The phase fluctuations of the Bessel-Gauss optical beams in randomly inhomogeneous media are studied. The results of calculation by the method of smooth perturbations of the variance of the fluctuations of a phase of the Bessel-Gauss beams in turbulent atmosphere are presented. The effect of relative weakening of the fluctuations of a phase of the Bessel-Gauss beam in comparison with the case of the plane wave is found. Weak dependence of the variance of fluctuations of a phase in the Bessel-Gauss beam on parameters of the Gaussian factor of the beam is observed. The phase fluctuations of the Bessel beam are non-uniform in space: the relation of the variance of fluctuations of a phase of Bessel beam in a point, displaced from the optical axis of a beam, to the variance of the fluctuations of a phase of Bessel beam on its optical axis is minimal in maxima of the Bessel beam and is maximal in minima.
Bessel beam, phase fluctuations, atmospheric turbulence