FREE-ELECTRON LASER IN A PARTIALLY FILLED WAVE-GUIDE

A linear theory for a free electron laser with a one-dimensional helic al wiggler and axial magnetic field in the collective regime is presen ted. The configuration consists of-a cylindrical waveguide with arbitr ary ratio of electron beam radius a to waveguide inner radius R. Param etric decay of the wiggler pump wave, in the beam frame, into a space- charge wave and an electric-magnetic (EH) waveguide mode is analyzed i n three dimensions. A nonlinear wave equation for the three-wave inter action is derived and employed to obtain a formula for the spatial gro wth rate of the excited eigenmodes. It was found that the relativistic treatment of the electron oscillations in the wiggler field destroys the cyclotron resonance which appears in the nonrelativistic case. Nev ertheless, appreciable amplification was found. Numerical analysis is conducted to study the growth rate, radiation wavelength, and required relativistic factor as functions of axial magnetic field Bo and radiu s ratio a/R. The suitable value for a/R was found to be around 0.65 fo r our choice of parameters. (C) 1997 American Institute of Physics.