Nonlinear theory of a FEL-amplifier based on a profiled waveguide

The recent progress in the theory and experiment of free-electron lasers (FELs) and gyrotrons with Bragg cavities strongly indicates that the application of novel electrodynamical structures gives the opportunity to realize unique properties of FELs in more full measure. For example, Bragg cavities, which are periodic arrays of varying dielectric or metallic structures, attract interest for traditional microwave applications because they can be built oversized (quasioptical) and, therefore, employed at higher frequencies and higher power. At the same time the investigation of traveling wave tubes (TWT) [3] shows that the efficiency of the TWT based on a regular (along the interaction region) electrodynamical structure is far from its possible maximal value. In fact, the difference between the cold phase velocity and the average velocity of the beam is the control parameter of the beam-wave interaction. Changing this parameter along the interaction region one can control the beam bunching and the energy transfer between bunches and microwaves. The local variation of the cold phase velocity along the region depends on the local variation of the waveguide profile. Then, to control the beam-wave interaction we must use irregular electrodynamical structures. The analysis of a planar FEL-amplifier with an axial magnetic field based on an irregular waveguide is the issue of the current research. We focus our attention on this FEL scheme because it is well known that using the axial magnetic field one can substantially enhance the efficiency as the cyclotron frequency tends to the undulator one.