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Electromagnetic radiation emitted by charged particles is an indispensable part of majority of courses on general electrodynamics. There are special monographs available, dedicated to some of the typical cases – such as synchrotron, transition, and Vavilov–Cherenkov radiation. As a rule, it is usually emphasized that the radiation field is the self-field of a charged particle in the far-field zone, where it decreases in inverse proportion to a distance from the emitter so that the total energy flow through a closed surface remains constant while the surface expands to infinity.

Even the qualitative considerations given above do indicate that the radiation emission by a charged particle moving uniformly in vacuum is impossible because the conditions of synchronism cannot be satisfied for any of free space proper waves. As is known, these waves propagate with the velocity of light, which always exceeds the velocity of a charged particle. Moreover, the radiation emission is a phenomenon invariant with respect to the choice of a reference frame. Therefore, impossibility of its realization in vacuum becomes obvious when one transfers to the rest frame of the charged particle, where the particle proper field in vacuum is of a purely electrostatic nature. The situation changes radically in the presence of a medium or another environment. This situation is not invariant under transition to new coordinates. In these systems, among their proper waves, there could be at least one wave synchronous with the particle over a long period of time and possessing the electric field component parallel to the particle velocity. The very possibility of the particle energy transfer to this wave—together with the fact that the latter can freely leave the radiation source—guarantees realization of the effect of radiation emission.

Existence of the charged particle acceleration (i.e, temporal variations in either a magnitude or a direction of its velocity) always causes the emission of a specific radiation called bremsstrahlung.

In the previous sections, almost all the results are obtained under the supposition that a character of the emitter motion has been prescribed. The physical factors providing this motion are deliberately ignored. Evidently, such statement of the problem is not quite correct. Really, the electromagnetic radiation always carries away certain amounts of the emitter energy and momentum. These losses either alter the corresponding characteristics of the emitter motion or have to be compensated by an external field providing the given motion.

Notion of individual emitters coherence is a keystone for physics of the processes of the cooperative interaction between flows of charged particles and electromagnetic waves in structures used in microwave electronics and charged particle accelerators. As it has been mentioned above, it follows even from the direct comparison of the magnitudes of the energy losses of individual charged particles with those typical for intense flows of the same emitters.

We have already mentioned the term ‘spontaneous radiation’ in Chap. 5. It was used as a synonym with the notion of the random–phase wave fields summation. In terms of statistics, radiation emitted at random phases is characterized by a spectral–angular distribution of the average power flow. The total field phase is also random in this context. At the same time, it is clear that any realization of the emitter ensemble could be, in a sense, coherent if capable of preserving the fixed correlation between individual emitters during a time interval sufficiently long. For instance, the process of the regular wave scattering by a fixed lattice of charged particles meets these conditions (see Sect. 5.2.2). Surely, the oscillation phase of each particle, prescribed by the wave under scattering, remains correlated with the particle location even if the latter is random. Therefore, a certain degree of coherence is inherent in the total radiation, emitted by this ensemble. Naturally, if the emitters are characterized by a regular spatial distribution, the effects of the radiation coherence are more expressive.

Up to this point it has been assumed that individual charged particles interact only via their collective radiation field. That is, the short–range interaction via Coulomb fields has been neglected. However, it is physically evident that this approach is justified in the only case of low–density beams. As regards many modern microwave devices, the Coulomb interaction must be taken into account (especially in the high–current electronics). In these cases, Coulomb fields can exert substantial influence on the process of grouping charged particles into bunches emitting coherent radiation. At least, even the trivial Coulomb ‘repulsion’ of charged particles in an inhomogeneous beam exerts influence on the processes of the beam spatial modulation.

In this chapter, we will consider those processes of waves amplification that are conditioned by the elementary mechanism of the Cherenkov radiation emission. To distinguish this effect from others, we assume that the external magnetic field strength is very high. In this case, the cyclotron frequency of the electron rotation around the magnetic field lines essentially exceeds all characteristic frequencies emitted by the system in question. So, motion of the electrons can be treated as one-dimensional and directed along the magnetic field lines.

From the viewpoint of principles of the stimulated radiation emission, any of the systems that emit radiation and contain an electron beam may be called free–electron lasers or masers. This implies that emitting elements are not bound in atoms or in a crystal lattice.

In the broad sense of the word, the term “Free Electron Laser”(FEL) implies a device the operation of which is based on the stimulated emission of undulator and/or Cherenkov radiation of relatively short wavelengths. However, Cherenkov mechanism, based on applying dielectric channels and diffraction lattices, is limited by the above–mentioned difficulties in slowing the wave velocity down to the velocity of the beam. The corresponding devices rather should be called the free electron masers.