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

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.