Unified theory and comparative study of cyclotron masers, ion-channel lasers, and free electron lasers

A unified small-signal amplification theory is developed to compare growth mechanisms responsible for a number of relativistic radiation generators. The theory is formulated from the basis that the electron resonance frequency produced by the external fields of the devices depends on γ^-q, where γ is the beam Lorentz factor and q is a constant (q = 1 for cyclotron masers, q = 1/2 for ion-channel lasers, and q = 0 for free electron lasers). It is concluded that for wave amplification, the sign of the electron mismatch frequency is required to be the same as the sign of bunching parameter that is determined by the total bunching both axial and azimuthal; this depends on the q value. The two bunching mechanisms exist, not only in the single electron resonance regime, but also in the collective gain regime. Competition or reinforcement between the two bunching mechanisms is determined by the q value, the electron axial velocity, and the wave phase velocity.