High-gain free-electron lasers, conceived in the 1980s, are nowadays the only bright sources of coherent X-ray radiation available. In this article, we review the theory developed by R. Bonifacio and coworkers, who have been some of the first scientists envisaging its operation as a single-pass amplifier starting from incoherent undulator radiation, in the so called self-amplified spontaneous emission (SASE) regime. We review the FEL theory, discussing how the FEL parameters emerge from it, which are fundamental for describing, designing and understanding all FEL experiments in the high-gain, single-pass operation.
A Review of High-Gain Free-Electron Laser Theory