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A Smith-Purcell device can operate as a backward-wave oscillator for intense, narrow-bandwidth, continuous wave radiation at terahertz wavelengths. We determine the requirements on electron beam current and emittance for the system to oscillate based on a three-dimensional extension of our previous two-dimensional analysis. It is found that specially designed electron beams are required with a current that exceeds a certain threshold value and a flat transverse profile that allows the beam to travel very close to the grating surface. Two methods for producing electron beams with the required characteristics are discussed

Electron beam requirements for a three-dimensional Smith-Purcell backward-wave oscillator for intense terahertz radiation