Based on dynamical diffraction theory, we study nonlinear processes in the hard X-ray region. First, we consider the process of frequency doubling in perfect crystals in the general case where the process of Bragg rescattering of the generated harmonic field should be taken into account. The optimum conversion conditions for the Bragg and Laue interaction geometry are determined and the efficiency is calculated. Secondly, we consider the modulation of X-ray diffraction by a wave of coherent optical phonons produced by an intense laser pulse. We show that in the optimum regime the modulation period of the X-ray beam may be even shorter than the period of the excited optical phonons, as a result of higher order Raman scattering. Generation of extremely short X-ray pulses using this technique is discussed. Our results suggest that synchronous interaction schemes analogous to the schemes long known in nonlinear optics can significantly increase the efficiency of nonlinear processes in the hard X-ray region.
