Starting from the broadband X-rays that are generated
from a dipole, the development went on to Wigglers -
sequences of magnetic dipoles, where the radiation intensity
grows with the number of poles. In an undulator, the radiation
from different poles interferes constructively at certain wavelengths.
In an FEL, also the radiation from different electrons interferes
constructively, producing extremely bright pulses, that
require very special electron sources and lead to
ultrashort X-ray pulses.
Free-electron lasers (FELs) produce coherent radiation, like more common lasers. They use a beam of free-electrons as the gain medium. Like in a synchrotron, the radiation is produced in an undulator. There, the light field itself acts back on the electron beam and induces density variations in the electron distribution. This leads to the generation of radiation coherently from the whole bunch. As typical electron bunches in an FEL contain up to 10^10 electrons, the number of generated photons can ideally increase also by ten orders of magnitude.
Nevertheless, in the X-ray region there are no mirrors available to build a laser cavity, so that X-ray lasers are based on a single pass through a very long undulator section (several 100 m). In this single pass, the whole lasing process takes place. To generate the high gain in one pass, a very dense electron pulse is needed to ensure enough overlap with the driving radiation field. The electron pulses are extremely compressed to a length of typically sub-200 femtoseconds and of sub-100µm diameter. Nowadays, these bunches can only be produced in long linear accelerators and only few of them exist around the world.
Current X-ray FELs are based on the SASE (self-amplification of spontaneous emission) principle, where the first photon that is spontaneously emitted in the undulator seeds the whole gain process. As this is a stochastic process, the properties of the produced radiation vary from shot to shot in pulse energy and the photon energy spectrum. Nevertheless, the produced pulses can contain up to 10^13 photons in 100fs and thus are the most brilliant sources for X-rays.
The average brilliance of those sources is instead limited, because instead of MHz repetition rates of synchrotron pulses, FELs produce between 100 (for normal conducting accelerators) and up to 100,000 (for superconducting accelerators) pulses per second. So that the average brilliance is comparable to modern synchrotron sources.
Therefore, FELs allow to conduct similar experiments than at synchrotrons, but enable to conduct these experiments with femtosecond time resolution due to the short pulsed nature of the radiation. In the X-ray region, only some sources worldwide are in operation or under construction, namely FLASH, LCLS, SACLA, FERMI and XFEL.