By using the four-dimensional propagation code including the model of a realistic adaptive optics system, adaptive optics phase compensation for nonlinear thermal blooming effects of the high energy laser them propagation in the atmosphere is numerical simulated. The phase compensation instability (PCI) characteristics are analysed. The influence of the bandwidth (time delaying) and the deformable mirror interactuator spacing of the adaptive optics system on the phase compensation efficiency are discussed in detail.