Spontaneous emission and gain in a waveguide free-electron laser

A free-electron laser (FEL) enclosed in a waveguide of narrowly spaced parallel plates has been proposed as a compact, coherent source of far-infrared radiation. The spontaneous emission and small-signal gain of such a device are analyzed. Maxwell´s equations are solved for the fields of a relativistic electron beam passing through a linearly polarized undulator in the presence of a parallel-plane waveguide. The radiation intensity is resolved into its component waveguide modes for the fundamental frequency and for all harmonics. The intensity profile in a given harmonic mode is altered significantly when a parameter involving the undulator period, beam energy, and transverse dimension of the guide is such that the radiation group velocity is close to the electrons´ axial velocity. The small-signal gain in the waveguide FEL is calculated and related to the spontaneous emission. Near zero slip, the gain curve is significantly different from that of a free-space FEL with the same parameters