One important issue in the development of compact waveguide free electron l
asers (FELs) is to reduce the necessary electron energy for radiation at a
given frequency. Recently, an electron energy reduction technique was sugge
sted by exploiting a second harmonic coupling between the longitudinal elec
tron velocity and the longitudinal electric field of TM modes of the wavegu
ide electromagnetic wave. It was shown that these second harmonic waveguide
FELs have a greater small signal gain than comparable conventional wavegui
de FELs. Tn this paper, the gain dependence on wiggler field in second harm
onic waveguide FELs is studied numerically to assess how high-gain operatio
n may implicate their bandwidth and saturation power. It is shown that a la
rge small signal gain can be achieved very efficiently by increasing the wi
ggler field without sacrificing bandwidth while it does lead to a low satur
ation power. Nevertheless, the rate of gain increment is significantly grea
ter than that of power reduction. (C) 2000 Elsevier Science B.V. All rights
reserved.