## 1 Introduction  
Non-terrestrial networks (NTNs) were developed as next-generation wireless backhaul systems to provide network services everywhere. Because of several advantages, such as higher bandwidth, greater security, and immunity to electromagnetic interference, and network flexibility, free-space optical (FSO) communication has been thoroughly studied for implementation in NTNs [1]. Recently, unmanned aerial vehicle (UAV)-assisted FSO communication has been actively studied to connect regions hundreds of kilometers away. High-altitude platform (HAP) UAVs establish FSO-based backhaul networks to resolve atmospheric fading and connect regions hundreds of kilometers away. Because an FSO system establishes point-to-point communication links, maintaining alignment among the transceivers is a critical challenge [2]. The mechanical vibrations in UAVs and building sway cause pointing errors. Therefore, appropriate pointing, acquisition, and tracking (PAT) procedures require directing the laser beam from the transmitter to the receiver and maintaining the alignment between them during communication. There are two ways to maintain line of sight in FSO communication: transmitting a broad beam for pointing error and increasing the transmitter power using a narrow beam. However, transmitting a broad beam results in geometric loss, and using a narrow beam causes pointing loss [3]. Hence, considering the abovementioned trade-off and deciding on a proper beam divergence angle on the basis of the signal-to-noise ratio (SNR) or capacity of the FSO link is a well-known technique [4, 5, 6, 7]. In the case of a horizontal link, a UAV altitude of 20 km is considered to mitigate the turbulence effect, as shown in Figure 1. However, atmospheric turbulence causes significant signal loss in an FSO vertical link for the optical ground station (OGS) [8]. Even in clear weather conditions, transmitted optical signals suffer significant scintillation losses due to random variations in the atmospheric refractive index [9; 10]. This effect is induced by the variation in the refractive index of the atmosphere, which can cause the light to bend and scatter as it travels through the air. Consequently, it causes random fluctuations in received signal intensity. Thus, the effect of atmospheric turbulence should be considered, and scintillation mitigation methods have been studied accordingly [11; 12; 13]. The present investigation is based on two aspects: first, a rapid increase in scintillation index with a slight increment in pointing error [14]; second, less affection by scintillation in a larger beam width due to the broad beam propagation from spherical wave to plane wave [15]. The narrow beam propagates as a Gaussian beam from the aspect of beam divergence angle. By contrast, the broad beam propagation is from the Gaussian beam to a spherical wave. Accordingly, the wider the divergence angle, the less is the affection caused by scintillation. The scintillation effect increases exponentially as the number of pointing errors increases. Therefore, the use of wider beams is proposed to reduce the scintillation effect when pointing errors constantly occur. In this paper, we propose an adaptive beam that adjusts its divergence angle according to the pointing error between the communicating optical transceivers to mitigate the effect of scintillation due to pointing error. Adaptive beam divergence control has been investigated for several purposes [16; 17; 18; 19; 20]. In the work of [PERSON] et al. [16], the beam was controlled for a variable distance, and [PERSON] and [PERSON] attempted to improve link availability or save transmitter power while preserving target link availability [17]. [PERSON] and [PERSON] also reported a beaconless PAT system [18] and adaptive beam control to mitigate the effects of angle-of-arrival fluctuation and pointing error [19; 20]. However, most of the research focuses on the horizontal link without considering scintillation.