Free-electron lasers with very slow wiggler taper

A highly accurate, explicit asymptotic solution of the electron energy and phase is found for a class of free-electron lasers (FELs) with very long wavelength beams, very low electron energies, and very slow taper of the wiggler field relative to the wiggler period. Dimensionless variables are defined and normalized, and three small parameters which characterize the operation of the FEL are identified. Due to the explicit asymptotic nature of the solution, the results may be directly used to calculate features such as the escape distance of the electron from the potential well and the effects of the various physical parameters. One important advantage of the very slow wiggler taper is the increased efficiency of the energy transfer from the electron beam to the signal field due to increased bucket width. Numerical calculations are performed to verify all results