Kinetic description of a wiggler-pumped ion-channel free-electron laser by applying the Einstein coefficient technique

A kinetic theory is used to investigate the theory of a free-electron laser with a helical wiggler and an ion channel based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency, propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.