Spontaneous emission in the waveguide free-electron laser

The incoherent emission from an undulating electron beam in the presence of metallic boundaries is analyzed. A general method of solving Maxwell's equations is used to express the field of a single particle in terms of vector waveguide modes. It is shown that the radiation characteristics depend upon a parameter involving the energy, wiggler wavelength, and the waveguide transverse dimension. At some values of this parameter the energy spectrum and angular distribution will differ significantly from the analogous free-space results. The amount of energy emitted into resonator modes is also analyzed in terms of a similar expansion.