Radiation by an Electron Beam Interacting with a Diffraction Grating. Two-Dimensional Theory

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Abstract
Expressions are obtained for the power radiated by a modulated electron beam passing near the surface of a (perfectly conducting) diffraction grating. The electromagnetic fields are calculated in terms of the two‐dimensional scalar Green's function for the grating surface. The grating profile may be chosen as any function that can be represented by a Fourier series, and the Green's function is developed as a power series in the grating groove depth. By superposition, the radiation by a moving line charge is also considered. The results are compared with those of previous treatments.