Smith-Purcell radiation from a narrow tape helix

A theoretical investigation of a narrow tape helix excited by a modulated electron beam gives quantitative results which can be used to estimate the strengths of interactions obtainable in experimental configurations. Extensive results are presented for the radiation emitted by a single fast space harmonic when a slow beam is in synchronism with the azimuthally symmetric space harmonic. The effects of beam velocity, frequency, beam diameter, tape width, and pitch angle are illustrated. The analysis also demonstrates the influence of the synchronism or electromagnetic resenance condition on the interaction and, further, points out the usefulness of the complex Brillouin (k - β) diagram in predicting some of the quantitative as well as most of the qualitative properties of this influence.