Smith-Purcell radiation is a well-known phenomenon, which provides a noninvasive scheme for diagnostics of charged particle beams and is used as an effective source of electromagnetic waves, e.g., in the orotron, the free electron laser, etc. In this paper we develop the theory of Smith-Purcell radiation (SPR) for the little-investigated case of arbitrary angles between the charged particle trajectories and the rulings of a grating. The effect of conical diffraction arising here changes drastically the space distribution of the radiation. By contrast to the only existing approach, described by Haeberle et al. [Phys. Rev. E 55, 4675 (1997)], which requires difficult numerical calculations, we give a fully analytic theory of SPR. Also, in this paper we present for the first time the theory of x-ray Smith-Purcell radiation. Evanescent waves on the surface are shown to lead to strong enhancement of Smith-Purcell radiation, through a resonant mechanism. The results are important for the description of real divergent high-brightness beams and for the development of novel noninvasive diagnostic schemes based on the Smith-Purcell effect.

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