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In this paper conceptual points regarding electrons elastic (Kapitza-Diraceffect) and inelastic diffraction effect on the different type slowedelectromagnetic wave structures/light gratings are considered. From the unifiedpoint of view it is analyzed the main works on this subject for last fourdecades in chronological order, pointing out the essential peculiarity inherentin induced Cherenkov, Compton, and undulator/wiggler processes too. This reviewarticle has also a goal to resolve confusion in scientific literature connectedwith the recently appeared paper [6] relating the electrons diffraction on atraveling wave in a dielectric medium.

Electrons diffraction scattering on a traveling wave - "Inelastic Kapitza-Dirac effect"