Kinetic description of self-field effects on laser and betatron emission in wiggler-pumped ion-channel free electron lasers

The effects of self-fields on the free electron lasers (FELs) with a helical wiggler and ion-channel guiding are considered. The steady-state orbits for a single electron in this configuration are obtained. The rate of change of axial velocity with energy, the characteristic function Φ, is derived and studied numerically. A kinetic approach has been used to get the effects of self-field on the FEL and betatron gain formula in the low-gain-pre-pass limit. It is shown that betatron gain is smaller than FEL gain. We also found a gain decrement (enhancement), arising from diamagnetism (paramagnetism) generated by the self-magnetic field for group I (group II) orbits. It is interesting that the gain enhancement is found for the non-relativistic part of group II orbits. The FEL gain and betatron gain have also been investigated for different relativistic factors γ.