Thermal blooming can have a major impact on high energy laser (HEL) beam propagation in the atmosphere. Previous analyses about this effect are mainly focus on monolithic beam. In this paper, the numerical framework of atmospheric propagation of coherently combined beams is established. The corresponding time-dependent wave optics simulation code is also developed and utilized to investigate the propagation properties of coherently combined beams under various thermal blooming conditions. For the purpose of comparison, the simulations of atmospheric propagations of incoherently combined and monolithic beam are also included. In the end, the effect of fill factor is investigated in a preliminary manner. The beam propagation efficiency (BPE) as the performance metric of coherently combined beam is employed in this paper. The results show that the thermal blooming places a significant limit on the ability of coherently combined beams. The BPE is degraded significantly under the strong thermal blooming condition. Consequently, coherent beam combining is ineffective under typical atmospheric conditions.
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