Stimulated coherent Smith-Purcell radiation from a metallic grating

A relativistic electron beam with velocity v(b)(z) over cap passing over a metallic grating, with deep periodic depressions of wavenumber k(0)(z) over cap, excites a slow wave (omega, k(z)) via Cerenkov interaction, omega = (k(2) + k(0))v(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 lambda = (2 pi/k(0)l)(c/v(b) - sin theta) where l is an integer and 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.