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. The highest frequency is emitted in the forward direction and in zero order it is determined by the periodicity of the wiggler, L, and the electron energy, γ. In Sect. 3.2.3 it was shown that for relativistic electrons (ß ~ 1) this frequency is given by ω ≃ 2γ2(2πc/L).
KeywordsRadiation Field Filling Factor Energy Spread Magnetic Vector Potential Stable Trajectory
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