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

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.