Greenʹs function of homogeneous overmoded waveguide with finite conductivity walls

We describe an approach for developing the numerical simulation codes for the FEL amplifier with the homogeneous overmode waveguide. The radiation field are calculated using Greenʹs function method. We start with the rigorous solutions for the eigenfunctions of a passive waveguide. Using these eigenfunctions, we find the Greenʹs function. Finally, the Greenʹs function is simplified using paraxial approximation. This algorithm of electromagnetic field calculation can be implemented in linear and nonlinear code for simulation of the waveguide FEL.