A two-dimensional theory of the splitting effect of the far-field pattern of diffraction radiation caused by the excitation of plasma waves of the space charge in the electron flow is developed. The electron flow is moving close to one or more localized inhomogeneities in the form of rectangular cavities on the metal surface. The problem is reduced to a singular integral equation for the amplitudes of the radiation field. The far-field patterns of Smith - Purcell radiation are obtained in the particular case where a sequence of cavities forms a uniform grating of finite length. Features of the splitting effect are determined depending on the electron flow parameters that are verified by the experimental measurements. The theory results are perspective for the determination of the radiation characteristics of spatially developed periodic structures in the devices of diffraction electronics.

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