atoms Review A Review of High-Gain Free-Electron Laser Theory Nicola Piovella 1,* and Luca Volpe 2 1 Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy 2 Centro de Laseres Pulsados (CLPU), Parque Cientifico, 37185 Salamanca, Spain;
[email protected] * Correspondence:
[email protected] Abstract: 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. Keywords: free-electron laser; X-ray emission; collective effects 1. Basic Concepts The free-electron laser is essentially a device that transforms the kinetic energy of a relativistic electron beam (e-beam) into e.m. radiation [1–4]. The e-beam passing through a transverse periodic magnetic field oscillates in a direction perpendicular to the magnetic Citation: Piovella, N.; Volpe, L. field and the propagation axis, and emits radiation confined in a narrow cone along the A Review of High-Gain Free-Electron propagation direction. The periodic magnetic field is provided by the so-called undulator, an Laser Theory. Atoms 2021, 9, 28. insertion device usually realized with two arrays of permanent magnets with alternating https://doi.org/10.3390/atoms9020028 polarities (see Figure1) or with two helical coils with current circulating in opposite directions.