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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.
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