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Deformation of steady-state trajectories of an electron, due to
transverse inhomogeneity in a realizable three-dimensional helical
wiggler field with ion-channel guiding, is studied. The $\Phi$
function that determines the rate of change of axial velocity with
energy is derived and shows that transition to negative mass
regime remains approximately unchanged under the influence of the
three-dimensional effect of the wiggler. A detailed stability
analysis of orbits is performed, with variation in relativistic
factor $\gamma$ included in the formalism, and a new stable branch
is found for group-II orbit. Finally a formula for the small
signal gain is derived with radiation forces in transverse
components of the equation of motion included and results are
compared with previous works in one-dimensional case.
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