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摘要:
为研究10 cm口径发散磁场离子推力器内部的放电过程并对后续工程改进提供参考，采用COMSOL多物理场耦合软件建立推力器放电模型，获得关键放电参数，并根据试验结果进行验证。模拟结果表明：放电室内部上游磁极和下游磁极之间形成具有强烈发散特性的磁场，并在正交电场的影响下，使电子发生以磁力线为导向中心的霍尔漂移运动；放电室内部气体压强分布均匀且基本在0.1~0.11 Pa范围内，大部分区域的中性原子密度约为1.5×1019 m−3，流体速度在0.2~0.9 m/s的范围内且呈现明显的黏滞流特性；电子密度峰值出现在阴极出口区域，约为8.57×1018 m−3，阳极壁面附近及栅极上游区域的等离子密度约为6.8×1017 m−3。试验结果显示：采用E×B探针测量得到双核离子占总束流离子比为14.1%，根据COMSOL计算值得到的0.353 mA束流理论值与0.323 mA的束流实测值比对误差为9%，误差主要来自于仿真条件设置及试验测量。研究结果可为离子推力器工程化改进提供快速的放电参数分析及优化设计参考。
Abstract:A discharge model of the divergent magnetic field ion thruster (Kaufman thruster) of 10 cm diameter is established with COMSOL multi-physical field coupling software to study the internal discharge process of the thruster and to provide reference for subsequent engineering improvement. The key discharge parameters are obtained and verified through experiments. The calculation results show a magnetic field formed between the upstream and downstream magnetic poles in the discharge chamber with strong divergent characteristics. Due to the orthogonal electric field, the Hall drift of the electrons occur with the magnetic field line as the guiding center. The gas pressure in the discharge chamber is uniformly distributed in the range of 0.1−0.11 Pa, with the neutral atom density in most areas about 1.5×1019 m−3, and the fluid velocity in the range of 0.2−0.9 m/s. The fluid shows obvious characteristics of viscous flow. The peak electron density appears in the cathode outlet region, which is about 8.57×1018 m−3, while the plasma density near the anode wall and the upstream of the screen grid is about 6.8×1017 m−3. The results measured by E×B probe show that the proportion of divalent ions in the total beam ions is 14.1%. The comparison error between the theoretical beam current value of 0.353 mA and the measured beam current value of 0.323 mA is 9%, which is mainly due to the simulation setting and the measurement error. The discharge model established in this paper can provide rapid discharge parameter analysis and reference for optimal design of the thruster.
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Key words:
- divergent magnetic field /
- ion thruster /
- discharge model /
- plasma density /
- electron temperature
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图 1 10 cm口径发散磁场离子推力器及放电室结构示意图
Figure 1. Schematic diagram of structure of 10 cm diameter divergent magnetic field ion thruster and discharge chamber
图 2 放电室电势分布和磁场分布
Figure 2. Electric potential distribution and magnetic field distribution in discharge chamber
图 3 放电室内部中性流体特性仿真结果
Figure 3. Simulation of neutral fluid characteristics inside discharge chamber
表 1 10 cm口径发散磁场离子推力器20 mN主工况点的工作参数
Table 1. Parameters of 10 cm diameter divergent magnetic field ion thruster with 20 mN main work point
参数 数值 阴极流量/（mg·s−1） 0.08 阳极流量/（mg·s−1） 0.5 中和器流量/（mg·s−1） 0.08 屏栅电势/V 1150 加速栅电势/V −150 触持电势/V 1162 励磁电流/A 0.56 励磁电势/V 1150 挡板电势/V 1150 上磁极电势/V 1150 下磁极电势/V 1150 阳极电势/V 1185 
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表 2 迁移扩散模块的参数设置
Table 2. Parameter setting of drift diffusion module
参数 表达式 $ k_{1} $ $1.99^{-14} T_{\mathrm{e} }^{0.93} \mathrm{e}^{-0.41 / T_{\mathrm{e} } }$ $ k_{2} $ $1.93^{-19} \mathrm{e}^{-11.6 /T_{\rm{e} } } / {\left[T_{\mathrm{e} }^{0.5}\left(8 {e} T_{\mathrm{e} } / {\text{π} } / m_{\mathrm{e} }\right)^{0.5}\right]}$ $ k_{3} $ $10 ^{-20}\left(3.97+0.643T_{\rm{e} }-0.036\;8T_{\rm{e} }^2\right){\rm{e} }^{-12.127/T_{\rm{e} } } \left(8{{e} }T_{\rm{e} }/\text{π}/m_{\rm{e} }\right)^{0.5}$ $ r_{1} $ $k_{1} n_{0} n_{{\rm{e}}}$ $ r_{2} $ $k_{2} n_{0} n_{{\rm{e}}}$ $r_3$ $k_{3} n_{0} n_{{\rm{e}}}$ $\mu_{\mathrm{e} }$ ${{e} } /\left[m_{\mathrm{e} }\left(\nu_{\mathrm{en} }+\nu_{\mathrm{ei} }\right)\right]$ $R_{{\rm{e}}}$ $ r_{2}+r_{3} $ $S_{\mathrm{en} }$ $-{{e} }\left(r_{1} d_{ {\rm{e} } 1}+r_{2} d_{ {\rm{e} } 2}+r_{3} d_{ {\rm{e } }3}\right)$ $\sigma_{\mathrm{en} }$ $6.6^{-19}\left(T_{\rm{e} }/ 4-0.1\right) / {\left[1+\left(T_{ {\rm{e} } } / 4\right)^{1.6}\right]}$ $\ln \mathrm{\varLambda}$ $23^{0.5} \ln \left(10^{-6} n_{ {\rm{e} } } / T_{\rm{e} }^{3}\right)$ $v_{\mathrm{en} }$ $\sigma_{ {\rm{en} } }n_0 \left(8 k T _{\rm{e} }/ \text{π}/ m_{\mathrm{e} }\right)^{0.5}$ $v_{\text {ei } }$ $2.9^{-12} n_{\rm{e} } \ln {{\varLambda} } / T_{ {\rm{e} } }^{1.5}$ de1 0 de2 8.31 de3 12.13
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