Discussion of the High-Gain FEL Equations

Abstract

In the first part of this chapter we want to exploit the third-order differential equation for the amplitude of the FEL wave in order to gain a deeper understanding of the properties and peculiarities of high-gain Free-Electron Lasers. It will turn out that a remarkable number of predictions can be deduced from the analytic description of the high-gain FEL although we have made rather simplifying assumptions in deriving (4.50), for example by neglecting any dependencies on the transverse coordinates x and y. The coupled first-order equations are evaluated in the second part. They contain even more physics.