Impact of branch points in adaptive optics compensation of thermal blooming and turbulence

Adaptive optics (AO) can be used to mitigate turbulence; however, when a single deformable mirror is used for phaseonly compensation of thermal blooming, analysis predicts the possibility of instability. This instability is appropriately termed phase compensation instability (PCI) and arises with the time-dependent development of spatial perturbations found within the high-energy laser (HEL) beam. These spatial perturbations act as local hot spots that produce negativelens- like optical effects in the atmosphere. An AO system corrects for the hot spots by applying positive-lens-like phase compensations. In turn, this increases the strength of the thermal blooming and leads to a runaway condition, i.e., positive feedback, in the AO control loop. This study uses computational wave-optics simulations to model horizontal propagation with the effects of thermal blooming and turbulence for a focused Gaussian HEL beam. A point-source beacon and nominal AO system are used for phase compensation. Previous results show that a high number of branch points limit the development of PCI for phase compensation of only thermal blooming. For phase compensation of thermal blooming and turbulence, the number of branch points decreases and system performance is reduced. A series of computational wave-optics experiments are presented which explore the possibility for PCI.