## 4 Instrument Design
### Detailed Designs
#### 4.2.4 Design of Geometric Factor  
When conducting measurements, we assume that the particle flux is isotropic. Next, the instrument's counting rate has the following relationship to the particle flux in the environment.  
\[\mathrm{S(cm^{-2}s^{-1}sr^{-1})=\frac{N\big{(}\frac{counts}{s}\big{)}}{G(cm^{2}sr )}} \tag{1}\]  
where S represents the measured value of the instrument's flux, N represents the instrument's count rate, and G represents the instrument's geometric factor. It can be seen from the above formula that the measurement range of the instrument flux is related to the counting ability per unit time and geometric factor [36].  
The geometric factor is very important. It is related to the geometric structure of the detector and the interference of different energies and different types of particles in the counts of each energy range. The geometric factor determines the ability of the instrument to accept space particles and also determines the final count rate state of the instrument. Through the scientific and rational design of the geometric factor of the instrument, it cannot only ensure that the counting of each channel of the instrument will not be saturated, but also avoid the phenomenon where the counting rate is too low and the statistical fluctuation is too large.  
According to the basic structure of the collimator and sensor system in the high-energy particle probe, the detection opening angle of each probe can be determined, as shown in Figure 11.  
The detection opening angle of each high-energy proton probe is 40\({}^{\circ}\), and the geometric factor is about 0.30 cm\({}^{2}\)sr. According to this geometric factor, the counting of each energy range can be evaluated, as shown in Table 4.  
Figure 11: Schematic diagram of detection opening angle structure in the high-energy particle detector.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Energy Channel** & **Energy Range** & **Logical Working Modes** \\ \hline E1 & 0.15–0.35 MeV & \(\mathrm{A1_{0.14}\cdot\overline{A1_{0.35}}\cdot\overline{A2_{0.1}}\cdot \overline{A3_{0.1}}}\) \\ E2 & 0.35–0.65 MeV & \(\overline{A1_{0.65}}\cdot\mathrm{A2_{0.1}}\cdot\overline{A2_{0.56}}\cdot \overline{A3_{0.1}}\) \\ E3 & 0.65–1.20 MeV & \(\overline{A1_{0.0}}\cdot\mathrm{A2_{0.56}}\cdot\overline{A2_{1,14}}\cdot \overline{A3_{0.1}}\) \\ E4 & 1.2–2.0 MeV & \(\overline{A1_{0.0}}\cdot(\mathrm{A2}+\mathrm{A3})_{1.14}\cdot(\overline{A2+A3})_{ 1.94}\) \\ E5 & 2.0–5.7 MeV & \(\overline{A1_{0.0}}\cdot(\mathrm{A2+A3})_{1.94}\cdot(\overline{A2+A3})_{ 3,0}\) \\ E6 & 3.0–5.7 MeV & \(\overline{A1_{0.0}}\cdot(\mathrm{A2+A3})_{3.0}\cdot(\overline{A2+A3})_{ 5,0}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Logical working modes of high-energy electron probe.  
The detection opening angle of the high-energy electron probe is 30\({}^{\circ}\), and the geometric factor is about 0.05 cm\({}^{2}\)sr. According to the measurement results of POES [37; 38], the electron flux of \(>\)100 keV was about 106 cm\({}^{2}\)ssr, and the electron flux of \(>\)300 keV was about 5 \(\times\) 10\({}^{5}\) cm\({}^{2}\)ssr.  
According to the geometric factor of the high-energy electron probe and the maximum electron flux measured by the POES satellite, the counting of each energy range is shown in Table 5. It can be seen that the design of the geometric factor of the high-energy electron probe is reasonable and can meet the electronic requirements of below 10\({}^{5}\) counts/s.  
The minimum particle resolution time of the hardware circuit was 3 uS, and the corresponding maximum counting ability was 3.3 \(\times\) 10\({}^{5}\) particles. Considering the random incident effect, the maximum count of general counting is controlled at about 1/5 of the maximum counting ability, which is 6.6 \(\times\) 10\({}^{4}\) particles, within the reasonable range of processing.