Electron bunching at large wiggler field in a second harmonic waveguide free electron laser

Second harmonic waveguide free electron lasers (FELs) have recently been considered as an electron energy reduction technique for compact waveguide FELs operated from microwave to the far-infrared. As their gain mechanism is based on a strong coupling between the oscillatory component of the axial electron velocity and the axial electric field of TM modes in a cylindrical waveguide, second harmonic waveguide FELs are preferably operated with large wiggler field to obtain sufficiently high interaction gain. Under these high wiggler field conditions, the electron trajectory becomes a highly nonlinear and complex function of the wiggler field and as such electron bunching may be significantly altered from previously approximated analytically. In this paper, we employ a recently developed computer code for compact waveguide FELs to compare to our previously obtained analytical gain formulation in the small-signal regime. By modifying our computer code to mimic the mathematical treatment of our analytical analysis, we demonstrate that detailed features of the axial electron velocity, excluded in our analytical analysis, result in an enhanced electron bunching and thus an increased gain. Simple compensation measures are then suggested such that the original analytical gain formulation can still be used as a simple and reasonably accurate design tool for second harmonic waveguide FELs. (C) 2001 Elsevier Science B.V. All rights reserved.