Smith-Purcell radiation from small gratings

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Abstract
A series of metallic gratings, having grating spacing of 2180 Å and known numbers of grooves ranging from 1000 to 4, were seen to produce Smith-Purcell radiation when exposed to a 50-keV electron beam. Bandwidths for the radiation from these gratings were measured and found to be dependent upon the number of grating grooves as well as the beam angle of incidence. This is interpreted as indicating a one-to-one correspondence between grooves in the grating and undulations in the radiated wave train produced by a single passing electron. With this assumption, a height for the zone of effective interaction for the electron is calculated to be ∼1500 Å from the grating surface.