Stimulated coherent Smith-Purcell radiation from a metallic grating

A relativistic electron beam with velocity /spl nu//sub b/z passing over a metallic grating, with deep periodic depressions of wavenumber k/sub 0/z, excites a slow wave (/spl omega/, k/sub z/) via Cerenkov interaction, /spl omega/=(k/sub z/+k/sub 0/)/spl nu//sub b/. The beam bunches induce currents in the fins of the grating that act as a phased radiating dipole array, thereby generating coherent radiation at a wavelength /spl lambda/=(2/spl pi//k/sub 0/l)(c//spl nu//sub b/-sin/spl theta/) where l is an integer and /spl theta/ is the angle of emission measured from the normal of the grating. The current threshold for the instability and radiation power scaling with beam current are discussed.