The anomalous passage of X-and gamma-rays beams by the three waves difraction

We consider a three-wave dynamical problem of the diffraction of x- and gamma rays in the case of non-coplanar diffraction, when the two reflected waves do not interact directly with each other. We obtain approximate equations which describe the propagation of confined beams during three-wave diffraction in perfect crystals. We estimate the conditions of applicability of plane-wave approximation, and present numerical estimates.