Growth rate and start current in Smith–Purcell free-electron lasers

Abstract

This letter reports a theory to calculate the growth rate and start current of a Smith–Purcell free-electron laser, which is a promising radiation source in the terahertz domain. A two-dimensional model was used to investigate the interaction between a sheet electron beam and the surface wave above a lamellar grating. After deriving the growth rate from the dispersion equation, the start current was carefully estimated by considering the power flow above the grating. The agreement between the predictions of our theory and the results from the particle-in-cell simulations is acceptable.