Numerical studies of (partial-) waveguide FELs

We investigate two different approaches to analyze the excitation of 3D-time dependent fields by short electron bunches in parallel-plate waveguide FELs. In the first approach the Lienard–Wiechert solution of the four vector electromagnetic wave equation is adopted to the waveguide-FEL problem by means of image currents method. The second approach is based on the commonly used method of solving paraxial wave equation for the amplitudes of the excited waveguide modes in time and axial dimension. The loss mechanism in a partially waveguided cavity with toroidal mirrors is incorporated into the latter formalism accounting for the outcoupling of the radiation fields through a hole, mode conversion and clipping-off due to the waveguide apertures.