采用多层相屏法和快速傅里叶变换法数值求解热晕方程，研究了复合贝塞尔高斯（cBG）光束大气传输过程中受热晕效应的影响。研究发现：由于热晕效应造成的光强和相位畸变，cBG光束会发生相位奇点移动和轨道角动量谱展宽，并产生模式串扰。当风速较小时，大气介质吸收激光产生的热效应较强，导致光束的模式串扰也较强。对于初始角量子数差值较大的cBG光束，其相对串扰能量较小，受热晕效应影响导致的模式串扰较弱。此外，还研究了旋转cBG光束的热晕效应，该光束的旋转特性使其在传输过程中四周都能得到均匀的扩展。因此，相较于非旋转cBG光束，旋转cBG光束的光强分布比更均匀，模式串扰更小。并且，随着旋转cBG光束的径向波数差值的增大，模式串扰减弱。综上，增大初始角量子数差值以及径向波数差值可以有效降低cBG光束的模式串扰。

Bessel-Gaussian beams have potential applications in laser atmospheric engineering applications such as directed energy and space optical communication. The influence of the thermal blooming effect on composite Bessel-Gaussian (cBG) beams propagating in the atmosphere is studied using the multi-phase screen method and the fast Fourier transform to solve the thermal blooming equation. The Fast Fourier Transform (FFT) is capable of processing the propagation between the phase screens. Consequently, the propagation process of the cBG beam from z_n to z_n+1 can be divided into three steps: the first step is the vacuum propagation Δz/2 via the fast Fourier transform; The second step is the phase change caused by the atmospheric refractive index fluctuations; The last step is the remaining vacuum propagation Δz/2 via the fast Fourier transform again. Thus, the atmospheric propagation of the beam is converted into the propagation between the multi-phase screens, and the phase screens represent the disturbance of thermal blooming on the beam. Based on the above method, a 4D computer code is designed to simulate the time-dependent propagation of cBG beams in the atmosphere. To be convenient to analyze the thermal blooming effect of cBG beams, we provide the expression for the amplitude factor. Considering both the diffraction of the optical field and the time scale of the thermal blooming effect, we study the beam distortion, orbital angular momentum spectrum, and mode crosstalk of cBG beams under the thermal blooming effect. Due to the wind-dominated thermal blooming effect, the phase singularity positions cBG beams are irregularly shifted. By analyzing the orbital angular momentum spectrum of the cBG beam under the thermal blooming effect, we found that the energy between the initial modes of the beam is transferred to each other, producing mode crosstalk.With the increase of propagation distance or the decrease of crossing wind velocity, the strength of the thermal blooming effect increases, resulting in the enhancement of mode crosstalk. The relative crosstalk energy of the cBG beams gradually increases with time; until the absorption of beam power by the atmosphere is balanced by the heat exchange caused by the crossing wind, the thermal blooming effect reaches a steady state. The relative crosstalk energy no longer changes with time. The flow rate of a medium determines the speed of its energy transport. The thermal effects during beam propagation are stronger for lower wind speeds, resulting in stronger mode crosstalk. The relative crosstalk energy decreases with the difference value of an initial angular quantum number. Therefore, the cBG beam with a larger difference value of an initial angular quantum number has the weaker mode crosstalk affected by thermal blooming. The thermal blooming effect of rotating cBG beams is studied. A rotating cBG beam can spread uniformly in the atmosphere due to the thermal blooming effect controlled by the wind. Moreover, the mode crosstalk of rotating cBG beams is smaller than that of non-rotating cBG beams. The mode crosstalk of rotating cBG beams decreases with the difference value of radial wave number. To sum up, increasing the differences values of the initial angular quantum number and radial wave number can effectively reduce the mode crosstalk of cBG beams. The results obtained in this paper have important implications for the applications of BG beams in laser atmospheric engineering, such as directed energy and space optical communication.