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Abstract-An exhaustive description of the parametric X-ray (PXR) generation by relativistic electrons in a crystal excited by an acoustic wave is proposed. A principal question as to whether it is possible to enhance the PXR yield under these conditions is considered.Increasing interest in the analysis of high-energy electromagnetic processes in oriented crystals under the action o f external factors (e.g., acoustic waves) is related to the possibility o f controlling these processes. In particular, the effect o f acoustic waves was studied w ith respect to the coherent bremsstrahlung radiation [ 1,2], coherent electron-positron pair production in a crystal [3,4], diffraction of free photons [5,6], X-ray transition radiation [7], and param etric X-ray (PXR) generation [8][9][10][11][12][13].

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