Abstract
A linear theory for a free electron laser with a three-dimensional helical wiggler and axial magnetic field in the collective regime is presented. The configuration consists of an annular electron beam propagating inside a cylindrical waveguide. Parametric decay of the wiggler pump wave, in the beam frame, into a space-charge wave and an electric-magnetic waveguide mode is analyzed in three dimensions. A nonlinear wave equation for the three-wave interaction is derived and employed to obtain a formula for the spatial growth rate of the excited eigenmodes. Numerical analysis is conducted to study the growth rate, radiation wavelength, and required relativistic factor as functions of axial magnetic field B0. Variation of growth rate with the beam thickness and the radius of the equilibrium trajectory was also studied.
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