氦气空心阴极放电动力学过程的模拟研究

何寿杰; 张宝铭; 王鹏; 张钊; 韩育宏

doi:10.11884/HPLPB201830.170211

氦气空心阴极放电动力学过程的模拟研究

doi: 10.11884/HPLPB201830.170211

河北大学物理科学与技术学院, 河北保定 071002

基金项目:

国家自然科学基金项目 11205046

河北省自然科学基金项目 A2016201025

河北大学研究生创新资助项目 X201733

详细信息

作者简介:
何寿杰(1979－), 男，副教授，从事空心阴极放电相关方向的研究；heshouj@hbu.edu.cn

中图分类号: O53
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出版历程
- 收稿日期: 2017-06-16
- 修回日期: 2017-08-29
- 刊出日期: 2018-02-15

Simulation on the dynamics of hollow cathode discharge in helium

College of Physics Science and Technology, Hebei University, Baoding 071002, China

摘要

摘要: 利用流体模型模拟研究了氦气空心阴极放电的时空动力学过程，计算得到了不同放电时刻电子和亚稳态氦原子密度、电势、电场、基态电离速率和分步电离速率等的时空分布特性。特别是讨论了亚稳态原子和分步电离对于放电的影响。结果表明，随着电流的增长，放电处于五个不同的放电模式：第一阶段电流上升非常缓慢，为汤生放电模式，带电粒子密度、亚稳态原子密度和径向电场均很弱；第二阶段电流迅速上升，放电模式由汤生放电向空心阴极放电过渡，带电粒子密度、亚稳态原子密度和径向电场迅速增强；第三阶段达到准稳态阶段，放电电流增长速度变缓，形成了明显的阴极鞘层结构；第四阶段为空心阴极效应形成阶段，向稳态阶段过渡；第五阶段为稳态放电阶段。研究结果同时表明，亚稳态氦原子和分步电离在放电的初始阶段对于放电的发展作用较弱，在前三阶段中，电子的产生以基态电离为主。随着放电的发展，由亚稳态原子引起的分步电离对新的电子产生的作用逐渐接近并超过基态电离，对总电离的贡献率越来越高。
- 空心阴极放电 /
- 流体模型 /
- 分步电离速率 /
- 电势 /
- 电子密度
Abstract: In this paper, the spatiotemporal dynamics of hollow cathode discharge in helium is simulated by using the fluid model. The spatiotemporal distribution of electrons density, metastable helium atoms density, potential, electric field, direct ionization rate and step-wise ionization are calculated. In particular, the effects of metastable atoms and step-wise ionization on the discharge are discussed. The results show that the discharge is divided into five different discharge modes with the increase of current. In the first stage, the discharge is Townsend discharge mode, the current rises very slowly, and the charged particle density, metastable atom density and radial electric field are very weak. In the second stage, the current increases rapidly, and the discharge mode changes from the Townsend discharge to the hollow cathode discharge. The charged particle density, metastable atom density and radial electric field increase rapidly. The third stage reaches the quasi steady state, and the discharge current increases slowly, resulting in an obvious cathode sheath structure; The fourth stage is the formation stage of the hollow cathode effect, and transits to the steady state. The fifth stage is the steady-state discharge stage. The results also show that the metastable helium atoms and the stepwise ionization are weak in the initial stage of the discharge, and in the initial three stages, the formation of new electrons are dominated by ground ionization. With the development of the discharge, the stepwise ionization caused by the metastable atoms gradually approaches and exceeds the ground ionization, and the contribution rate to the total ionization is getting higher and higher.
- hollow cathode discharge /
- fluid model /
- step-wise ionization rate /
- potential /
- electron density

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图 1 空心阴极放电系统截面图

Figure 1. Cross section of hollow cathode discharge

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图 2 电流随时间变化图

Figure 2. Discharge current as a function of time

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图 3 第一阶段t=0.76 μs时，电势、电子密度亚稳态氦原子密度分布图

Figure 3. Distribution of electric potential, electron density, metastable helium atom density in first stage at t=0.76 μs

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图 4 径向电场随时间变化图

Figure 4. Radial electric field at different time

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图 5 第一阶段t=0.76 μs时，基态电离速率和分步电离速率分布图

Figure 5. Distribution of ground ionization and step-wise ionization rates in first stage at t=0.76 μs

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图 6 第二阶段t=1.32 μs时，电势、电子、亚稳态氦原子分布图

Figure 6. Distribution of potential, electron, metastable helium atom density in second stage at t=1.32 μs.

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图 7 第二阶段t=1.32 μs时，基态直接电离速率和分步电离速率的空间分布

Figure 7. Distribution of ground ionization rate, step-wise ionization rates in second stage at t=1.32 μs

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图 8 第三阶段t=1.72 μs时，电势、电子密度、亚稳态原子密度分布图

Figure 8. Distribution of electric potential, electron density, metastable atom density in third stage at t=1.72 μs

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图 9 第三阶段t=1.72 μs时基态直接电离速率分步电离速率分布图

Figure 9. Distribution of ground ionization rate and step-wise ionization rate in third stage at t=1.72 μs

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图 10 未考虑亚稳态原子时电流随时间变化图

Figure 10. Current versus time without metastable atoms

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图 11 第四阶段t=3.29 μs时，电势、电子和亚稳态氦原子分布图

Figure 11. Distribution of potential, electron density, metastable helium atom density in fourth stage at t=3.29 μs

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图 12 第四阶段t=3.29 μs时基态直接电离速率和分步电离速率分布图

Figure 12. Distribution of ground ionization rate and step-wise ionization rate in fourth stage at t=3.29 μs

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图 13 稳态放电时t=10 μs电势、电子密度、亚稳态氦原子密度和电子平均能量分布图

Figure 13. Distribution of potential, electron density, metastable helium density and mean electron energy in steady state discharge at t=10 μs

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图 14 稳态阶段t=10 μs时, 基态直接电离速率和分步电离速率的空间分布

Figure 14. Distribution of ground ionization rate, and stepwise ionization rates in steady state stage at t=10 μs

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表 1 放电反应类型及反应速率系数

Table 1. Types of discharge reactions and reaction rate coefficients

reaction equation	reaction type	reaction rate coefficient/(cm³s^-1)	energy threshold/eV
1 He+e→He⁺+2e	ground state ionization	K_gi ^[14]	24.6(U_i)
2 He+e→He^m+e	ground state excitation	K_m^[14]	19.8(U_m)
3 He^m+e→He⁺+2e	step-wise ionization	K_si[14]	4.8(U_s)
4 He^m+ He^m→He⁺+He+e	Penning ionization	K_pi=4.5×10^-10^[14]
5 He^m+ e→He+hν+e	de-excitation	K_d=4.2×10^-9^[15]
6 He^m+ He→He+He	two-body collision	K_2B=6.0×10^-15^[16]
7 He^m+ 2He→He₂^m+He	three-body collision	K_3B=1.3×10^-33^[14]

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