# Link Budget Analysis with Laser Energy for Time Transfer Using the Ajisai Satellite
## 4 Discussion  
The purpose of this paper is to investigate an analytical approach to finding the optimal laser energy of a transmitting station via analysis of the geometric effects on the TLTT link budget for TLTT implementation using the Ajisai satellite. The minimum geometric terms of space loss, atmospheric attenuation and cirrus cloud cover in the TLTT link budget have values of 0.055%, 0.075% and 0.077%, respectively, when compared to the peak values of each combination. The peak values can be obtained when the slant range and zenith angle of receiving path are at minimum under the maximum zenith angle of the transmitting path. Another term affected by the geometric configuration is the effective cross section of the Ajisai's convex mirror, which has a range of 93.9%\(-\)99.9% when compared to the peak value of effective cross section at the minimum phase angle of each combination. Consequently, the geometric effects reduce the TLTT link budget by three orders of magnitude when compared to the peak value of the TLTT link budget in the simulation; the cross section effect of the Ajisai's convex mirror is relatively smaller than other geometric effects coming from free space loss and atmospheric degradation. The reduced value of TLTT link budget increases the required laser energy to receive one photoelectron by the same order at every epoch during the entire TLTT passage time, because the peak value of the TLTT link budget in the target network is close to the critical value for TLTT link establishment. The chance of establishing a TLTT link can be determined as the ratio between the detection probability and the threshold value \(P_{TH}=0.2\) for 1 kHz repetition rate of laser  
Figure 8: Time series of detection probability with 25 mJ energy at transmitting station (Sejong). Figure 9: Ratio of detecting probability to threshold value for receiving one photoelectron from Ajisai’s reflective mirror in satellite elevation space. (**a**) Sejong\(-\)Geochang, (**b**) Sejong\(-\)Beijing and (**c**) Sejong\(-\)Koganei. pulse and the passage duration time of 5 msec. When employing the original value of laser energy \(E_{t}\) = 2.5 mJ at Sejong SLR station, all the detection probabilities are less than the threshold ratio (i.e., \(P_{\mathrm{D}}/P_{\mathrm{T}H}<1\)). This means that there is no chance to establish the TLTT link and zero TLTT path in the target network during the simulation period. When the laser energy of the transmitting station increases to \(E_{t}\) = 25 mJ, the ratio of the detection probability improves 3-5 times for each combination, which can be interpreted as the maximum number of photoelectrons to receive at each station; the TLTT paths also increase to 50% of total observable paths during the simulation period. By increasing the laser energy of the transmitting station from 2.5 mJ to 50 mJ, the number of TLTT paths increases from 0% to 94.1% of the total observable paths; total TLTT passage times gradually increase from 0% to 66.4% of the total passage times for all observable paths in the period of 30 days with 20 degrees cut-off angle. Therefore, using these simulation data, the optimal laser energy of the transmitting station can be selected following the operational concept for TLTT implementation (i.e., frequency of TLTT paths and total TLTT passage times) in the target network. It was demonstrated that a few tens of mJ level of laser pulse energy at the transmitting station is quite enough for TLTT realization in the target network, and that optimal laser energy can be selected through an analytical approach based on not only the operation concept of the TLTT network but also the threshold of detection probability. Conceptualization, J.U.P. ; Formal analysis, J.U.P. and M.C. ; Software, J.U.P. and H.-C.L. ; Writing--original draft, J.U.P. ; Writing--review and editing, H.-C.L. and K.-P.S. ; Project administration, M.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.