Research on a Low Energy Tele-focus Electron Gun
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摘要: 针对可移动非接触式月球表面电位探测器的电位无扰动测量单元对低能远焦电子束的需求，设计了低能远焦电子枪。以平板二极管电子枪为电子源，匹配两个静电聚焦透镜，将电子源引出的发散电子束聚焦为需要的形状，并加速至所需能量。优化电子枪的几何参数以及施加在电极上的电位，电子枪引出的电子束能量在5~500 eV内，并且具有良好的电子光路特性。电子束能量为5 eV时，初始半径r为5 mm，束腰至电子枪出口的距离p约为133 mm。随着能量增加，r逐渐减小至500 eV时的3 mm左右，p逐渐减小至105 mm。电子束经月球表面电场反射被电子收集平极接收，仿真数据和理论分析结果均表明，电子枪的工作距离为400~600 mm，平板接收的电子占发射电子比例在96%以上。电子枪结构质量仅408 g，满足探测器对电子枪的质量需求。Abstract: A low energy tele-focus electron gun is designed based on a subsystem of movable non-contact lunar surface potential detector. The electron gun consists of a diode extraction source and two three-element electrostatic lenses. The source produces a divergent beam which is then accelerated to energy Ke by lenses, and is focused into the shape of interest. By optimizing the geometric parameters of electron gun and the voltage applied to electrode, the electron beam has good optical characteristics and the electron energy is adjustable from 5 eV to 500 eV continuously. The initial radius r equals to 5 mm, and the distance p from the output electrode to the beam waist equals to 133 mm when the beam energy is 5 eV. As the beam energy increases to 500 eV, initial radius r decreases to 3 mm, and the distance p decreases to 105 mm. The electron beam reflected by lunar electric field is received by the collector plate. When working length H is between 400 mm and 600 mm, the electrons received by plate account for more than 96% of the beam electrons. The mass of the electron gun is only 408 g, which can meet the requirements of electron guns for lunar exploration.
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图 1 可移动非接触式月球表面电位探测器技术方案
Figure 1. Scheme of movable non-contact lunar surface potential detector
图 2 月球车与月球表面电位关系
Figure 2. Relationship between rover potential and lunar surface potential
图 4 月表电位无扰动测量单元与月球车的电连接
Figure 4. Electrical connection between potential undisturbed measuring unit and rover
图 5 利用反射电流反演电位原理
Figure 5. Schematic diagram of potential inversion using reflected current
图 6 月球经典鞘层及饱和鞘层的月表电势随高度变化曲线
Figure 6. Variation of lunar surface potential with altitude in the classical and saturated lunar sheaths
图 7 月球表面电位测量电子束光路（r为电子束的初始半径，p为束腰到电子枪出口的距离，H为电子枪的工作距离，θ为电子束收敛全角。蓝色箭头为理想状态下电子束的外轮廓，黑色虚线箭头为实际情况下电子束的外轮廓）
Figure 7. Electron optical diagram for measuring the lunar surface potential (r is initial radius of electron beam, p is distance from output electrode to beam waist, H is working length, and the θ is full angle of beam convergence. The blue arrow represents the outline of the ideal electron beam, and the black dashed arrow represents the outline of the electron beam in practice)
图 9 收敛高斯电子束的相图（a）及电子收敛角的统计分布（b）
Figure 9. Phase diagram of a convergent Gaussian electron beam (a), and statistical distribution of electron convergence angles (b)
图 12 电子枪内沿轴的电位分布以及电位梯度分布
Figure 12. Potential distribution and the potential gradient distribution along the axis
图 15 电子束束腰位置长度与电子枪能量的关系
Figure 15. Relationship between electron beam waist position and electron gun energy
图 16 阳极与透镜的最后电极以及电子束的电流占阴极发射电流的比例（红色曲线为电子枪引出电流）
Figure 16. Ratio of anode, last lenses electrode and electron beam current to the total emitted current (red curve is the current drawn from the electron gun)
图 17 电子束在电子枪出口的相图
Figure 17. Phase space diagram of the electron beam at the exit of the electron gun
图 18 电子束收敛全角的半高全宽。蓝色曲线为电子枪出口处电子束在x方向的收敛角，红色曲线为电子枪出口处电子束在y方向的收敛角
Figure 18. Full width at half-maximum of the beam convergence angle. The blue curve is the convergence angle of the electron beam in the x direction at the exit of the electron gun, and the red curve is the convergence angle of the electron beam at the exit of the electron gun in the y direction
图 19 电子束初始直径的半高全宽。蓝色曲线为电子枪出口处电子束在x方向的初始直径，红色曲线为电子枪出口处电子束在y方向的初始直径
Figure 19. Full width at half-maximum of the beam initial diameter. The blue curve is the initial diameter of the electron beam in the x direction, and the red curve is the initial diameter of the beam in the y direction
图 21 电子收集平板收集的反射电子占发射总电子的比例
Figure 21. Ratio of the reflected electrons collected by the colleting plate to the total electrons emitted
图 22 不同工作距离电子收集平板接收的反射电流占发射电流的比例
Figure 22. Ratio of the reflected current received by the collecting plate at different working distances to the emitted current
表 1 各电极的电压设置（电子束能量为Ke，电压为相对于阴极电压的测量值）
Table 1. Voltages applied to electrode, where electron beam energy equals to Ke, and the operating voltages are referred to the cathode voltage
Electrode Aperture diameter /mm Potentials /V Cathode － –Ke A 0.5 0 B 20 0.5 Ke C 20 10.25 Ke D 20 0 E 30 0.5 Ke F 30 4.4 Ke G 30, 10 0 
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表 2 月球表面各区域的电子、离子、次级电子以及光电子电流
Table 2. Electron, ion, secondary electron, and photoelectron currents density in various regions of the lunar surface
Current density/(A·m–2) Day Term Night Crater Far edge $j_{\rm{e}} $ 1×10–6 3.52×10–8 4×10–10 5.1×10–10 1.6×10–8 $j_{\rm{i}} $ 3.2×10–7 3.52×10–8 4×10–10 1.6×10–11 7.5×10–9 $j_{\rm{s}} $ 0 0 4×10–11 5×10–10 4×10–9 $j_{\rm{p}} $ 4×10–6 0 0 0 0
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