Adaptive Optics (AO) plays a key role in large-aperture ground-based telescopes, which corrected the wavefront distortions of atmospheric turbulence, and a diffraction image can be obtained. The first step for working AO is the phase aberrations sensed by a Wavefront Sensor (WFS) with a bright beacon adjacent to the science object. Unfortunately, the natural beacon is not populated with sufficient number in the sky, while the Rayleigh beacon is generated near 10 km with a significant cone effect. The sodium beacon was generated by the sodium atoms at 90 km excited with a laser tuned to D₂ line, which can probe the turbulence along the cylinder path more completely. Thus, the sodium beacon becomes an essential facility for 10 m class telescopes and the next-generation telescopes.The accuracy of the Shack-Harmann WFS is severely affected by the sodium beacon spot profile. The more compact the spot size and the greater the flux of photon return, the better the measurement accuracy. So, it is essential to estimate the sodium beacon spot profile during the AO system's design phase.The spot profile is determined by the power density at the sodium layer and the photon return efficiency of the laser interaction with the sodium atoms. The power density distribution at the sodium layer is spread by many factors, such as the diameters of the Laser Launch Telescope (LLT), the beam quality of the laser, the turbulence along the uplink path, the static aberrations in the laser launch optical path and so forth. Most of the factors can be optimized in the design of the laser launch system. Thus, the turbulence along the uplink path is a critical factor that should be considered.In this paper, the analyzation was based on the second generation LLT at Gaomeigu Lijiang astronomy observatory with a diameter of 300 mm, the laser is a Quasi-continuous Wave (QCW) solid state sodium laser with a power of 20 W, fabricated by the Technical Institute of Physics and Chemistry (TIPC), the atmospheric turbulence (value of Fried parameter r₀ at 550 nm) varies from 5 cm to 30 cm.Firstly, the continuous atmosphere was divided into 4 layers, with altitudes of 0 km, 4 km, 8 km and 12 km, the phase disturbance of turbulence was simulated by phase screen theory. The model of sodium laser propagated in the turbulence was established by angular spectrum propagation, the power density at the sodium layer can be obtained, the photon return efficiency was calculated by Monte Carlo method and rate equation, and the spot profile can be obtained.Secondly, a numerical simulation with 250 frames for the sodium beacon spot profile was conducted; the atmospheric turbulence was discrete into 4 layers, and the power density in each layer and sodium layer was affected by the phase aberrations on the previous layer and described by Fresnel diffraction. The spot profile of FWHM (in x and y direction) and photon return for r₀ values varies from 5 cm to 30 cm were exhibited. In order to survey the dispersion of the photon return, a box plot was also exhibited.Thirdly, some factors that affected the spot profile were discussed. The first factor is the layers of the continuous atmosphere discrete, including the number of the layers, the height and the relative strength of each layer. The atmosphere divided into 6 layers at Cerro Pachon in Chile was compared. The spot size is nearly the same with the 4 layers, while the photon return is maximized at r₀ of 10 cm, which is caused by diffraction of the phase disturbance. The second factor is the pointing direction of the laser beam, that is, the beam wander caused by tip-tilt. The centroids at different values of r₀ were obtained by the statistical method, the maximum value of beam wander can reach 60 cm, while the media value is nearly 22~25 cm when r₀ is 5 cm. The precision of centroid extraction is also affected by the high-order aberrations, and the number of layers affects the dispersion of the centroid spot. At last, the scintillation caused by the amplitude fluctuation of the atmosphere was discussed. For the 4 layers condition, the scintillation index increased first and then decreased, the maximum value occurs when r₀ is 10 cm, the reason is the scintillation saturation. For the 6 layers condition, the scintillation index is decreased with the increase of the r₀.We analyzed the spot profile of sodium beacon which was disturbed by turbulence, the FWHM varies from 0.26 m to 0.22 m, the photon return is at the order of $\left(\mathrm{1.3}~\mathrm{1.4}\right)\times {\mathrm{10}}^{\mathrm{7}}\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{s}?{\mathrm{s}}^{-\mathrm{1}}?{\mathrm{m}}^{-\mathrm{2}}$. The number of layers was a critical factor that should be considered, and the beam wander and scintillation were also discussed.