Effects of non-resonant electron velocity components in a second harmonic waveguide free electron laser

As a technique to reduce the size and hence the cost of compact waveguide free electron lasers (FELs) operated in the spectrum from microwave to the far infrared, a longitudinal interaction mechanism was recently proposed to operate waveguide free electron lasers at the second harmonic. Unlike conventional waveguide FELs based on the electron interaction with the transverse electric field component of the waveguide electromagnetic wave, these second harmonic waveguide FELs have electron velocity components that are not in resonance with the waveguide electromagnetic wave. These non-resonant components were considered to be negligible. In this contribution, we consider the effects of these non-resonant velocity components on the interaction gain. With a new gain formulation in the small signal regime, it is shown that the non-resonant velocity components affect the interaction gain significantly. Energy spread effects are then considered and compared to that in conventional waveguide free electron lasers.