We consider theoretically and numerically the suppression of fluctuations (scintillations) of a laser
beam propagating through turbulent atmospheres by applying a phase modulator. Both spatial and
temporal phase variations introduced by this phase modulator are analyzed. The explicit
dependences of the scintillation index on the initial correlation length and finite-time phase
variations for long propagation paths are obtained. Results of modeling and numerical simulations
are presented. We demonstrate that an appropriately chosen phase modulator can significantly
suppress the scintillations of the laser beam caused by turbulent atmospheres.