A self-consistent investigation of Smith–Purcell radiation from a narrow tape helix
The interaction of a modulated electron beam and a narrow tape helix is considered using a confined flow model for the beam. With this model, the analysis is self-consistent in that it takes into account the first-order effects of the interaction on the beam. The interaction is studied by means of complex waves on the composite system of the beam and the helix. The role of these waves is established in part on the basis of their complex wave numbers which are solutions of the appropriate determinantal equation. Although coupling similar to that used in traveling wave tubes is considered initially, the investigation concentrates on coupling which can be used to produce Smith–Purcell radiation. The results of the numerical evaluation of the wave numbers demonstrate that for the latter type of coupling, the modulation changes very slowly along the length of the interaction. This establishes the heretofore questionable validity of the prescribed source model for evaluating the interaction of a modulated electron beam and a narrow tape helix. Similar results are expected to hold for other interaction geometries.