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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
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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m3/s, 三体反应(三种反应物)的速率常数单位是m6/s. 
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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] De/(m2·s–1) $2.3 \times {10^{24}}{T_{\rm{e}}}/{N_{{\rm{He}}}}$ [17] $ + 1.93 p{ {\rm{e} }^{ - 84.541 p/E} } $ Dp/(m2·s–1) $3.25 \times {10^{22}}{T_{\rm{e}}}/{N_{{\rm{He}}}}$ [17] μe/(m2·s–1·V–1) $2.83 \times {10^{24}}/{N_{{\rm{He}}}}$ [17] Di/(m2·s–1) $4.88 \times {10^{22}}{T_{\rm{e}}}/{N_{{\rm{He}}}}$ [17] μp/(m2·s–1·V–1) $3.25 \times {10^{22}}/{N_{{\rm{He}}}}$ [17] Dm/(m2·s–1) $\dfrac{ {5.6} }{ {133.3 p} }{\left( {\dfrac{ { {T_{\rm{g} } } }}{ {0.025} } } \right)^{1.5} }$ [17] μi/(m2·s–1·V–1) $4.88 \times {10^{22}}/{N_{{\rm{He}}}}$ [17] Dj/(m2·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. 下载:
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边界 $ \varphi $ $ {n}_{\rm{e}} $ $ {n}_{\rm{\varepsilon }} $ ni $ {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 $ 下载:
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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 $2.64 \times {10^{ - 9}}$ $5.00 \times {10^{ - 6}}$ 下载:
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