Phase compensation instability (PCI) is a runaway process associated with the operation of a closed-loop phase-only adaptive-optics system transmitting through the atmosphere a large-diameter laser beam with a high power density. Under most conditions such an operation introduces positive feedback; if the laser power density is sufficiently high, there is the possibility of PCI-type runaway of the adaptive-optics servo. It is now known that the occurrence of PCI is inhibited by wind shear (wind-shear induced stabilization of PCI, or WISP) because at every different position along the propagation path the turbulent wind has a (slightly) different component of velocity in the plane transverse to the laser beam’s propagation direction. We develop a set of equations from which the conditions for the onset of PCI can be determined. Sample results are presented for propagation through an atmosphere with a negative exponential absorption profile—which nominally corresponds to ground-to-space propagation. The results indicate that for typical conditions (as a consequence of wind shear) one can transmit a rather substantial laser power density without encountering PCI. As an example of the application of our theory, the expected Strehl ratio for a HV5/7 turbulence model is evaluated for the parameters of a nominal ground-to-space high-energy laser beam propagation system.
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