## 3 Results and Discussion  
### The Results of the Triode Field Emission Structure Simulation  
In this section, the electron transmittance simulation results are discussed. Figure 2 is a schematic diagram of the CST simulation results. Figure 2a shows the flight trajectory of the electrons. Figure 2b shows the electron distribution on the anode plate. The red part in Figure 2b shows the distribution of electrons, while the white part indicates that some electrons have been intercepted by gate. Figure 2c shows the electric field intensity distribution of the model in space, and Figure 2d shows the electric field direction at the emission tip of the cathode. The electric field intensity on the surface of the cathode tip is the highest. The flight trajectory of electrons only depends on the electric field intensity in space. \begin{table}
\begin{tabular}{c c c c} \hline
**System Parameters** & **Initial Value** &
\begin{tabular}{c} **Structure Parameters of** \\ **the Model** \\ \end{tabular} & **Initial Value** \\ \hline Smallest cell & 0.005 mm & Cathode–Gate distance & 700 \(\upmu\)m \\ Largest cell & 0.43 mm & Anode–Gate distance & 2 cm \\ Number of iterations & 4 & Height of cathode & 500 \(\upmu\)m \\ Relative accuracy & \(-\)20 dB & Gate Voltage & 3000 V \\ Relaxation parameter & 0.3 & Anode voltage & 7000 V \\ Number of emission points & 52,934 & Distance between the grid wires & 0.01 mm \\ Boundary conditions & open & Width of the grid wire & 0.02 mm \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the simulation mode. Figure 3a illustrates the variation in electrode current at different grid wire distances. Figure 3b displays the trends in electron transmittance and grid aperture ratio at varying grid wire distances. The simulation results revealed that as the aperture ratio increased, the cathode current initially decreased, followed by an increase and then another decrease. When the distance between the grid wires was between 10 \(\upmu\)m and 30 \(\upmu\)m, the cathode current gradually decreased due to the broader grid wires, resulting in the grid wire intercepting most of the electrons. From 30 \(\upmu\)m to 147 \(\upmu\)m, the cathode current increased gradually because the electric field distribution between the cathode and grid altered with increasing grid wire distance, enhancing the tunneling ability of electrons and enabling more significant emission from the cathode. However, from 147 \(\upmu\)m to 600 \(\upmu\)m, the cathode current gradually declined as the effective projection area of the grid wire on the cathode decreased rapidly, weakening the cathode surface electric field and diminishing the field emission capacity, so the cathode current gradually tended to decrease. Due to the reduction in the number of electrons intercepted by the grid wire, the gate current decreased gradually while the anode current increased, ultimately approaching saturation. The trends in electron transmittance correspond to the variation in grid aperture ratio, increasing gradually with an increase in the grid aperture ratio. Figure 3c depicts the current variations in each electrode at varying grid wire distances. Figure 3d shows the changes in electron transmittance at different grid wire distances. The grid wire width was set to 20 \(\upmu\)m, while the anode voltage, gate voltage, distance between the grid and anode were fixed at 7.0 kV, 3.0 kV, 700 \(\upmu\)m, and 2.0 cm, respectively. The gate voltage and anode voltage were kept constant, while the width of the grid wire and the distance between the grid wires were adjusted to achieve an aperture ratio of 70%. The anode current decreased from 0.0434 A to 0.0422 A, the gate current decreased from 0.0228 A to 0.0185 A, and the cathode current decreased  
Figure 2: The simulation results of the model in CST. (**a**) The trajectory of the electron beam. (**b**) The anode electron beam spot. (**c**) The electric field intensity distribution of the entire model. (**d**) The electric field distribution at the cathode tip. from 0.0664 A to 0.0607 A.