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.