  Detuning of the fundamental is a way to enhance harmonic generation . By this
method, the wiggler is composed of two segments in such a way that the
fundamental resonance of the second segment to coincide with the third harmonic
of the first segment of the wiggler to generate extreme ultraviolet radiation
and x-ray emission. A set of coupled, nonlinear, and first-order differential
equations in three dimensions describing the evolution of the electron
trajectories and the radiation field with warm beam is solved numerically by
CYRUS 3D code in the steady-state for two models (1) seeded free electron laser
(FEL) and (2) shot noise on the electron beam (self-amplified spontaneous
emission FEL). Thermal effects in the form of longitudinal velocity spread is
considered. Three-dimensional simulation describes self-consistently the
longitudinal spatial dependence of radiation waists, curvatures, and amplitudes
together with the evaluation of the electron beam. The evolutions of the
transverse modes are investigated for the fundamental resonance and the third
harmonic. Also, the effective modes of the third harmonic are studied. In this
paper, we found that detuning of the fundamental with shot noise gives more
optimistic result than the seeded FEL.
