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the electrons, they will start to oscillate with different frequencies because the gyrotron frequency depends on the energy of the electron. Hence the electron beam will form phase bunches. For a small mismatch, when the frequency of the electron oscillations is slightly smaller than the frequency of the radiation field, this bunch is formed in the decelerating phase. Therefore, the bunch will give its energy to the radiation field. The wavelength of the generated radiation depends inversely on the magnetic field strength. Technical limitations on magnets limits the frequency to about 40 GHz when magnets at room temperature are used. Superconducting magnets are required to go to shorter wavelengths. Harmonic operation is also possible but the efficiency is much poorer for harmonics above the second. Nevertheless, the Gyrotron has been operated at sub-millimetre wavelengths and is capable of generating an average power of close to a megaWatt at millimetre wavelengths. The tunability of these devices is limited. The Gyrotron was one of the first devices which used induced Bremsstrahlung to avoid the restriction on the transverse dimension of the interaction space, and therefore it is capable of generating radiation at higher frequencies and higher power levels. As the operating frequency is determined by the strength of the magnetic field used, the (superconducting) magnets will eventually limit the maximum obtainable frequencies. New schemes were required to reach higher frequencies. It was recognised that the Doppler effect can be used to increase the operating frequency of electron beam based radiation sources.13 The first study making use of this Doppler shift was done on an electron beam moving through a static periodic magnetic field produced by the so called undulator or wiggler.14 The term Free-Electron Laser (FEL) for these devices was introduced by Madey.15 At present time, free-electron lasers have operated over a considerable part of the electromagnetic spectrum, from about 1 m wavelength16 down to about 13 nm17. 2. PRINCIPLES OF OPERATION 2.1. Operation principle In an FEL, electrons emit coherent radiation as in a conventional laser. In a conventional laser radiation is produced by a transition between bound states of the electrons in the lasing medium, whereas in an FEL it is produced by free streaming electrons. Therefore the radiation wavelength can span a much larger range compared to conventional lasers as, in a quantum mechanical picture, the electrons radiate by transitions between energy levels in the continuum. In principle, the description of the FEL should require a quantum mechanical description. However, except for the start-up phase, the process can be completely described by classical (electromagnetic) theory. A large variety of FELs exist. They can be distinguished not only with respect to accelerator type but also with respect to interaction mechanism. The latter can be divided into Cerenkov FEL, Smith-Purcell FEL and undulator FEL. These concepts are shown in fig. 1. In this figure, b=v/c, c is the speed of light in vacuum and v is the velocity of the electrons, v=|v|, and g is the relativistic factor, g2 = (1-b2). The total energy of the electron is given by gmc2. The description in this paper will focus on undulator FELs. The other two devices are similar in many aspects. The radiation is produced by an interaction between three elements: an electron beam, an electromagnetic wave with wavelength l travelling in the same direction as the electrons and a periodic magnetic field with period lu. The periodic magnetic field, or undulator field, induces a wiggling motion on the electrons. The acceleration associated with this motion produces the radiation. Therefore when the electrons pass through the undulator incoherent radiation is produced. This is the mechanism employed in synchrotron light sources. In order to produce coherent radiation by stimulated emission it is necessary for the electron beam to form coherent bunches. Bunching is possible when a light wave copropagates with the electron beam through the undulator as the spatial variations of the Figure 1. Overview of different FEL mechanisms: undulator FEL (a), SmithPurcell FEL (b) and Cerenkov FEL (c) together with the tuning characteristic (l is the radiation wavelength and g is related to the beam energy).