1 模型示意图
Figure 1. Schematic diagram of the simulation model.
图 2 短间隙放电中不同预电离下电子密度(a)和离子密度(b)的空间分布
Figure 2. Spatial distributions of electron densities (a) and ion densities (b) at different pre-ionization in the small-gap discharge.
图 3 不同预电离下带电粒子密度的空间分布 (a)正柱区空间分布; (b)正柱区空间分布的放大图; (c) y = 0.5 mm处电子密度峰值的空间分布; (d) y = 0.5 mm处离子密度峰值的空间分布
Figure 3. Spatial distributions of charged particles densities under different pre-ionization: (a) Spatial distributions of the positive column region; (b) enlarged view of spatial distributions of the positive column region; (c) spatial distributions at the peak of electron density at y = 0.5 mm; (d) spatial distributions at the peak of ion density at y = 0.5 mm.
图 4 短间隙放电中不同预电离下, 电场的空间分布 (a)纵向分量; (b)横向分量
Figure 4. Spatial distributions of electric field at different pre-ionization in the small-gap discharge: (a) Longitudinal component; (b) transverse component.
图 5 (a) 不同预电离下, 阴极处电场纵向分量的空间分布; (b)不同预电离下, 电场横向分量峰值处的空间分布
Figure 5. (a) Spatial distributions of longitudinal component of the electric field in the cathode under different pre-ionization; (b) spatial distributions at the peak of transverse component of the electric field under different pre-ionization.
图 6 不同预电离下, 电势(a)和电子温度(b)的空间分布
Figure 6. Spatial distributions of potential (a) and electron temperature (b) at different pre-ionization.
图 7 不同预电离下 (a) x = 0.8 mm处的电势空间分布; (b) y = 0.5 mm处电子温度峰值处的空间分布; (c)维持电压和放电电流的变化; (d)放电功率的变化
Figure 7. Under different pre-ionization: (a) Spatial distribution of potential at x = 0.8 mm; (b) spatial distributions at the peak of the electron temperature at y = 0.5 mm; (c) variations of sustaining voltage, discharge current; (d) variations of discharge power.
图 8 长间隙放电中不同预电离下, 电子密度(a)和离子密度(b)的空间分布
Figure 8. Spatial distributions of electron densities (a) and ion densities (b) at different pre-ionization in the large-gap discharge.
图 9 不同预电离下, 带电粒子密度的空间分布 (a)正柱区的空间分布; (b)正柱区空间分布的放大图; (c) y = 0.5 mm电子密度峰值的空间分布; (d) y = 0.5 mm离子密度峰值的空间分布
Figure 9. Spatial distributions of charged particles densities under different pre-ionization: (a) Spatial distributions of the positive column region; (b) enlarged view of spatial distributions of the positive column region; (c) spatial distributions at the peak of electron density at y = 0.5 mm; (d) spatial distributions at the peak of ion density at y = 0.5 mm.
图 10 长间隙放电中不同预电离下, 电场的空间分布 (a)纵向分量; (b)横向分量
Figure 10. Spatial distributions of electric field at different pre-ionization in the large-gap discharge: (a) Longitudinal component; (b) transverse component.
图 11 (a) 不同预电离下, 阴极处电场纵向分量的空间分布; (b)不同预电离下, 电场横向分量峰值处的空间分布
Figure 11. (a) Spatial distributions of longitudinal component of the electric field in the cathode under different pre-ionization; (b) spatial distributions at the peak of transverse component of the electric field under different pre-ionization.
图 12 不同预电离下, 电势(a)和电子温度(b)的空间分布
Figure 12. Spatial distributions of potential (a) and electron temperature (b) at different pre-ionization.
图 13 不同预电离下 (a) x = 8 mm处的电势空间分布; (b) y = 0.5 mm电子温度峰值处的空间分布; (c)维持电压、放电电流和(d)放电功率的变化
Figure 13. Under different pre-ionization: (a) Spatial distribution of potential at x = 8 mm; (b) spatial distributions at the peak of the electron temperature at y = 0.5 mm; (c) variations of sustaining voltage, discharge current and (d) discharge power.
表 1 模型中的化学反应
Table 1. Chemical reactions in the model.
No. Reaction Rate constant/
(cm–3·s–1)Ref. 1 e+He → e+He f(E/N) [31] 2 e+He → e+He* f(E/N) [32] 3 e+He → 2e+He+ f(E/N) [32] 4 2e+He+ → He*+e 7.1$ \times $10–20a) [32] 5 2e+$ {\text{He}}_{2}^{+} $ → 2He+e 2.0$ \times $10–20a) [32] 6 2e+$ {\text{He}}_{2}^{+} $ → He+He*+e 2.8$ \times $10–20a) [33] 7 e+He+$ {\text{He}}_{2}^{+} $ → 3He 2.0$ \times $10–27a) [33] 8 e+He* → 2e+He+ 1.28$ \times $10–7$ {T}_{{\mathrm{e}}}^{0.6} $
exp(–4.78/$ {T}_{{\mathrm{e}}} $)[33] 9 e+$ {\text{He}}_{2}^{+} $ → He*+He 1$ \times $10–8 [33] 10 He*+e → He+e 2$ \times $10–10 [33] 11 2e+$ {\text{He}}_{2}^{+} $ → 2He*+e 6.18$ \times $10–39$ {T}_{{\mathrm{e}}}^{4.4} $a) [33] 12 e+He+$ {\text{He}}_{2}^{+} $ → He*+2He 5.0$ \times $10–27a) [35] 13 e+$ {\text{He}}_{2}^{+} $ → $ {\text{He}}_{2}^{\text{*}} $ 5.0$ \times $10–16 [35] 14 e+He+$ {\text{He}}_{2}^{+} $ → $ {\text{He}}_{2}^{\text{*}} $+He 5.0$ \times $10–27a) [35] 15 e+$ {\text{He}}_{2}^{\text{*}} $ → 2e+$ {\text{He}}_{2}^{+} $ 3.8$ \times $10–9 [36] 16 e+He+ He+ → He*+He 1.0$ \times $10–27a) [36] 17 2e+$ {\text{He}}_{2}^{+} $ → $ {\text{He}}_{2}^{\text{*}} $+e 7.1$ \times $10–20a) [35] 18 2He+He+ → He+$ {\text{He}}_{2}^{+} $ 6.5$ \times $10–32a) [32] 19 He*+He → 2He+$ h\nu $ 6.0$ \times $10–15 [32] 20 He*+He* → e+$ {\text{He}}_{2}^{+} $ 2.0$ \times $10–9 [34] 21 He*+He* → e+He+He+ 2.9$ \times $10–9 [35] a) Rate constant is in cm6·s–1. 
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[1] Hansen L, Kohlmann N, Kienle L, Kersten H 2023 Thin Solid Films 765 139633
Google Scholar
[2] Marcus R K, Hoegg E D, Hall K A, Williams T J, Koppenaal D W 2021 Mass Spec. Rev. 42 652
Google Scholar
[3] Zheng P C, Luo Y J, Wang J M, Yang Y, Hu Q, Mao X F, Lai C H 2022 Microchem. J. 172 106883
Google Scholar
[4] Ibrahim J, Al-Bataineh S A, Michelmore A, Whittle J D 2021 Plasma Chem. Plasma P. 41 47
Google Scholar
[5] Schoenbach K H, Becker K 2016 Eur. Phys. J. D 70 29
Google Scholar
[6] Wanten B, Maerivoet S, Vantomme C, Slaets J, Trenchev G, Bogaerts A 2022 J. CO2 Util. 56 101869
Google Scholar
[7] Stolárik T, Henselová M, Martinka M, Novák O, Zahoranová A, Černák M 2015 Plasma Chem. Plasma P. 35 659
Google Scholar
[8] 刘定新, 何桐桐, 张浩 2019 高电压技术 45 14
Google Scholar
Liu D X, He T T, Zhang H 2019 High Voltage Engineering 45 14
Google Scholar
[9] Lei B Y, Xu B P, Wang J, Mao X L, Li J, Wang Y S, Zhao W, Duan Y X, Zorba V, Tang J 2023 Cell Rep. Phys. Sci. 4 101267
Google Scholar
[10] 朱海龙, 师玉军, 王嘉伟, 张志凌, 高一宁, 张丰博 2022 物理学报 71 145201
Google Scholar
Zhu H L, Shi Y J, Wang J W, Zhang Z L, Gao Y N, Zhang F B 2022 Acta Phys. Sin. 71 145201
Google Scholar
[11] 李成榕, 王新新, 詹花茂, 张贵新 2003 高压电器 39 4
Google Scholar
Li C R, Wang X X, Zhan H M, Zhang G X 2003 High Voltage Apparatus 39 4
Google Scholar
[12] Staack D, Farouk B, Gutsol A, Fridman A 2005 Plasma Sources Sci. Technol. 14 700
Google Scholar
[13] 王艳辉, 王德真 2003 物理学报 52 1694
Google Scholar
Wang Y H, Wang D Z 2003 Acta Phys. Sin. 52 1694
Google Scholar
[14] 齐兵, 田晓, 王静, 王屹山, 司金海, 汤洁 2022 物理学报 71 245202
Google Scholar
Qi B, Tian X, Wang J, Wang Y S, Si J H, Tang J 2022 Acta Phys. Sin. 71 245202
Google Scholar
[15] Massines F, Gherardi N, Naude N, Segur P 2009 Eur. Phys. J. Appl. Phys. 47 22805
Google Scholar
[16] Sremački I, Gromov M, Leys C, Morent R, Snyders R, Nikiforov A 2020 Plasma Process. Polym. 17 1900191
Google Scholar
[17] Mohamed A A H, Kolb J F, Schoenbach K H 2010 Eur. Phys. J. D 60 517
Google Scholar
[18] Rathore K, Wakim D, Chitre A, Staack D 2020 Plasma Sources Sci. Technol. 29 055011
Google Scholar
[19] Hansen L, Kohlmann N, Schürmann U, Kienle L, Kersten H 2022 Plasma Sources Sci. Technol. 31 035013
Google Scholar
[20] Bieniek M S, Hasan M I 2022 Phys. Plasmas 29 034503
Google Scholar
[21] Tochikubo F, Shirai N, Uchida S 2011 Appl. Phys. Express 4 056001
Google Scholar
[22] Saifutdinov A I 2021 J. Appl. Phys. 129 093302
Google Scholar
[23] Wang Q, Economou D J, Donnelly V M 2006 J. Appl. Phys. 100 023301
Google Scholar
[24] 齐冰, 任春生, 马腾才, 王友年, 王德真 2006 物理学报 55 331
Google Scholar
Qi B, Ren C S, Ma T C, Wang Y N, Wang D Z 2006 Acta Phys. Sin. 55 331
Google Scholar
[25] Tang J, Li S B, Zhao W, Wang Y S, Duan Y X 2012 Appl. Phys. Lett. 100 253505
Google Scholar
[26] Li X M, Tang J, Zhan X F, Yuan X, Zhao Z J, Yan Y Y, Duan Y X 2013 Appl. Phys. Lett. 103 033519
Google Scholar
[27] Jiang W M, Tang J, Wang Y S, Zhao W, Duan Y X 2014 Appl. Phys. Lett. 104 013505
Google Scholar
[28] Li J, Wang J, Lei B Y, Zhang T Y, Tang J, Wang Y S, Zhao W, Duan Y X 2020 Adv. Sci. 7 1902616
Google Scholar
[29] Sasaki K, Hosoda R, Shirai N 2020 Plasma Sources Sci. Technol. 29 085012
Google Scholar
[30] 王晓臣, 王宁会, 李国峰 2007 高电压技术 33 2
Google Scholar
Wang X C, Wang N H, Li G F 2007 High Voltage Engineering 33 2
Google Scholar
[31] Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722
Google Scholar
[32] Laca M, Kaňka A, Schmiedt L, Hrachová V, Morávek M J 2019 Contrib. Plasma Phys. 59 e201800190
Google Scholar
[33] Park G, Lee H, Kim G, Lee J K 2008 Plasma Process Polym. 5 569
Google Scholar
[34] Wang Y H, Wang D Z 2004 Chin. Phys. Lett. 21 2234
Google Scholar
[35] Kong M G, Xu T D 2003 IEEE Trans. Plasma Sci. 31 7
Google Scholar
[36] Yuan X, Raja L L 2003 IEEE Trans. Plasma Sci. 31 495
Google Scholar
[37] 张百灵, 王宇天, 李益文, 樊昊, 高岭, 段成铎 2016 高电压技术 42 7
Google Scholar
Zhang B L, Wang Y T, Li Y W, Fan H, Gao L, Duan C D 2016 High Voltage Engineering 42 7
Google Scholar
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