Electron trajectories and gain in free-electron lasers with three-dimensional helical wiggler and ion-channel guiding

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. (C) 2005 American Institute of Physics.