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本文建立了高气压下的氦气放电模型, 通过与试验对比, 验证了模型的有效性, 并利用该模型对高气压下“场致发射”的影响进行了探讨. 通过Fowler-Nordheim方程将电流密度转化为电子通量, 并将电子通量添加到COMSOL相应的壁边界条件中进行仿真, 在宏观层面(击穿电压)以及微观层面(空间电子密度)进行分析. 研究发现, 场致发射电流密度 J由电场强度 E、场增强因子
$\beta $ 以及金属逸出功 W共同决定;$\beta = 300$ 时场致发射的影响可以忽略, 而对于$\beta = 400$ 、电场强度10 MV/m以上的工况, 场致发射对击穿的影响较大; 对于以铜为平行平板电极的氦气击穿来说, 电场强度 E小于8 MV/m 时可以忽视场致发射的作用; 在微观层面上, 场致发射能够给放电空间提供新的“种子电子”, 进而提升整个空间的电子密度, 使得粒子碰撞反应加剧, 最终导致击穿.In this paper, a helium discharge model under high pressure is established. To qualitatively verify the validity of the model, we compare the results obtained from the previous experiments with those acquired from our model under similar operational conditions. In the simulation model, the electron temperature is obtained according to its relationship with the local electric field. According to the principle of electrical neutrality, the number density of He + and the number density of${\rm{He}}_2^+$ are also equal to the initial electron density, and we can assume that the He + and the${\rm{He}}_2^+$ account for 30% and 70%, respectively. For helium and copper electrodes, the secondary electron emission coefficient is 0.19 and the secondary electron average energy is15.3 eV. The Fowler-Nordheim equation is used to calculate the field-emission current density, and the electron flux is calculated according to the “charge conservation condition”. The electron flux is added to COMSOL's corresponding wall boundary, which can play the role of field emission. Finally, the analysis is carried out at a macro level (breakdown voltage) and micro level (spatial electron density). It is found that the field-emission current density is determined by the electric field intensity, the field enhancement factor, and the metal escaping work. The effect of field emission can be ignored when$\beta = 300$ . However, if$\beta = 400$ , the influence of field emission on the breakdown is significant when the electric field intensity is above$10\;{\rm{ MV}}/{\rm{m}}$ . For the breakdown of helium gas with copper serving as a parallel plate electrode, the effect of field emission can be ignored when the electric field intensity is lower than$8\;{\rm{ MV}}/{\rm{m}}$ . At a micro level, the field emission can provide new "seed electrons" for the discharge space, which can increase the electron density of the whole space and intensify the particle collision reaction, finally leading to the breakdown.-
Keywords:
- field emission /
- helium /
- high pressure /
- breakdown voltage
[1] 郑艳华, 石磊 2010 原子能科学技术 44 s253
Zheng Y H, Shi L 2010 Atom. Energ. Sci. Technol. 44 s253
[2] 岳珊, 刘兴男, 时振刚 2015 物理学报 64 105101
Google Scholar
Yue S, Liu X N, Shi Z G 2015 Acta Phys. Sin. 64 105101
Google Scholar
[3] 杨津基 1983 气体放电 (北京: 科学出版社)第53页
Yang J J 1983 Gas Discharge (Beijing: Science Press) p53 (in Chinese)
[4] Little R P, Whitney W T 1963 J. Appl. Phys. 34 2430
Google Scholar
[5] 张喜波, 苏建仓, 孙旭, 赵亮, 李锐 2015 现代应用物理 6 43
Zhang X B, Su J C, Sun X, Zhao L, Li R 2015 Mod. Appl. Phys. 6 43
[6] 徐翱, 金大志, 王亚军, 陈磊, 谈效华 2020 高电压技术 46 715
Xu A, Jin D Z, Wang Y J, Chen L, Tan X H 2020 High Volt. Engineer. 46 715
[7] 成永红, 孟国栋, 董承业 2017 电工技术学报 32 14
Cheng Y H, Meng G D, Dong C Y 2017 Trans. China Electrotechn. Soc. 32 14
[8] Wallash A, LevitL 2003 Reliability, Testing, and Characterization of MEMS/MOEMS Ⅱ San Jose, USA, 2003 p87
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Google Scholar
Qian L, Wang Y Q, Liu L, Fan S S 2011 Acta Phys. Sin. 60 028801
Google Scholar
[10] 孙强, 周前红, 宋萌萌, 杨薇, 董烨 2021 物理学报 70 015202
Google Scholar
Sun Q, Zhou Q H, Song M M, Yang W, Dong Y 2021 Acta Phys. Sin. 70 015202
Google Scholar
[11] Dmitry S, Daniel B, Dogyun H, Shin K, Valery K, Noriyasu O 2019 IEEE Trans. Plasma Sci. 47 5186
Google Scholar
[12] Shin K, Noriyasu O, Shuichi T 2013 IEEE Trans. Plasma Sci. 41 1889
Google Scholar
[13] You Q, Zhou Yan, Liu X N, Mo N, Luo H, Shi Z G 2020 J. Nucl. Sci. Technol. 57 624
Google Scholar
[14] 宁文军, 戴栋, 张雨晖, 郝艳捧, 李立浧 2017 高压电技术 43 1845
Ning W J, Dai D, Zhang Y H, Hao Y P, Li L C 2017 High Volt. Engineer. 43 1845
[15] Hagelaar G, Pitchford L 2005 Plasma Sources Sci. T. 14 722
Google Scholar
[16] Maric D, Radenovic M 2005 The European Physical Journal D-Atomic, Molecular, optical and Plasma Physics 35 313
[17] You Q, Mo N, Liu X N, Luo H, Shi Z G 2020 Ann. Nucl. Energy 141 107351
Google Scholar
[18] Zhang P, Kortshagen U 2005 J. Phys. D Appl. Phys. 39 153
[19] Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sources Sci. T. 28 075003
Google Scholar
[20] Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sci. Technol. 21 074003
Google Scholar
[21] Smirnov B M 2015 Theory of Gas Discharge Plasma (Switzerland: Springer International Publishing) p230
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图 3 1 MPa下实验值与仿真值 (a) 25 ℃; (b) 105 ℃; (c) 155 ℃ (d) 180 ℃
Fig. 3. Experimental value and simulation value at 1 MPa: (a) 25 ℃; (b) 105 ℃; (c) 155 ℃; (d) 180 ℃.
图 4 1 MPa和7 MPa下的实验值 (a) 25 ℃; (b) 105 ℃; (c) 155 ℃; (d) 180 ℃
Fig. 4. Experimental value at 1 MPaand7 MPa: (a) 25 ℃; (b) 105 ℃; (c) 155 ℃; (d) 180 ℃.
图 5 1 MPa和7 MPa下的实验击穿场强
Fig. 5. Experimental breakdown field strength at 1 MPa and 7 MPa.
图 6 电流密度的影响因素 (a)
$\beta $ ; (b) E; (c) WFig. 6. Influencing factors of current density: (a)
$\beta $ ; (b) E; (c) W.
图 10 7 MPa下实验值与仿真值 (a) 25 ℃; (b) 180 ℃
Fig. 10. Experimental value and simulation value at 7 MPa: (a) 25 ℃; (b) 180 ℃.
表 1 模型考虑的粒子碰撞过程
Table 1. Collision processes considered in the model.
反应式 速率常数 反应能/eV 参考文献 ${\rm{e}} + {\rm{He}} \to {\rm{2 e}} + {\rm{H}}{{\rm{e}}^ + }$ $\alpha {V_{\rm{e}}}/{N_{{\rm{He}}}}$ 24.6 [ 13] ${\rm{e }}+ {\rm{H}}{{\rm{e}}^{\rm{*}}} \to {\rm{2 e}} + {\rm{H}}{{\rm{e}}^ + }$ $1.5 \times {10^{ - 13} }\sqrt { {T_{\rm{e} } } } \exp \left( { - \dfrac{ {4.77} }{ { {T_{\rm{e} } } } } } \right)$ 4.78 [ 13] ${\rm{e}} + {\rm{He}}_{\rm{2}}^{\rm{*}} \to {\rm{2 e}} + {\rm{He}}_{\rm{2}}^ + $ $9.75 \times {10^{ - 16} }T_{\rm{e} }^{0.71}\exp \left( { - \dfrac{ {3.4} }{ { {T_{\rm{e} } } } } } \right)$ 3.4 [ 13] ${\rm{H}}{{\rm{e}}^{\rm{*}}} + {\rm{H}}{{\rm{e}}^{\rm{*}}} \to {\rm{e}} +{\rm{ He }}+{\rm{ H}}{{\rm{e}}^ + }$ $8.7 \times {10^{ - 16} }\sqrt {\dfrac{ { {T_{\rm{g} } } }}{ {0.025} } }$ 0 [ 13] ${\rm{He}}_{\rm{2}}^{\rm{*}} + {\rm{He}}_{\rm{2}}^{\rm{*}} \to {\rm{e}} + {\rm{3 He }}+{\rm{ H}}{{\rm{e}}^ + }$ $8.7 \times {10^{ - 16} }\sqrt {\dfrac{ { {T_{\rm{g} } } }}{ {0.025} } }$ 0 [ 13] ${\rm{He}}_{\rm{2}}^{\rm{*}} + {\rm{He}}_{\rm{2}}^{\rm{*}} \to {\rm{e}} +{\rm{ 2 He}} +{\rm{ He}}_{\rm{2}}^ + $ $2.03 \times {10^{ - 15} }\sqrt {\dfrac{ { {T_{\rm{g} } } }}{ {0.025} } }$ 0 [ 13] ${\rm{e}} + {\rm{He}} \to {\rm{e }}+ {\rm{H}}{{\rm{e}}^{\rm{*}}}$ $\dfrac{ {1.6 \times { {10}^{ - 15} }\exp \left( { - 350/{x^2} } \right)} }{ { {x^{0.3} }\left( {1 + 0.43{x^{1.2} } } \right)} }$ 19.8 [ 13] ${\rm{e }}+ {\rm{H}}{{\rm{e}}^{\rm{*}}} \to {\rm{e}} + {\rm{He}}$ $3 \times {10^{ - 15} } + \dfrac{ {5 \times { {10}^{ - 13} }\exp \left( { - 1.398/{T_{\rm{e} } } } \right)} }{ {1 + 5\exp \left( { - 0.602/{T_{\rm{e} } } } \right)} }$ –19.8 [ 13] ${\rm{e}} + {\rm{He}} \to {\rm{e}} + {\rm{He}}$ 横截面数据 0 ${\rm{2 He }}+{\rm{ H}}{{\rm{e}}^ + } \to {\rm{He}} +{\rm{ He}}_{\rm{2}}^ + $ $1 \times {10^{ - 43}}$ 0 [ 13] ${\rm{2 He }}+{\rm{ H}}{{\rm{e}}^{\rm{*}}} \to {\rm{He}} +{\rm{ He}}_{\rm{2}}^{\rm{*}}$ $8.1 \times {10^{ - 48}}T\exp \left( { - 650/T} \right)$ 0 [ 13] ${\rm{e }}+ {\rm{H}}{{\rm{e}}^ + } \to {\rm{H}}{{\rm{e}}^{\rm{*}}}$ $6.76 \times {10^{ - 19}}{T_{\rm{e}}}^{ - 0.5}$ –4.78 [ 14] ${\rm{e }}+ {\rm{H}}{{\rm{e}}^ + } \to {\rm{He}}$ $1.327 \times {10^{ - 27}}{n_{\rm{e}}}T_{\rm{e}}^{ - 4.4}$ –24.6 [ 14] ${\rm{e}} + {\rm{He}}_{\rm{2}}^ + \to {\rm{He}} +{\rm{ H}}{{\rm{e}}^{\rm{*}}}$ $5 \times {10^{ - 15}}$ 0 [ 13] ${\rm{e}} + {\rm{He}}_{\rm{2}}^ + \to {\rm{He}}_{\rm{2}}^{\rm{*}}$ $5 \times {10^{ - 15} }({ { {T_{\rm{g} } } } }/{ { {T_{\rm{e} } } } })$ –3.4 [ 13] ${\rm{e}} +{\rm{ He }}+{\rm{ H}}{{\rm{e}}^ + } \to {\rm{He}} +{\rm{ H}}{{\rm{e}}^{\rm{*}}}$ $1 \times {10^{ - 38}}{\left( {{T_{\rm{e}}}/{T_{\rm{g}}}} \right)^{ - 2}}$ 0 [ 13] ${\rm{2 e}} + {\rm{He}}_{\rm{2}}^ + \to {\rm{e + 2 H}}{{\rm{e}}^{\rm{*}}}$ $6.186 \times {10^{ - 39}}{T_{\rm{e}}}^{ - 4.4}$ 0 [ 15] ${\rm{2 e}} + {\rm{He}}_{\rm{2}}^ + \to {\rm{e}} + {\rm{He}}_{\rm{2}}^{\rm{*}}$ $7.1 \times {10^{ - 32}}$ 0 [ 15] ${\rm{e }}+ {\rm{He }}+ {\rm{He}}_{\rm{2}}^ + \to {\rm{He}} +{\rm{ He}}_{\rm{2}}^{\rm{*}}$ $5 \times {10^{ - 39} }({ { {T_{\rm{g} } } } }/{ { {T_{\rm{e} } } } })$ 0 [ 13] ${\rm{e }}+ {\rm{He }}+ {\rm{He}}_{\rm{2}}^ + \to {\rm{2 He }}+{\rm{ H}}{{\rm{e}}^{\rm{*}}}$ $5 \times {10^{ - 39}}$ 0 [ 15] ${\rm{2 e}} + {\rm{He}}_{\rm{2}}^ + \to {\rm{e}} +{\rm{ He }}+{\rm{ H}}{{\rm{e}}^{\rm{*}}}$ $2.8 \times {10^{ - 32}}$ 0 [ 15] 注: ${V_{\rm{e}}}$表示电子迁移速度(迁移率与场强的乘积), ${N_{{\rm{He}}}}$是氦原子数密度, 由理想气体状态方程求得; ${T_{\rm{e}}}$和 ${T_{\rm{g}}}$分别是以eV表示的电子温度和气体温度, T 表示以K为单位的气体温度; x 表示以 ${\rm{Td}}$ ( $1~{\rm{ Td} } = {10^{ - 17} }\;{\rm{ V} } \cdot {\rm{c} }{ {\rm{m} }^{\rm{2} } }$)为单位的约化场强; 横截面数据来源于https://fr.lxcat.net/home/中的 Phelps 数据库; 表中二体反应(两种反应物)的速率常数单位是m 3/s, 三体反应(三种反应物)的速率常数单位是m 6/s. 
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表 2 模型中的
$\alpha $ 系数及输运参数Table 2.
$\alpha $ coefficient and transport parameters in the model.参数 计算式 参考文献 参数 计算式 参考文献 α/m –1 $0.41 p{ {\rm{e} }^{ - 18.116 p/E} }$ [ 16] D e/(m 2·s –1) $2.3 \times {10^{24}}{T_{\rm{e}}}/{N_{{\rm{He}}}}$ [ 17] $ + 1.93 p{ {\rm{e} }^{ - 84.541 p/E} } $ D p/(m 2·s –1) $3.25 \times {10^{22}}{T_{\rm{e}}}/{N_{{\rm{He}}}}$ [ 17] μ e/(m 2·s –1·V –1) $2.83 \times {10^{24}}/{N_{{\rm{He}}}}$ [ 17] D i/(m 2·s –1) $4.88 \times {10^{22}}{T_{\rm{e}}}/{N_{{\rm{He}}}}$ [ 17] μ p/(m 2·s –1·V –1) $3.25 \times {10^{22}}/{N_{{\rm{He}}}}$ [ 17] D m/(m 2·s –1) $\dfrac{ {5.6} }{ {133.3 p} }{\left( {\dfrac{ { {T_{\rm{g} } } }}{ {0.025} } } \right)^{1.5} }$ [ 17] μ i/(m 2·s –1·V –1) $4.88 \times {10^{22}}/{N_{{\rm{He}}}}$ [ 17] D j/(m 2·s –1) $\dfrac{ {4.1} }{ {133.3 p} }{\left( {\dfrac{ { {T_{\rm{g} } } }}{ {0.025} } } \right)^{1.5} }$ [ 17] 注: 电子(e)、氦原子离子(He +)、氦分子离子( ${\rm{He}}_2^+ $)、氦激发态原子(He *)以及氦激发态分子( ${\rm{He}}_2^* $), 分别对应下标e, p, i, m和j.
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表 3 模型边界条件
Table 3. Boundary conditions in the model.
边界 $ \varphi $ $ {n}_{\rm{e}} $ $ {n}_{\rm{\varepsilon }} $ n i $ {n}_{\rm{n}} $ AD $ {V}_{a} $ (6) (7) (8) (8) BC $ 0 $ (6) (7) (8) (8) AB, CD $\dfrac{\partial \varphi }{\partial r}=0$ $ -{{n}}\cdot {{\varGamma }}_{\bf{e}}=0 $ $ -{{n}}\cdot {{\varGamma }}_{\bf{\varepsilon }}=0 $ $ -{{n}}\cdot {{\varGamma }}_{{k}}=0 $ $ -{{n}}\cdot {{\varGamma }}_{{k}}=0 $
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表 4 实验与仿真参数
Table 4. Parameters of experimentand simulation.
参数 值 温度/℃ 25, 105, 155, 180 压强/ MPa 1, 7 间距/ mm 0.25, 031, 0.53, 3.02 半径/ cm 3 外加电压 直流
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表 5 场致电流
Table 5. Current of field emission.
温度/℃ 间距/mm 实验值/V 场强/(MV·m –1) I/A $\beta = 300$ $\beta = 400$ 25 0.25 2640 10.56 $7.01 \times {10^{ - 6}}$ $2.2 \times {10^{ - 3}}$ 0.31 3350 10.81 $1.17 \times {10^{ - 5}}$ $4.2 \times {10^{ - 3}}$ 0.53 5475 10.33 $4.24 \times {10^{ - 6}}$ $1.5 \times {10^{ - 3}}$ 0.71 7605 10.71 $9.65 \times {10^{ - 6}}$ $2.8 \times {10^{ - 3}}$ 180 0.31 2490 8.03 $6.20 \times {10^{ - 9}}$ $9.62 \times {10^{ - 6}}$ 0.53 3960 7.47 $7.02 \times {10^{ - 10}}$ $1.81 \times {10^{ - 6}}$ 0.71 5540 7.80 $2.64 \times {10^{ - 9}}$ $5.00 \times {10^{ - 6}}$
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[1] 郑艳华, 石磊 2010 原子能科学技术 44 s253
Zheng Y H, Shi L 2010 Atom. Energ. Sci. Technol. 44 s253
[2] 岳珊, 刘兴男, 时振刚 2015 物理学报 64 105101
Google Scholar
Yue S, Liu X N, Shi Z G 2015 Acta Phys. Sin. 64 105101
Google Scholar
[3] 杨津基 1983 气体放电 (北京: 科学出版社)第53页
Yang J J 1983 Gas Discharge (Beijing: Science Press) p53 (in Chinese)
[4] Little R P, Whitney W T 1963 J. Appl. Phys. 34 2430
Google Scholar
[5] 张喜波, 苏建仓, 孙旭, 赵亮, 李锐 2015 现代应用物理 6 43
Zhang X B, Su J C, Sun X, Zhao L, Li R 2015 Mod. Appl. Phys. 6 43
[6] 徐翱, 金大志, 王亚军, 陈磊, 谈效华 2020 高电压技术 46 715
Xu A, Jin D Z, Wang Y J, Chen L, Tan X H 2020 High Volt. Engineer. 46 715
[7] 成永红, 孟国栋, 董承业 2017 电工技术学报 32 14
Cheng Y H, Meng G D, Dong C Y 2017 Trans. China Electrotechn. Soc. 32 14
[8] Wallash A, LevitL 2003 Reliability, Testing, and Characterization of MEMS/MOEMS Ⅱ San Jose, USA, 2003 p87
[9] 潜力, 王昱权, 刘亮, 范守善 2011 物理学报 60 028801
Google Scholar
Qian L, Wang Y Q, Liu L, Fan S S 2011 Acta Phys. Sin. 60 028801
Google Scholar
[10] 孙强, 周前红, 宋萌萌, 杨薇, 董烨 2021 物理学报 70 015202
Google Scholar
Sun Q, Zhou Q H, Song M M, Yang W, Dong Y 2021 Acta Phys. Sin. 70 015202
Google Scholar
[11] Dmitry S, Daniel B, Dogyun H, Shin K, Valery K, Noriyasu O 2019 IEEE Trans. Plasma Sci. 47 5186
Google Scholar
[12] Shin K, Noriyasu O, Shuichi T 2013 IEEE Trans. Plasma Sci. 41 1889
Google Scholar
[13] You Q, Zhou Yan, Liu X N, Mo N, Luo H, Shi Z G 2020 J. Nucl. Sci. Technol. 57 624
Google Scholar
[14] 宁文军, 戴栋, 张雨晖, 郝艳捧, 李立浧 2017 高压电技术 43 1845
Ning W J, Dai D, Zhang Y H, Hao Y P, Li L C 2017 High Volt. Engineer. 43 1845
[15] Hagelaar G, Pitchford L 2005 Plasma Sources Sci. T. 14 722
Google Scholar
[16] Maric D, Radenovic M 2005 The European Physical Journal D-Atomic, Molecular, optical and Plasma Physics 35 313
[17] You Q, Mo N, Liu X N, Luo H, Shi Z G 2020 Ann. Nucl. Energy 141 107351
Google Scholar
[18] Zhang P, Kortshagen U 2005 J. Phys. D Appl. Phys. 39 153
[19] Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sources Sci. T. 28 075003
Google Scholar
[20] Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sci. Technol. 21 074003
Google Scholar
[21] Smirnov B M 2015 Theory of Gas Discharge Plasma (Switzerland: Springer International Publishing) p230
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