Simulation on complex dynamics of hollow cathode discharge in argon

He Shou-Jie; Zhou Jia; Qu Yu-Xiao; Zhang Bao-Ming; Zhang Ya; Li Qing

doi:10.7498/aps.68.20190734

Abstract

In this paper, the dynamics of hollow cathode discharge in argon is simulated by fluid model. In the numerical model considered are 31 reaction processes, including direct ground state ionization, ground state excitation, stepwise ionization, Penning ionization, de-excitation, two-body collision, three-body collision, radiation transition, elastic collision, and electron-ion recombination reaction. The electron density, Ar⁺ density, Ar^4s, Ar^4p, Ar^3dparticle density, electric potential and electric field intensity are calculated. At the same time, the contributions of different reaction mechanisms for the generation and consumption of electron, Ar^4s and Ar^4pare simulated. The results indicate that hollow cathode effect exists in the discharge, and the Ar^4s density is much higher than electron density. The penning ionization 2Ar^4s→ Ar⁺ + Ar⁺ + e and stepwise ionization involving Ar^4s make important contributions to the generation of new electrons and the balance of electron energy. In particular, the penning ionization reaction 2Ar^4s→ Ar₂⁺ + e, which is generally ignored in previous simulation, also has an significant influence on electron generation. The spatial distribution of excited state argon atomic density is the result of the balance between the formation and consumption of various particles during discharge. Radiation reaction Ar^4p→ Ar^4s + hν is the main source of Ar^4s generation and the main way to consume Ar^4p. Ar^4s + e →Ar^4p + e is the main way of Ar^4s consumption and Ar^4p production. The simulation results also show that the Ar^4pdensity distribution can better reflect the optical characteristics in the hollow cathode discharge.

Keywords:

Authors and contacts

Hebei Key Laboratory of Optic-electronic Information and Materials, College of Physics Science and Technology, Hebei University, Baoding 071002, China

Corresponding author: He Shou-Jie, heshouj@hbu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11205046, 51777051), the Science Foundation of Hebei Province, China (Grant No. A2016201025), and the Post-Graduate’s Innovation Fund Project of Hebei University, China (Grant No. hbu2019ss078).

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References

[1]	欧阳吉庭, 张宇, 秦宇 2016 高电压技术 42 673 Google Scholar Ouyang J T, Zhang Y, Qin Y 2016 High Volt. Eng. 42 673 Google Scholar
[2]	Hou X Y, Fu Y Y, Wang H, Zou X B, Luo H Y, Wang X X 2017 Phys. Plasma 24 083506 Google Scholar
[3]	Fu Y Y, Verboncoeur J P, Christlieb A J 2017 Phys. Plasmas 24 103514 Google Scholar
[4]	Baguer N, Bogaerts A, Donko Z, Gijbels R, Sadeghi N 2005 J. Appl. Phys. 97 123305 Google Scholar
[5]	Ferreira N P, Strauss J A, Human H G C 1982 Spectrochimica Acta Part B 37 273 Google Scholar
[6]	Slevin P J, Harrison W W 1975 Appl. Spectrosc. Rev. 10 201 Google Scholar
[7]	Roberto M, Smith H B, Verboncoeur J P 2003 IEEE Trans. Plasma- Sci. 31 1292 Google Scholar
[8]	Wiese W L, Braulk J W, Danzmann K, Kock M 1989 Phys. Rev. A 39 2461 Google Scholar
[9]	Miclea M, Kunze K, Heitmann U, Florek S, Franzke J, Niemax K 2005 J. Phys. D: Appl. Phys. 38 1709 Google Scholar
[10]	Penache C, Miclea M, Bräuning-Demian A, Hohn O, Schössler S, T Jahnke T, Niemax K, Schmidt-Böcking H 2002 Plasma Sources Sci. Technol. 11 476 Google Scholar
[11]	张增辉, 张冠军, 邵先军, 常正实, 彭兆裕, 许昊 2012 物理学报 24 245205 Google Scholar Zhang Z H, Zhang G J, Shao X J, Chang Z S, Peng Z Y, Xu H 2012 Acta Phys. Sin. 24 245205 Google Scholar
[12]	Lazzaroni C, Chabert P 2016 Plasma Sources Sci. Technol. 25 065015 Google Scholar
[13]	Eggarter E 1975 J. Chem. Phys. 62 833 Google Scholar
[14]	Eduardo C M, Moisan M 2010 Spectrochimica Acta B 65 199 Google Scholar
[15]	Lymberopoulos D P, Economou D J 1993 J. Appl. Phys. 73 3668 Google Scholar
[16]	Shon J W, Kushner M J 1994 J. Appl. Phys. 75 1883 Google Scholar
[17]	Gudmundsson J T, Thorsteinsson E G 2007 Plasma Sources Sci. Technol. 16 399 Google Scholar
[18]	Li Z, Zhao Z, Li X H 2012 Phys. Plasma 19 033510 Google Scholar
[19]	Epstein I L, Gavrilovic M, Jovicevic S, Konjevic N, Lebedev Y A, Tatarinov A V 2014 Eur. Phys. J. D 68 334 Google Scholar
[20]	Shkurenkov I A, Mankelevich Y A, Rakhimova T V 2009 Phys. Rev. E 79 046406 Google Scholar
[21]	Moravej M, Yang X, Barankin M, Penelon J, Babayan S E, Hicks R F 2006 Plasma Source Sci. Tech. 15 204 Google Scholar
[22]	Annemie B, Renaat G, Wim G 1999 Jpn. J. Appl. Phys. 38 4404 Google Scholar
[23]	夏广庆, 薛伟华, 陈茂林, 朱雨, 朱国强 2011 物理学报 60 015201 Google Scholar Xia G Q, Xue W H, Chen M L, Zhu Y, Zhu G Q 2011 Acta Phys. Sin. 60 015201 Google Scholar
[24]	何寿杰, 张钊, 赵雪娜, 李庆 2017 物理学报 66 055101 Google Scholar He S J, Zhang Z, Zhao Xue N, Li Q 2017 Acta Phys. Sin. 66 055101 Google Scholar
[25]	付洋洋, 罗海云, 邹晓兵, 王强, 王新新 2014 物理学报 63 095206 Google Scholar Fu Y Y, Luo H Y, Zou X B, Wang Q, Wang X X 2014 Acta Phys. Sin. 63 095206 Google Scholar
[26]	Fu Y Y, Verboncoeur J P, Christlieb A J, Wang X X 2017 Phys. Plasmas 24 083516 Google Scholar
[27]	Hagelaar G J, Hoog F J, Kroesen G M 2000 Phys. Rev. E 62 1452
[28]	徐学基, 诸定昌 1996 气体放电物理 (上海: 复旦大学出版社) Xue X J, Zhu D C 1996 Physics of Gas Discharge (Shanghai: Fudan University Press) (in Chinese)
[29]	Fu Y Y, Krek J, Parsry G M, Verboncoeur J P 2018 Phys. Plasma 25 033505 Google Scholar
[30]	Bogaerts A, Guenard R D, Smith B W 1997 Spectrochimica Acta Part B 52 219 Google Scholar
[31]	Uzelac N I, Leis F 1992 Spectrochim. Acta B 47 877 Google Scholar
[32]	Strauss J A, Ferreira N P, Human H G C 1982 Spectrochim Acta B 37 273
[33]	Bogaerts A, Gijbels R 1995 Phys. Rev. A 52 3743 Google Scholar
[34]	Bánó G, Donkó Z 2012 Plasma Sources Sci. Technol. 21 035011 Google Scholar
[35]	Bogaerts A, Gijbels R 2002 J. Appl. Phys. 92 6408 Google Scholar
[36]	Kutasi K, Donkó Z 2000 J. Phys. D: Appl. Phys. 33 1081 Google Scholar
[37]	Bogaerts A, Gijbels R, Vlcek J 1998 Spectrochimica Acta Part B 53 1517 Google Scholar

Cited By

图 1 圆筒形空心阴极放电单元截面图

Figure 1. Schematic of cylindrical hollow cathode discharge.

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图 2 电势分布图

Figure 2. Distribution of electric potential.

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图 3 带电粒子密度分布图　(a) 电子; (b) Ar⁺

Figure 3. Distribution of charged particle density: (a) Electron; (b) Ar⁺.

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图 4 激发态原子密度分布图　(a) Ar^4s; (b) Ar^4p; (c) Ar^3d

Figure 4. Distribution of excited state atoms: (a) Ar^4s; (b) Ar^4p; (c) Ar^3d.

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图 5 不同电离速率分布图　(a) G1基态电离; (b) G7潘宁电离; (c) G10潘宁电离; (d) G5分步电离

Figure 5. Different ionization rates: (a) G1 ground state ionization; (b) G7 Penning ionization; (c) G10 Penning ionization; (d) G5 stepwise ionization

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图 6 不同电离速率一维径向分布图(x = 1.2 mm)

Figure 6. Radial distribution of different ionizations at x = 1.2 mm

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图 7 平均电子能量和电子密度一维径向分布图(x = 1.2 mm)

Figure 7. Radial distribution of averaged electron energy and electron density at x = 1.2 mm.

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图 8 氩原子Ar^4s能级生成速率　(a) G2, 直接激发; (b) G20, 氩原子Ar^4p能级辐射跃迁

Figure 8. Production rate of Ar^4s: (a) G2, direct excitation; (b) G20, radiation transition from Ar^4p.

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图 9 生成4s能级的径向分布图

Figure 9. Radial production rate of Ar^4s.

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图 10 消耗Ar^4s能级的反应速率　(a) G17, Ar^4s + e → Ar^3d + e; (b) G18, Ar^4s + e → Ar^4p + e

Figure 10. The Ar^4s consuming rates of different reactions: (a) G17, Ar^4s + e → Ar^3d + e; (b) G18, Ar^4s + e → Ar^4p + e.

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图 11 消耗Ar^4s能级的反应速率一维分布图

Figure 11. Radial distribution of the Ar^4s consuming rates.

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图 12 激发态氩原子Ar^4p生成速率　(a) G3, Ar + e → Ar^4p + e; (b) G21, Ar^3d→ Ar^4p

Figure 12. The Ar^4p production rates of different reactions: (a) G3, Ar + e → Ar^4p + e; (b) G21, Ar^3d→ Ar^4p.

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图 13 Ar^4p生成速率的径向分布图

Figure 13. Radial distribution of the production rates of Ar^4p.

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图 14 消耗Ar^4p能级的反应速率一维分布图

Figure 14. Radial distribution of the Ar^4p consuming rates.

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表 1 放电反应类型

Table 1. Discharge reactions in the model.

反应标号	反应方程	反应标号	反应方程
G1	Ar + e → Ar⁺ + 2e^[12]	G17	Ar^4s + e → Ar^3d + e^[16]
G2	Ar + e → Ar^4s + e^[13]	G18	Ar^4s + e → Ar^4p + e^[12]
G3	Ar + e → Ar^4p + e^[13]	G19	Ar^4p + e → Ar^4s + e^[12]
G4	Ar + e → Ar^3d + e^[13]	G20	Ar^4p → Ar^4s + hν^[17]
G5	Ar^4s + e → Ar⁺ + 2e^[14]	G21	Ar^3d → Ar^4p^[16]
G6	Ar^4p + e → Ar⁺ + 2e^[14]	G22	Ar⁺ + 2e → Ar + e^[14]
G7	2Ar^4s → Ar⁺ + Ar + e^[15]	G23	Ar⁺ + e → Ar^4s^[12]
G8	2Ar^4p → Ar⁺ + Ar + e^[16]	G24	Ar⁺ + 2e → Ar^4s + e^[12]
G9	2Ar^4s → Ar₂⁺ + e^[17]	G25	Ar₂⁺ + e → 2Ar^[19]
G10	Ar^4s + Ar → 2Ar^[18]	G26	Ar₂⁺ + e → Ar⁺ + Ar + e^[20]
G11	Ar^4s + 2Ar → 3Ar^[18]	G27	Ar₂⁺ + e → Ar^4s + Ar^[16]
G12	2Ar + Ar⁺ → Ar₂⁺ + Arr^[16]	G28	Ar₂⁺ + e → 2Ar^4s^[21]
G13	Ar^4s + 2Ar → Ar₂ + Ar^[15]	G29	Ar₂⁺ + e → Ar^4p + Ar^[16]
G14	Ar^4s + e → Ar + e^[12]	G30	Ar₂⁺ + e → Ar^3d + Ar^[16]
G15	Ar^4s → Ar + hν^[12]	G31	Ar + e → Ar + e^[22]
G16	Ar^4p +e → Ar + e^[12]

DownLoad: CSV

表 2 不同电离反应速率的平均值

Table 2. Average values of the different ionization rates in the discharge region.

反应标号	反应方程	速率平均值/cm^–3·s^–1
G1	Ar + e → Ar⁺ + 2e	2.5 × 10¹⁷
G5	Ar^4s + e → Ar⁺ + 2e	2.6 × 10¹⁶
G6	Ar^4p + e → Ar⁺ + 2e	1.1 × 10¹⁵
G7	2Ar^4s→ Ar⁺ + Ar + e	3.9 × 10¹⁶
G8	2Ar^4p→ Ar⁺ + Ar + e	2.9 × 10¹²
G10	2Ar^4s→ Ar₂⁺ + e	3.8 × 10¹⁶

DownLoad: CSV

表 3 Ar^4s生成速率平均值

Table 3. Average values of the different production rates of Ar^4s in the discharge region.

反应标号	反应方程	源项平均值/cm^–3·s^–1
G2	Ar + e → Ar^4s + e	1.6 × 10¹⁷
G19	Ar^4p + e → Ar^4s + e	9.1 × 10¹⁵
G20	Ar^4p→ Ar^4s + hν	11.8 × 10¹⁷
G24	Ar⁺ + 2e → Ar^4s + e	55.3
G23	Ar + e → Ar^4s	4.4 × 10¹²
G27	Ar₂⁺ + e → Ar^4s + Ar	4.3 × 10¹⁵
G28	Ar₂⁺ + e → 2Ar^4s	3.9 × 10¹⁴

DownLoad: CSV

表 4 消耗Ar^4s的不同反应速率的平均值

Table 4. Average values of the different consuming rates of Ar^4s in the discharge region.

反应标号	反应方程	源项平均值/cm^–3·s^–1
G5	Ar^4s + e → Ar⁺ + 2e	2.6 × 10¹⁶
G7	2Ar^4s → Ar⁺ +Ar + e	7.9 × 10¹⁶
G9	Ar^4s + Ar → 2Ar	3.0 × 10¹⁵
G10	2Ar^4s → Ar₂⁺ + e	7.6 × 10¹⁶
G11	Ar^4s + 2Ar → 3Ar	4.5 × 10¹⁵
G13	Ar^4s + 2Ar → Ar₂ + Ar	3.5 × 10¹⁶
G14	Ar^4s + e → Ar + e	1.2 × 10¹⁵
G15	Ar^4s → Ar + hν	1.9 × 10¹⁷
G17	Ar^4s + e → Ar^3d + e	1.2 × 10¹⁷
G18	Ar^4s + e → Ar^4p + e	8.2 × 10¹⁷

DownLoad: CSV

表 5 Ar^4p生成速率平均值

Table 5. Average values of the different production rates of Ar^4p in the discharge region.

反应标号	反应方程	源项平均值/cm^–3·s^–1
G3	Ar + e → Ar^4p + e	2.2 × 10¹⁷
G18	Ar^4s + e → Ar^4p + e	8.2 × 10¹⁷
G21	Ar^3d → Ar^4p	1.4 × 10¹⁷
G29	Ar₂⁺ + e → Ar^4p + Ar	4.3 × 10¹⁴

DownLoad: CSV

表 6 消耗Ar^4p的不同反应速率的平均值

Table 6. Average values of the different consuming rates of Ar^4p in the discharge region

反应标号	反应方程	源项平均值/cm^–3·s^–1
G6	Ar^4p + e→Ar⁺ + 2e	1.1 × 10¹⁵
G8	2Ar^4p→Ar⁺ + Ar + e	5.8 × 10¹²
G16	Ar^4p +e→Ar + e	1.3 × 10¹³
G19	Ar^4p + e→Ar^4s + e	9.1 × 10¹⁵
G20	Ar^4p→Ar^4s + hν	11.8 × 10¹⁷

DownLoad: CSV

[1]	欧阳吉庭, 张宇, 秦宇 2016 高电压技术 42 673 Google Scholar Ouyang J T, Zhang Y, Qin Y 2016 High Volt. Eng. 42 673 Google Scholar
[2]	Hou X Y, Fu Y Y, Wang H, Zou X B, Luo H Y, Wang X X 2017 Phys. Plasma 24 083506 Google Scholar
[3]	Fu Y Y, Verboncoeur J P, Christlieb A J 2017 Phys. Plasmas 24 103514 Google Scholar
[4]	Baguer N, Bogaerts A, Donko Z, Gijbels R, Sadeghi N 2005 J. Appl. Phys. 97 123305 Google Scholar
[5]	Ferreira N P, Strauss J A, Human H G C 1982 Spectrochimica Acta Part B 37 273 Google Scholar
[6]	Slevin P J, Harrison W W 1975 Appl. Spectrosc. Rev. 10 201 Google Scholar
[7]	Roberto M, Smith H B, Verboncoeur J P 2003 IEEE Trans. Plasma- Sci. 31 1292 Google Scholar
[8]	Wiese W L, Braulk J W, Danzmann K, Kock M 1989 Phys. Rev. A 39 2461 Google Scholar
[9]	Miclea M, Kunze K, Heitmann U, Florek S, Franzke J, Niemax K 2005 J. Phys. D: Appl. Phys. 38 1709 Google Scholar
[10]	Penache C, Miclea M, Bräuning-Demian A, Hohn O, Schössler S, T Jahnke T, Niemax K, Schmidt-Böcking H 2002 Plasma Sources Sci. Technol. 11 476 Google Scholar
[11]	张增辉, 张冠军, 邵先军, 常正实, 彭兆裕, 许昊 2012 物理学报 24 245205 Google Scholar Zhang Z H, Zhang G J, Shao X J, Chang Z S, Peng Z Y, Xu H 2012 Acta Phys. Sin. 24 245205 Google Scholar
[12]	Lazzaroni C, Chabert P 2016 Plasma Sources Sci. Technol. 25 065015 Google Scholar
[13]	Eggarter E 1975 J. Chem. Phys. 62 833 Google Scholar
[14]	Eduardo C M, Moisan M 2010 Spectrochimica Acta B 65 199 Google Scholar
[15]	Lymberopoulos D P, Economou D J 1993 J. Appl. Phys. 73 3668 Google Scholar
[16]	Shon J W, Kushner M J 1994 J. Appl. Phys. 75 1883 Google Scholar
[17]	Gudmundsson J T, Thorsteinsson E G 2007 Plasma Sources Sci. Technol. 16 399 Google Scholar
[18]	Li Z, Zhao Z, Li X H 2012 Phys. Plasma 19 033510 Google Scholar
[19]	Epstein I L, Gavrilovic M, Jovicevic S, Konjevic N, Lebedev Y A, Tatarinov A V 2014 Eur. Phys. J. D 68 334 Google Scholar
[20]	Shkurenkov I A, Mankelevich Y A, Rakhimova T V 2009 Phys. Rev. E 79 046406 Google Scholar
[21]	Moravej M, Yang X, Barankin M, Penelon J, Babayan S E, Hicks R F 2006 Plasma Source Sci. Tech. 15 204 Google Scholar
[22]	Annemie B, Renaat G, Wim G 1999 Jpn. J. Appl. Phys. 38 4404 Google Scholar
[23]	夏广庆, 薛伟华, 陈茂林, 朱雨, 朱国强 2011 物理学报 60 015201 Google Scholar Xia G Q, Xue W H, Chen M L, Zhu Y, Zhu G Q 2011 Acta Phys. Sin. 60 015201 Google Scholar
[24]	何寿杰, 张钊, 赵雪娜, 李庆 2017 物理学报 66 055101 Google Scholar He S J, Zhang Z, Zhao Xue N, Li Q 2017 Acta Phys. Sin. 66 055101 Google Scholar
[25]	付洋洋, 罗海云, 邹晓兵, 王强, 王新新 2014 物理学报 63 095206 Google Scholar Fu Y Y, Luo H Y, Zou X B, Wang Q, Wang X X 2014 Acta Phys. Sin. 63 095206 Google Scholar
[26]	Fu Y Y, Verboncoeur J P, Christlieb A J, Wang X X 2017 Phys. Plasmas 24 083516 Google Scholar
[27]	Hagelaar G J, Hoog F J, Kroesen G M 2000 Phys. Rev. E 62 1452
[28]	徐学基, 诸定昌 1996 气体放电物理 (上海: 复旦大学出版社) Xue X J, Zhu D C 1996 Physics of Gas Discharge (Shanghai: Fudan University Press) (in Chinese)
[29]	Fu Y Y, Krek J, Parsry G M, Verboncoeur J P 2018 Phys. Plasma 25 033505 Google Scholar
[30]	Bogaerts A, Guenard R D, Smith B W 1997 Spectrochimica Acta Part B 52 219 Google Scholar
[31]	Uzelac N I, Leis F 1992 Spectrochim. Acta B 47 877 Google Scholar
[32]	Strauss J A, Ferreira N P, Human H G C 1982 Spectrochim Acta B 37 273
[33]	Bogaerts A, Gijbels R 1995 Phys. Rev. A 52 3743 Google Scholar
[34]	Bánó G, Donkó Z 2012 Plasma Sources Sci. Technol. 21 035011 Google Scholar
[35]	Bogaerts A, Gijbels R 2002 J. Appl. Phys. 92 6408 Google Scholar
[36]	Kutasi K, Donkó Z 2000 J. Phys. D: Appl. Phys. 33 1081 Google Scholar
[37]	Bogaerts A, Gijbels R, Vlcek J 1998 Spectrochimica Acta Part B 53 1517 Google Scholar

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Vol. 68, Issue 21 - 2019-11-05

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