Stimulated coherent Smith-Purcell radiation from a metallic grating

A relativistic electron beam with velocity ν_bz passing over a metallic grating, with deep periodic depressions of wavenumber k₀z, excites a slow wave (ω, k_z) via Cerenkov interaction, ω=(k_z+k₀)ν_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 λ=(2π/k₀l)(c/ν_b-sinθ) where l is an integer and θ 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