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Paper IPM / P / 6654  


Abstract:  
A threedimensional theory for a free electron laser with a positive or
reversed axialguide magnetic field in the collective regime is presented.
A relativistic electron beam partially fills a cylindrical and metallic
waveguide. A onedimensional helical magnetic wiggler field, in the
beam frame, decays into a forwardscattered spacecharge wave and a
backscattered EH waveguide mode. With relativistic mass correction in
the beam frame a nonlinear wave equation is derived which describes the
interaction between the wiggler field and the excited waves. Dispersion
characteristics of the eignmodes are studied. A formula for the labframe
spatial growth rate of the parametrically excited waves is derived for a
positive and reversed axialguide magnetic field. The growth rate for the
reversed axialguide magnetic field was found to be around one order of
magnitude smaller than for the positive field. Figures are presented to
show the variation of the growth rate with axialguide field and the
ratio of the beam radius to the waveguide radius.
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