Electron trajectories and gain in free electron laser with ion channel guiding

A detailed analysis of electron trajectories and gain in a helical wiggler free electron laser (FEL) with ion channel focusing using single particle dynamics is presented. Conditions for stability of electron orbit have been obtained and stable regimes have been identified. Gain has been evaluated in the low-gain-per-pass limit with the help of the self-consistent pendulum equation. It is seen that the presence of ion channel leads to significant gain enhancement under appropriate conditions.