Pulsed single-photon Bessel beams propagation in non-Kolmogorov turbulent atmosphere

► The long-term temporal broadening and the acquisition probability of single-pulse density were modeled. ► The long-term temporal broadening are the nolinear-increase functions of the index of turbulence. ► The effect of turbulence on the acquisition probability can be described by a Gaussian function. ► There is the turbulent diffraction of Bessel beam but no free-space diffraction.