Simulation of a millimeter wave FEL amplifier with cylindrical waveguide

Based on single particle theory (when paraxial and adiabatic approximations are used, a wiggler field is considered only in the electron trajectory equations, and the longitudinal motion equations of the electron are averaged over the period of wiggler λω), we derived a set of coupled nonlinear differential equations of both TEmn and TMmn modes in a loss free cylindrical waveguide. The space charge potential is considered; the longitudinal guiding field is neglected.