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By Professor Dr. Dr. Rer. Nat. Habil. Pierre Meystre, Professor Murray Sargent III Ph. D. (auth.)

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1-4. Coherence Coherence plays a central role in modern physics. It is very hard to find a single domain of physics where this concept is not applied. In this book we use it a great deal, speaking of coherent light, coherent transients, coherent propagation, coherent states, coherent excitation, etc. Just what is coherence? The answer typically depends on whom you ask! In a very general sense, a process is coherent if it is characterized by the existence of some well-defined deterministic phase relationship, or in other words, if some phase is not subject to random noise.

This is a basic feature of the FEL that makes it hard to operate efficiently. Since pendulum trajectories are periodic, still longer times cause electrons that first decelerated to accelerate and vice versa as shown in Fig. 1-12. For such times the average electron energy increases, that is, the laser saturates. To maximize the energy transfer from the electrons to the laser field, the length of the wiggler should be chosen just short enough to avoid this backward energy transfer. This kind of saturation is quite different from that for two-level media discussed in Chap.

1-17) and that vz = we obtain e, (131) where M = m[I + (eAjmc)2]1/2 (132) is the effective (or shifted) electron mass, and we have at the last stage of the derivation approximated 'Yz by '1s =[I - v5 2/c 2 112. Equation (131) is the famous pendulum equation. Thus in the frame moving at velocity v5 , the dynamics of the electrons is the same as the motion of a particle in a sinusoidal potential. Note that the shifted mass M is used rather than the electron mass m. The pendulum equation describes the motion of particles on a corrugated rooftop.

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