Analysis of the AC free electron laser

An AC free-electron laser (FEL) with a superconductor cavity and a FEL with a plasma wave wiggler are analyzed. The AC FEL has a small effective wiggler wavelength and higher wiggler strength. Therefore, it can supply high-power coherent radiation with a short wavelength. From the linear fluid theory and Maxwell´s equations, the dispersion relation is derived. When the coupling term is much less than unity (F≪1), the growth rate of electromagnetic instability is calculated. The intrinsic efficiency of radiation production is also estimated. For the small-signal gain regime, the gain coefficient is formulated on the basis of the theorem of J.M.J. Madey (1979). In a FEL with a plasma wiggler, the electron beam passing through the wiggler plasma might begin to thermalize due to various particle-particle and wave-particle interactions. Thus, the effective interaction region becomes contracted, preventing the coherence of the electromagnetic wave. To avoid such interactions, the electron beam should be bunched and narrower than the skin depth