## 3 Results and Discussion
### The Electron Beam Fluorescence Imaging Experiments  
To study the variation in electron beam spot size at different aperture ratios, fluorescence imaging experiments were conducted. The gate voltage was maintained at 1.6 kV while the anode voltage was increased from 1.5 kV to 8.0 kV. The fluorescence images obtained are shown in Figure 6a. Figure 6b illustrates the relationship between the electron beam spot size and the anode voltage. The y-axis of Figure 6b represents the area of the electron beam spot. As the voltage increased, the area gradually decreased, and the electron beam spot narrowed inward. This phenomenon was attributed to the enhancement of the anode electric field, which reduced the time for electrons to reach the anode. It took less time for the electrons to spread around, and the electron beam became more concentrated. As a result, the electron beam spot on the anode was reduced.  
When the anode voltage was kept constant at 7.0 kV and the gate voltage was increased from 1.7 kV to 2.2 kV, a fluorescence image was produced, as shown in Figure 6c. The relationship between the electron beam spot size and the gate voltage is illustrated in Figure 6d. With an increase in the gate voltage, the area of the electron beam spot on the fluorescent plate gradually expands. This indicates that, under fixed anode voltages, an increase in gate voltage leads to a more significant emission of electrons from the cathode, resulting in an expansion of the electron beam's divergence angle.  
Figure 6e shows the fluorescent images at different aperture ratios. Figure 6f shows the area of the electron beam spot at different aperture ratios. The voltage of each electrode is unchanged, and it can be observed that an increase in the aperture ratio intensifies the divergence of cathode electrons, thus increasing the size of the electron beam spot, which is not conducive to subsequent focusing. Therefore, it is only possible to increase the aperture ratio of the grid with limitations.  
To summarize the work described above, from the simulation and experiment results, with an increase in the grid aperture ratio, the cathode current increased first and then decreased, the gate current decreased continuously, and the anode current increased until saturation when the anode voltage and the gate voltage remained constant. The electron transmittance increased as the aperture ratio increased. When the gate voltage was fixed and the grid aperture ratio remained constant, the cathode current remained stable. The higher the anode voltage, the greater the anode current and electron transmittance. Furthermore, if the anode voltage and gate voltage remained constant, the current of each electrode decreased as the gate distance increased, while the electron transmittance remained stable. Increasing the anode voltage could reduce the electron beam spot size, enhancing the electron transmittance. While increasing the gate voltage increased the cathode current, it also enlarged the size of the electron beam spot. Increasing the grid aperture ratio elevated the electron transmittance. However, it also caused a reduction in the field emission current of the cathode, and the electron divergence of the cathode increased. The electron transmittance was still low when the grid aperture ratio was less than 75%. When the aperture ratio was greater than 85%, the electron transmittance was saturated but exacerbated the electron beam dispersion, and the size of the anode electron beam spot also gradually increased.