Interaction Of Modulated Electron Beams With Open Periodic Structures
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Interaction of Modulated Electron Beams with Open Periodic Structures
Three electromagnetic boundary value problems involving the interaction of modulated electron beams with open periodic structures are studied theoretically with particular emphasis on producing Smith-Purcell radiation. The problem of an ideal sheet electron beam coupled to a sinusoidally-modulated reactance surface is considered. The purpose of this investigation is to demonstrate the influence of the synchronism or forced resonance condition on the interaction and to point out how the Brillouin diagram can be used to predict some of the quantitative as well as most of the qualitative properties of this influence. The more practical three dimensional problem of an ideal beam coupled to the narrow tape helix is treated rigorously. The results of this analysis give quantitative estimates of the interaction strength obtainable experimentally. Finally it is pointed out that the prescribed source model is limited in accurately predicting its own length of validity and in describing surface wave coupling. (Author).