Abstract
A linear theory for the parametric instability of a free-electron laser with a longitudinal electrostatic wiggler is presented. A space-charge wave and a predominantly transverse magnetic wave guide mode are excited when a relativistic electron beam is passed through a static spatially periodic longitudinal electric wiggler. The thick annular electron beam is contained in a cylindrical metal wave guide and an axial magnetic field of arbitrary magnitude. An expression for the wave-field components is derived and solved numerically along with the dispersion relations for the eigenmodes of a wave guide containing a magnetized annular electron beam. Effects of the variation of the beam radii, the axial magnetic field, and electron beam kinetic energy on the growth rate, efficiency, radiation wavelength, and the required pump wavelength are studied. A suitable range of parameters for the generation of millimeter wave is indicated.
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