An analysis of the propagation of a space-charge wave through the wiggler and axial magnetic fields of a free-electron laser is presented. The relativistic electron beam is contained within and only partially fills a cylindrical metallic waveguide. A theory is developed using lab-frame Maxwell and fluid equations in a form which is equivalent to the electrostatic approximation in the beam frame. The computational method of determining the dispersion relation is described and some numerical results are presented which illustrate effects arising from the wiggler and the partially filled waveguide. [S1063-651X(99)02208-4]. [References: 8]
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