Abstract: A nonlinear model of two-beam free-electron laser
(FEL) in the absence of slippage is presented. The two beams are
assumed to be cold with different energies and the fundamental
resonance of the higher energy beam is at the third harmonic of lower
energy beam. By using Maxwell-s equations and full Lorentz force
equations of motion for the electron beams, coupled differential
equations are derived and solved numerically by the fourth order
Runge–Kutta method. In this method a considerable growth of third
harmonic electromagnetic field in the XUV and X-ray regions is
predicted.
Abstract: Three-dimensional simulation of harmonic up
generation in free electron laser amplifier operating simultaneously
with a cold and relativistic electron beam is presented in steady-state
regime where the slippage of the electromagnetic wave with respect
to the electron beam is ignored. By using slowly varying envelope
approximation and applying the source-dependent expansion to wave
equations, electromagnetic fields are represented in terms of the
Hermit Gaussian modes which are well suited for the planar wiggler
configuration. The electron dynamics is described by the fully threedimensional
Lorentz force equation in presence of the realistic planar
magnetostatic wiggler and electromagnetic fields. A set of coupled
nonlinear first-order differential equations is derived and solved
numerically. The fundamental and third harmonic radiation of the
beam is considered. In addition to uniform beam, prebunched
electron beam has also been studied. For this effect of sinusoidal
distribution of entry times for the electron beam on the evolution of
radiation is compared with uniform distribution. It is shown that
prebunching reduces the saturation length substantially. For
efficiency enhancement the wiggler is set to decrease linearly when
the radiation of the third harmonic saturates. The optimum starting
point of tapering and the slope of radiation in the amplitude of
wiggler are found by successive run of the code.