Chaos in Free-Electron Lasers

Researchers in the field of chaos are concerned with the basic properties of the solutions of systems of nonlinear equations. This interest stems from the fact that almost every physical system can be described at some level of approximation by a system of nonlinear equations. The development of this field has led to several general conclusions about nonlinear systems. On the one hand, even the simplest deterministic nonlinear systems can exhibit behavior that is complicated and appears to be random. This behavior has been termed chaos. On the other hand, the chaotic behavior of much more complicated systems often seems to follow the same rules as the simple systems. Thus, there is order in the chaos. In this chapter, we introduce some basic concepts regarding chaos and nonlinear dynamics before going on to a discussion of the application of these concepts to the physics of free-electron lasers.