In Chap. 1 we have shown that the interaction of electrons with an electromagnetic wave is possible even when the phase velocity of the latter is larger than \( c \), provided that there is a way to conserve simultaneously both energy and momentum. In a free-electron laser (FEL) this is facilitated by the presence of a periodic magnetic field. In most cases, the components of this field are transverse to the initial velocity of the electron. An electron injected in a periodic magnetic field (wiggler) oscillates and, as a result, it emits radiation.