Undulator radiation in a waveguide

An analytical approach is proposed to describe undulator radiation near resonance, when the presence of the vacuum-pipe affects radiation properties. This is the case of the far-infrared undulator beamline at the Free-electron LASer (FEL) in Hamburg (FLASH) that is designed to deliver pulses in the TeraHertz (THz) range and can be used for pump-probe experiments as well as for the development of novel electron-beam diagnostics techniques. Since the THz radiation diffraction size exceeds the vacuum-chamber dimensions, characterization of infrared radiation must be performed accounting for the presence of a waveguide. We developed a theory of undulator radiation in a waveguide based on paraxial and resonance approximation. We solved the field equation with a tensor Green's function technique, and extracted figures of merit describing the influence of the vacuum pipe on the radiation pulse as a function of the problem parameters. Our theory makes consistent use of dimensionless analysis and allows treatment and understanding of many asymptotes of the parameter space, together with their region of applicability.