Instability of an optical beam in a moving turbulent atmosphere

The approximate method of smooth perturbations is used to analyze the instability of an optical beam in a moving medium with a scattering thermal nonlinearity. In the case of one-dimensional perturbations, the character of the instability is similar to that of pulsed radiation. In general, elongated perturbations having characteristic scales $a/\sqrt{S_0}$ along the wind velocity and $1/q_FS_0^{1/4}$ in the transverse direction ($a$ is the aperture size, $q_F$ is the Fresnel frequency, $S_0$ is the self-induced phase advance) are the most unstable. These perturbations grow proportionally to $\exp(1.16\sqrt{S_0})$. An analysis is made of the instability in the presence of background turbulence.