# Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite
## 3 Simulation Results
### Results
#### 3.2.2 Optimal Laser Energy  
It is essential to investigate the optimal laser energy of the transmitting SLR station in the simulation network for TLTT application using the Ajisai satellite. Therefore, we analyzed the detection probability to establish the TLTT link under the condition of the given system parameters and geometric configurations during the observable paths. Using Equation (14), we also analyzed the minimum laser energy corresponding to the threshold of detection probability at each epoch to receive one photoelectron. It is noteworthy that the minimum laser energy provides one chance to trigger the detector or establish the successful TLTT link during the passage duration time of 5 msec at minimum. As shown in Figure 6a, the peak values of detection probability for the three combinations are smaller than the threshold of the detection probability (\(P_{TH}\) = 0.2) for the 1 kHz repetition rate of laser pulses and the passage duration time of 5 msec. This means that there is no chance to successfully establish the TLTT link in the target network during the simulation period. The required or minimum laser energy, which makes the detection probability at each epoch equal to the threshold value during the reflecting duration of [PERSON]'s mirror, reaches approximately one thousand times the original transmitting laser energy (\(E_{t}\) =2.5 mJ), as shown in Figure 6b. The minimum laser energy is mainly caused by geometric effects with the same order analyzed in the previous section, because the peak value of the detection probability is close to the threshold (i.e., \(P_{TH}\)) for each combination. For the analytical approach to finding the optimal laser energy for the TLTT link in the target network, the number of TLTT paths (i.e., TLTT link available paths) and the total TLTT passage times, and the TLTT link available times in the TLTT path were also simulated in terms of changing the transmitting laser energy. As shown in Figure 7, the number of TLTT paths and the total passage time to allow TLTT link increase gradually to 96 paths and 732.5 min for Geochang station when the laser energy of 50 mJ is employed, which is 20 times the original energy of the transmitting laser at the Sejong SLR station. The averaged TLTT passage time per TLTT path at the Geochang SLR station is 7.6 min; this is quite enough time to receive the signal reflected by the Ajisai's convex mirror over 570 times (i.e., 7.6 min \(\times\) 60 s \(\times\) 1.25 Hz). For the Sejong-Beijing and Sejong-Koganei combinations with transmitting laser energy of 50 mJ, the number of TLTT paths and total TLTT passage times to allow TLTT link are 94 paths with 618.1 min and 65 paths with 400.7 min, respectively, as shown in Table 3.  
Figure 6: Time series of (**a**) detection probability and (**b**) minimum laser energy corresponding to threshold of detection probability. The optimal laser energy of the transmitting SLR station in the target network can be determined from the simulation results based on the operational concept of the TLTT application. If the averaged chance of the TLTT link is required to be more than one time per day in the target network, the laser energy of the Sejong SLR station should increase from 2.5 mJ to 10.0 mJ because Sejong-Koganei has the minimum number of TLTT paths, at 34 orbital paths, enabling the TLTT link for the period of 30 days. Figures 8 and 9 show the time series of detection probability and the ratio of more than one between the detection probability and its threshold (i.e., \(P_{D}/P_{TL}\geq 1\)), respectively, when employing a laser energy of transmitting station of 25 mJ, which was used at the Graz SLR station to track space debris with kHz repetition [23]. It is worth noting that this ratio indicates that the TLTT link occurs more than once during the duration of the light flash.