A FEL has three fundamental components: an electron beam of given energy and intensity and the associated accelerator used to produce it; the undulator magnet; and the electromagnetic wave and the associated optical components controlling its propagation. A schematic representation of a FEL is given in Fig.1.
The accelerators used to provide the electron beam are of many types: electrostatic, induction line, radio-frequency (rf) linac, pulsed diode, or storage rings. Some of their basic characteristic, their energy ranges, and the FEL wavelengths for which they are more commonly used are given in Table 1.
| Energy | Peak Current | Pulse Length | Wavelength | |
| Electrostatic | 1-10 MeV | 1-5 A | 1000-20000 ns | mm to 0.1 mm |
| Induction Linac | 1-50 MeV | 1-10 kA | 10-100 ns | cm to microns |
| Storage ring | 0.1-10 GeV | 1-1000 A | 30-1000 ps | 1 micron to nm |
| RF linac | 0.01-25 GeV | 100-5000 A | 0.1-30 ps | 100 microns to 0.1nm |
Tab.1: Particle accelerators for FELs.
Undulator magnets are of two main types: helical or planar. In the first case the magnetic field vector rotates around the axis as a function of axial distance; in the second case its direction is fixed, and its amplitude oscillates along the axis. These magnets can be, and have been, built using a wide variety of technologies: pulsed or dc electromagnets, permanent magnets, and superconducting magnets. The field amplitude can vary from a fraction of a tesla to over 1 T, and the period from 1 cm to many centimeters. A great effort is under way to develop undulators with periods in the millimeter range; these would allow a reduction of the beam energy for a given radiation wavelength, thus reducing the cost and complexity of the FEL. A helical undulator was used by Madey and co-workers [10] in the
first FEL. This undulator was a superconducting magnet, built with two helical windings with current flowing in opposing direction.
The FEL can be operated as an oscillator, using an optical cavity to confine the radiation in the undulator region, as shown in Fig.1, or it can be used as an amplifier. Oscillator-amplifier combination [master oscillator, power amplifier (MOPA)], as well as systems in which one amplifies the electron spontaneous radiation emitted in traversing the undulator [self-amplified spontaneous radiation (SASE) [12]], have been also used.