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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. DownLoad:
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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 $ DownLoad:
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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 DownLoad:
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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 $2.64 \times {10^{ - 9}}$ $5.00 \times {10^{ - 6}}$ DownLoad:
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