Generation spectrum of long-pulse free-electron terahertz lasers: quasilinear theory

A quasilinear theory is developed for free-electron lasers in which intense electron beams with a significant velocity dispersion are used to implement the kinetic regime of electron–wave interaction. Under the assumption that the field is stored in a high-$Q$ cavity, stationary distributions of the spectral density of excited cavity modes are found for various levels of the excess of the beam current above the threshold. It is shown that, if the excess is large, the energy distribution of the electrons that exit the cavity includes a plateau with the width proportional to the generation spectrum width. Parameters are estimated for long pulse free-electron lasers that can be implemented on the basis of linear induction accelerators. It is shown that the energy of high-dispersion electron beams can be efficiently converted into broadband terahertz radiation.