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Classical discharge theory (Townsend theory and streamer theory) has limitations in explaining nanosecond pulsed gas discharge. In recent years, the research on nanosecond pulsed gas discharge theory based on the high-energy runaway electrons has attracted extensive attention. But so far, there have been few studies of the generation mechanism of runaway electrons in atmospheric-pressure-air nanosecond pulsed plate-to-plate discharge, which seriously hinders the application and development of nanosecond pulse discharge plasma. In this paper, a one-dimensional implicit particle-in-cell/Monte Carlo collision (PIC/MCC) model is developed to investigate the mechanism of runaway electron generation and breakdown in a 1 mm-long atmospheric-pressure-air gap between the plate electrode and plate electrode driven by a negative nanosecond pulse voltage with an amplitude of 20 kV. The results show that under the influence of space charge dynamic behavior, the electric field enhancement region appears between the plate electrode and plate electrode, so that electrons can satisfy the electron runaway criteria and behaves in the runaway mode. In addition, it is also observed that the pre-ionization effect of the runaway electrons in front of the discharge channel can cause the secondary electron avalanches. As the secondary electrons avalanche and the discharge channel continues to converge, the discharge is guided and accelerated, eventually leading to the breakdown of the air gap. This study further reveals the mechanism of nanosecond pulsed plate-plate discharge, expands the basic theory of nanosecond pulsed gas discharge, and opens up new opportunities for the application and development of nanosecond pulsed discharge plasma.
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Keywords:
- nanosecond pulse discharge /
- runaway electron /
- electric field enhancement /
- pre-ionization
[1] Bogaerts A, Tu X, Whitehead J C, Centi G, Lefferts L, Guaitella O, Azzolina Jury F, Kim H H, Murphy A B, Schneider W F, Nozaki T, Hicks J C, Rousseau A, Thevenet F, Khacef A, Carreon M 2020 J. Phys. D: Appl. Phys. 53 443001
Google Scholar
[2] Wang S, Yang D Z, Zhou R S, Zhou R W, Fang Z, Wang W C, Ostrikov K 2019 Plasma Process. Polym. 17 1900146
Google Scholar
[3] Cai Y K, Lyu L, Lu X P 2021 High Volt. 6 1092
Google Scholar
[4] Bekeschus S, Favia P, Robert E, Woedtke T V 2019 Plasma Process. Polym. 16 1800033
Google Scholar
[5] Huang B D, Zhang C, Zhu W C, Lu X P, Shao T 2021 High Volt. 6 665
Google Scholar
[6] Tang J F, Tang M, Zhou D S, Kang P T, Zhu X M, Zhang C H 2019 Plasma Sci. Technol. 21 044001
Google Scholar
[7] Zhang S, Wang W C, Yang D Z, Yuan H, Zhao Z L, Sun H, Shao T 2019 Spectrochim. Acta A Mol. Biomol. Spectrosc. 207 294
Google Scholar
[8] Shao T, Tarasenko V F, Zhang C, Baksht E K, Zhang D, Erofeev M V, Ren C, Shutko Y V, Yan P 2013 J. Appl. Phys. 113 093301
Google Scholar
[9] Shkurenkov I, Burnette D, Lempert W R, Adamovich I V 2014 Plasma Sources Sci. Technol. 23 065003
Google Scholar
[10] Yatom S, Gleizer J Z, Levko D, Vekselman V, Gurovich V, Hupf E, Hadas Y, Krasik Y E 2011 Europhys. Lett. 96 65001
Google Scholar
[11] Shao T, Wang R X, Zhang C, Yan P 2018 High Volt. 3 14
Google Scholar
[12] Kunhardt E E, Byszewski W W 1980 Phys. Rev. A 21 2069
Google Scholar
[13] Zhang C, Gu J W, Wang R X, Ma H, Yan P, Shao T 2016 Laser Part. Beams 34 43
Google Scholar
[14] Frankel S, Highland V, Sloan T, Dyck O V, Wales W 1966 Nucl. Instrum. Method 44 345
Google Scholar
[15] Bratchikov V B, Gagarinov K A, Kostyrya I D, Tarasenko V F, Tkachev A N, Yakovlenko S I 2007 Tech. Phys. 52 856
Google Scholar
[16] Byszewski W W, Reinhold G 1982 Phys. Rev. A 26 2826
Google Scholar
[17] Kostyrya I D, Tarasenko V F 2015 Plasma Phys. Rep. 41 269
Google Scholar
[18] Tarasenko V F 2020 Plasma Sources Sci. Technol. 29 034001
Google Scholar
[19] Beloplotov D V, Tarasenko V F, Shklyaev V A, Sorokin D A 2021 J. Phys. D: Appl. Phys. 54 304001
Google Scholar
[20] Levko D 2019 J. Appl. Phys. 126 083303
Google Scholar
[21] Babaeva N Y, Zhang C, Qiu J T, Hou X M, Tarasenko V F, Shao T 2017 Plasma Sources Sci. Technol. 26 085008
Google Scholar
[22] Kozhevnikov V Y, Kozyrev A V, Semeniuk N S 2015 Europhys. Lett. 112 15001
Google Scholar
[23] Huang B D, Zhang C, Ren C H, Shao T 2022 Plasma Sources Sci. Technol. 31 114002
Google Scholar
[24] Ivanov S N 2013 J. Phys. D: Appl. Phys. 46 285201
Google Scholar
[25] Levko D 2012 J. Appl. Phys. 111 083303
Google Scholar
[26] Langdon A B, Cohen B I, Friedman A 1983 J. Comput. Phys. 51 107
Google Scholar
[27] Ivanov S N, Lisenkov V V 2018 J. Appl. Phys. 124 103304
Google Scholar
[28] Raizer Y P 1991 Gas Discharge Physics (Berlin: Springer) pp69–70
[29] Wang H Y, Jiang W, Wang Y N 2010 Plasma Sources Sci. Technol. 19 045023
Google Scholar
[30] Friedman A 1990 J. Comput. Phys. 90 292
Google Scholar
[31] Nanbu K 2000 IEEE Trans. Plasma Sci. 28 971
Google Scholar
[32] Kossyi I A, Kostinsky A Y, Matveyev A A, Silakov V P 1992 Plasma Sources Sci. Technol. 1 207
Google Scholar
[33] Lxcat Program of IST-Lisbon Database https://lxcat.net/ [2022-10-10]
[34] Jiang W, Wang H Y, Bi Z H, Wang Y N 2011 Plasma Sources Sci. Technol. 20 035013
Google Scholar
[35] Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179
Google Scholar
[36] Li Y T, Fu Y Y, Liu Z G, Li H D, Wang P, Luo H Y, Zou X B, Wang X X 2022 Plasma Sources Sci. Technol. 31 045027
Google Scholar
[37] Mesyats G A, Yalandin M I, Zubarev N M, Sadykova A G, Sharypov K A 2020 Appl. Phys. Lett. 116 063501
Google Scholar
[38] Tarasenko V F, Yakovlenko S I 2004 Physics-Uspekhi 47 887
Google Scholar
[39] 章程, 马浩, 邵涛, 谢庆, 杨文晋, 严萍 2014 物理学报 638 085208
Google Scholar
Zhang C, Ma H, Shao T, Xie Q, Yang W J, Yan P 2014 Acta Phys. Sin. 638 085208
Google Scholar
[40] Zubarev N M, Ivanov S N 2017 Plasma Phys. Rep. 44 445
Google Scholar
[41] Naidis G V, Tarasenko V F, Babaeva N Y, Lomaev M I 2018 Plasma Sources Sci. Technol. 27 013001
Google Scholar
[42] Shao T, Tarasenko V F, Zhang C, Kostyrya I D, Jiang H, Xu R, Rybka D V, Yan P 2011 Appl. Phys. Express 4 066001
Google Scholar
[43] Askaryan G A 1975 Proc. (Tr.) P. N. Lebedev Phys. Inst. (USSR) (Engl. Transl.) 66 66
[44] Kozhevnikov V Y, Kozyrev A V, Semeniuk N S 2017 Russ. Phys. J. 60 1425
Google Scholar
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图 1 (a)几何模型示意图, dg代表空气间隙长度; (b)纳秒脉冲电压波形
Figure 1. (a) Schematic diagram of the model, dg represents the air gap width; (b) the waveform of nanosecond pulse voltage.
图 2 隐式PIC/MCC模型计算流程图
Figure 2. Computational flow chart of the implicit PIC/MCC model.
图 3 F(ε)/e对电子能量的依赖曲线
Figure 3. Dependence of F(ε)/e on the electron energy.
图 4 330 ps时气隙中的实际电场, 外施均匀电场和净电荷密度的分布
Figure 4. Distribution of the actual electric field, the applied external uniform electric field and the net charge density at 330 ps in the air gap.
图 5 最大能量电子的位置和能量
Figure 5. Positions and energies of maximum energy electrons.
图 6 400 ps时气隙中净电荷密度和实际电场分布
Figure 6. Distribution of the net charge density and the actual electric field at 400 ps in the air gap.
图 7 到达阳极的电子数量
Figure 7. Number of electrons reaching the anode.
图 8 气隙中电子数密度(a)和电场(b)的分布, 最大能量电子的位置用三角形标记
Figure 8. Distribution of the electron density (a) and the electric field (b) in the air gap. The positions of maximum energy electrons are marked with triangles.
图 9 342 ps时放电通道头部和阳极之间所有电子的能量和位置分布
Figure 9. Energy and position of all electrons (macroparticles) between the head of the discharge channel and the anode at 342 ps
图 10 342 ps时放电通道头部和阳极之间的逃逸电子和预电离电子的数密度分布
Figure 10. Number densities of runaway and pre-ionized electrons between the head of the discharge channel and the anode at 342 ps.
图 11 电子数密度的空间分布
Figure 11. Spatial distribution of electron number density.
表 1 模型中的化学反应
Table 1. Chemical reactions in the model.
序号 反应方程式 能量损耗阈值/eV 1 e+N2 → e +N2 0 2 e +O2 → e +O2 0 3 e +N2 → e +N2 A(3$ {{\Sigma }}_{\rm{u}}^+ $) 6.169 4 e +N2 → e +N2 B(3$ {{\Pi }} $g) 7.353 5 e +N2 → e +N2 W(3$ \Delta $u) 7.362 6 e +N2 → e +N2 B'(3$ {{\Sigma }}_{\rm{u}}^- $) 8.165 7 e +N2 → e +N2 a'(1$ {{\Sigma }}_{\rm{u}}^+ $) 8.399 8 e +N2 → e +N2 a(1$ \Pi $g) 8.549 9 e +N2 → e +N2 w(1$ \Delta $u) 8.890 10 e +N2 → e +N+N 9.754 11 e +N2 → e +N2 C(3$ \Pi $u) 11.032 12 e +O2 → e +O2 a(1$ \Delta $g) 0.977 13 e +O2 → e +O2 b(1$ \Sigma _{\rm{g}}^+$) 1.627 14 e +O2 → e + O + O 5.58 15 e +O2 → e +O + O1D 8.4 16 e +O2 → e + O1D + O1D 9.97 17 e +N2 → 2e + N${}_2^+ $ 15.58 18 e +O2 → 2e + O${}_2^+ $ 12.06 19 e +O2 → O${}_2^- $ — 
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[1] Bogaerts A, Tu X, Whitehead J C, Centi G, Lefferts L, Guaitella O, Azzolina Jury F, Kim H H, Murphy A B, Schneider W F, Nozaki T, Hicks J C, Rousseau A, Thevenet F, Khacef A, Carreon M 2020 J. Phys. D: Appl. Phys. 53 443001
Google Scholar
[2] Wang S, Yang D Z, Zhou R S, Zhou R W, Fang Z, Wang W C, Ostrikov K 2019 Plasma Process. Polym. 17 1900146
Google Scholar
[3] Cai Y K, Lyu L, Lu X P 2021 High Volt. 6 1092
Google Scholar
[4] Bekeschus S, Favia P, Robert E, Woedtke T V 2019 Plasma Process. Polym. 16 1800033
Google Scholar
[5] Huang B D, Zhang C, Zhu W C, Lu X P, Shao T 2021 High Volt. 6 665
Google Scholar
[6] Tang J F, Tang M, Zhou D S, Kang P T, Zhu X M, Zhang C H 2019 Plasma Sci. Technol. 21 044001
Google Scholar
[7] Zhang S, Wang W C, Yang D Z, Yuan H, Zhao Z L, Sun H, Shao T 2019 Spectrochim. Acta A Mol. Biomol. Spectrosc. 207 294
Google Scholar
[8] Shao T, Tarasenko V F, Zhang C, Baksht E K, Zhang D, Erofeev M V, Ren C, Shutko Y V, Yan P 2013 J. Appl. Phys. 113 093301
Google Scholar
[9] Shkurenkov I, Burnette D, Lempert W R, Adamovich I V 2014 Plasma Sources Sci. Technol. 23 065003
Google Scholar
[10] Yatom S, Gleizer J Z, Levko D, Vekselman V, Gurovich V, Hupf E, Hadas Y, Krasik Y E 2011 Europhys. Lett. 96 65001
Google Scholar
[11] Shao T, Wang R X, Zhang C, Yan P 2018 High Volt. 3 14
Google Scholar
[12] Kunhardt E E, Byszewski W W 1980 Phys. Rev. A 21 2069
Google Scholar
[13] Zhang C, Gu J W, Wang R X, Ma H, Yan P, Shao T 2016 Laser Part. Beams 34 43
Google Scholar
[14] Frankel S, Highland V, Sloan T, Dyck O V, Wales W 1966 Nucl. Instrum. Method 44 345
Google Scholar
[15] Bratchikov V B, Gagarinov K A, Kostyrya I D, Tarasenko V F, Tkachev A N, Yakovlenko S I 2007 Tech. Phys. 52 856
Google Scholar
[16] Byszewski W W, Reinhold G 1982 Phys. Rev. A 26 2826
Google Scholar
[17] Kostyrya I D, Tarasenko V F 2015 Plasma Phys. Rep. 41 269
Google Scholar
[18] Tarasenko V F 2020 Plasma Sources Sci. Technol. 29 034001
Google Scholar
[19] Beloplotov D V, Tarasenko V F, Shklyaev V A, Sorokin D A 2021 J. Phys. D: Appl. Phys. 54 304001
Google Scholar
[20] Levko D 2019 J. Appl. Phys. 126 083303
Google Scholar
[21] Babaeva N Y, Zhang C, Qiu J T, Hou X M, Tarasenko V F, Shao T 2017 Plasma Sources Sci. Technol. 26 085008
Google Scholar
[22] Kozhevnikov V Y, Kozyrev A V, Semeniuk N S 2015 Europhys. Lett. 112 15001
Google Scholar
[23] Huang B D, Zhang C, Ren C H, Shao T 2022 Plasma Sources Sci. Technol. 31 114002
Google Scholar
[24] Ivanov S N 2013 J. Phys. D: Appl. Phys. 46 285201
Google Scholar
[25] Levko D 2012 J. Appl. Phys. 111 083303
Google Scholar
[26] Langdon A B, Cohen B I, Friedman A 1983 J. Comput. Phys. 51 107
Google Scholar
[27] Ivanov S N, Lisenkov V V 2018 J. Appl. Phys. 124 103304
Google Scholar
[28] Raizer Y P 1991 Gas Discharge Physics (Berlin: Springer) pp69–70
[29] Wang H Y, Jiang W, Wang Y N 2010 Plasma Sources Sci. Technol. 19 045023
Google Scholar
[30] Friedman A 1990 J. Comput. Phys. 90 292
Google Scholar
[31] Nanbu K 2000 IEEE Trans. Plasma Sci. 28 971
Google Scholar
[32] Kossyi I A, Kostinsky A Y, Matveyev A A, Silakov V P 1992 Plasma Sources Sci. Technol. 1 207
Google Scholar
[33] Lxcat Program of IST-Lisbon Database https://lxcat.net/ [2022-10-10]
[34] Jiang W, Wang H Y, Bi Z H, Wang Y N 2011 Plasma Sources Sci. Technol. 20 035013
Google Scholar
[35] Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179
Google Scholar
[36] Li Y T, Fu Y Y, Liu Z G, Li H D, Wang P, Luo H Y, Zou X B, Wang X X 2022 Plasma Sources Sci. Technol. 31 045027
Google Scholar
[37] Mesyats G A, Yalandin M I, Zubarev N M, Sadykova A G, Sharypov K A 2020 Appl. Phys. Lett. 116 063501
Google Scholar
[38] Tarasenko V F, Yakovlenko S I 2004 Physics-Uspekhi 47 887
Google Scholar
[39] 章程, 马浩, 邵涛, 谢庆, 杨文晋, 严萍 2014 物理学报 638 085208
Google Scholar
Zhang C, Ma H, Shao T, Xie Q, Yang W J, Yan P 2014 Acta Phys. Sin. 638 085208
Google Scholar
[40] Zubarev N M, Ivanov S N 2017 Plasma Phys. Rep. 44 445
Google Scholar
[41] Naidis G V, Tarasenko V F, Babaeva N Y, Lomaev M I 2018 Plasma Sources Sci. Technol. 27 013001
Google Scholar
[42] Shao T, Tarasenko V F, Zhang C, Kostyrya I D, Jiang H, Xu R, Rybka D V, Yan P 2011 Appl. Phys. Express 4 066001
Google Scholar
[43] Askaryan G A 1975 Proc. (Tr.) P. N. Lebedev Phys. Inst. (USSR) (Engl. Transl.) 66 66
[44] Kozhevnikov V Y, Kozyrev A V, Semeniuk N S 2017 Russ. Phys. J. 60 1425
Google Scholar
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