The main goal of the book is to provide a systematic and didactic approach to the physics and technology of free-electron lasers. Numerous figures are used for illustrating the underlying ideas and concepts and links to other fields of physics are provided. After an introduction to undulator radiation and the low-gain FEL, the one-dimensional theory of the high-gain FEL is developed in a systematic way. Particular emphasis is put on explaining and justifying the various assumptions and approximations that are needed to obtain the differential and integral equations governing the FEL dynamics. Analytical and numerical solutions are presented and important FEL parameters are defined, such as gain length, FEL bandwidth and saturation power. One of the most important features of a high-gain FEL, the formation of microbunches, is studied at length. The increase of gain length due to beam energy spread, space charge forces, and three-dimensional effects such as betatron oscillations and optical diffraction is analyzed. The mechanism of Self-Amplified Spontaneous Emission is described theoretically and illustrated with numerous experimental results. Various methods of FEL seeding by coherent external radiation are introduced, together with experimental results. The world s first soft X-ray FEL, the user facility FLASH at DESY, is described in some detail to give an impression of the complexity of such an accelerator-based light source. The last chapter is devoted to the new hard X-ray FELs which generate extremely intense radiation in the Angstrom regime. The appendices contain supplementary material and more involved calculations."

The high scienti?c interest in coherent X-ray light sources has stimulated world-wide e?orts in developing X-ray lasers. In this book a particularly promising approach is described, the free-electron laser (FEL), which is p- sued worldwide and holds the promise to deliver ultra-bright X-ray pulses of femtosecond duration. Other types of X-ray lasers are not discussed nor do we try a comparison of the relative virtues and drawbacks of di?erent concepts. The book has an introductory character and is written in the style of a universitytextbookforthemanynewcomerstothe?eldoffree-electronlasers, graduate students as well as accelerator physicists, engineers and technicians; it is not intended to be a scienti?c monograph for the experts in the ?eld. Building on lectures by one of us (J. R.) at the CERN Accelerator School, and motivated by the positive response to a series of seminars on "FEL t- ory for pedestrians," given by P. S. within the framework of the Academic Training Program at DESY, we have aimed at presenting the theory of the low-gainandthehigh-gainFELinaclearandconcisemathematicallanguage. Particular emphasis is put on explaining and justifying the assumptions and approximations that are needed to obtain the di?erential equations descr- ing the FEL dynamics. Although we have tried our best to be "simple," the mathematical derivations are certainly not always as simple as one would like them to be. However, we are not aware of any easier approach to the FEL theory. Some of the more involved calculations are put into the appendices.