  Using a time-dependent approach the analysis and optimization of a planar
FEL-amplifier with an axial magnetic field and an irregular waveguide is
performed. By applying methods of nonlinear dynamics three-dimensional
equations of motion and the excitation equation are partly integrated in an
analytical way. As a result, a self-consistent reduced model of the FEL is
built in special phase space. The reduced model is the generalization of the
Colson-Bonifacio model and takes into account the intricate dynamics of
electrons in the pump magnetic field and the intramode scattering in the
irregular waveguide. The reduced model and concepts of evolutionary computation
are used to find optimal waveguide profiles. The numerical simulation of the
original non-simplified model is performed to check the effectiveness of found
optimal profiles. The FEL parameters are chosen to be close to the parameters
of the experiment (S. Cheng et al. IEEE Trans. Plasma Sci. 1996, vol. 24, p.
750), in which a sheet electron beam with the moderate thickness interacts with
the TE01 mode of a rectangular waveguide. The results strongly indicate that
one can improve the efficiency by a factor of five or six if the FEL operates
in the magnetoresonance regime and if the irregular waveguide with the
optimized profile is used.
