## 3 Results and Discussion
### Uniformity of Protection  
Since the protective measures outlined in this paper are intended to be implemented on an upgraded instrument, real-life orbit verification has not yet been conducted. As a result, we have relied on structural modeling and material simulation analysis to achieve our verification goals.  
This paper takes a specific model as an example to analyze the omnidirectional shielding thickness for the edge devices on the top surface of a PCB in a local protective box. FR4 epoxy board was selected as the board's substrate, with a PCB density recorded as 0.93 g/cm\({}^{3}\) due to the multi-layer structure, PP adhesive, aperture, and copper. Three widths of the outer edge \(D_{E}\) were used for calculation: 0, 3 mm and 6 mm. Specific parameters are shown in Table 2.  
A spherical color temperature diagram can be used to represent the calculation result of the path length of an omnidirectional ray. Path lengths over 4 mm are indicated with the same color to distinguish the weak area of radiation protection more clearly, as shown in Figure 7. When PCB protection or the outer edge of the box are not taken into account, the lower half space of the edge points will appear as weak areas, that is, the zenith angle in the range of 100\({}^{\circ}\) to 140\({}^{\circ}\). The protective thickness is less than 0.5 mm, accounting for more than 1/4 of the total 4\(\pi\) omnidirectional space. When the width of the outer edge \(D_{E}\) increases to 3 mm and 6 mm, the proportion of space area with a protective thickness less than 0.5 mm decreases significantly. The weak area eventually tends to be close to the parallel direction of the PCB.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Group** & \(D_{K}\) & \(D_{P}\) & \(D_{T}\) & \(D_{E}\) & \(\rho_{eff}\) & \(\rho_{P}\) \\ \hline
3 & 3 mm & 3 mm & 2 mm & 6 mm & 2.8 g/cm\({}^{3}\) & 0.93 g/cm\({}^{3}\) \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of the protective box.  
Figure 7: Omnidirectional protection thickness in the absence of PCB protection. (a) \(D_{E}\) = 0 mm; (b) \(D_{E}\) = 3 mm; (c) \(D_{E}\) = 6 mm.  
Furthermore, when considering the protective factors of the PCB at a zenith angle of 100\({}^{\circ}\), as illustrated in Figure 8, the range of particles within the PCB can reach over 17 mm, which is equal to a 5 mm thick Al layer. The worst position of the protective thickness occurs when the zenith angle is equal to 130\({}^{\circ}\), where the equivalent Al thickness would be only about 1.5 mm, even with PCB protection. To offset the incident range of particles in the zenith angle range of 110\({}^{\circ}\)-140\({}^{\circ}\), the outer edge of the boundary should be increased. This would equate to an equivalent Al thickness of 4 mm with a 6 mm wide outer edge. Additionally, the protective thickness over the whole 4\(\pi\) omnidirectional space can exceed 3 mm.  
In cases of extreme weight constraints, the width of the outer edge can be designed at 3 mm. This results in protective thickness, which is relatively uniform in the overall space, with the weak area being reduced to 2.9 mm only when the zenith angle is approximately 110\({}^{\circ}\). The outer edge of the enclosure should be combined with the range of particles in the PCB. It is important to maintain radiation protection while minimizing the size of the outer edge to keep the overall weight of the protective box as low as possible.  
Due to the high sensitivity of the photon-counting imaging detector mentioned in Section 2.1, an outer edge structure may also be considered in order to provide protection for the detector inlet. As the exposed area of the peripheral wall of the detector is dominant, applying three layers of materials, as mentioned in Section 3.2, would be beneficial in these areas to prevent charged particles from penetrating too far, thus improving the sensitivity of the detection system.