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Paper IPM / P / 7124  


Abstract:  
An analysis of the parametric instability which forms the basis
for operation of a free electron laser with a longitudinal
electrostatic wiggler is presented. A theory is developed that
allows for an arbitrary axial magnetic field and arbitrary ratio
of the electron beam radius a to the waveguide inner radius
R without imposing the electrostatic approximation on the
spacecharge wave. Dispersion characteristic of the eigenmodes of
a magnetized electron beam inside a waveguide specially
EH_{01} electromagneric and SC_{01} spacecharge
mode have been studied. A formula for the spatial growth rate of
parametrically excited eigenmodes is derived. variations of the
growth rate, efficiency, radiation wavelength, and required pump
wavelength as functions of the ratio a/R are
studied numerically. It is shown that excitation of the upper
branch or lower branch of an EH_{01} waveguide mode can
be achieved with suitable chosen values for the system parameters,
and a fully electromagnetic analysis can produce modest changes on
the operative quantities, as compared to the imposition of
electrostatic approximation on the spacecharge wave.
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