Self-modulation instability in a free electron laser amplifier with electromagnetic pumping

In vacuum microwave electronics the most important example of a parametric device is a scattron FEL oscillator (T.C. Marshall, Free Electron Lasers, Macmillan, New York, 1985). In this paper, we discuss nonlinear dynamics of a model of a scattron FEL amplifier. We consider the electromagnetic waves to be fast waves with group velocities equal to the speed of light. For numerical simulation we developed a simplified model described by nonlinear wave equations.