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

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