“Optical guiding” limits on extraction efficiencies of single-pass, tapered wiggler amplifiers

Single-pass, tapered wiggler amplifiers have an attactive feature of being able, in theory at least, of extracting a large portion of the electron beam energy into light. In circumstances where an optical FEL wiggler length is significantly longer than the Rayleigh length zR corresponding to the electron beam radius, diffraction losses must be controlled via the phenomenon of optical guiding. Since the strength of the guiding depends upon the effective refractive index n exceeding one, and since (n − 1) is inversely proportional to the optical electric field, there is a natural limiting mechanism to the on-axis field strength and thus the rate at which energy may be extracted from the electron beam. In particular, the extraction efficiency for a prebunched beam asymptotically grows linearly with z rather than quadratically. We present analytical and numerical simulation results concerning this behavior and discuss its applicability to various FEL designs including oscillator/amplifier-radiator configurations.