Electromagnetic-Wave Wigglers

The physical mechanism in the free-electron laser depends upon the propagation of an electron beam through a periodic magnetic field. Both incoherent and coherent radiation result from the undulatory motion of the electron beam in the external fields, which permits a wave-particle coupling to the output radiation. Coherent radiation depends upon the stimulated emission due to the ponderomotive wave formed by the beating of the radiation and wiggler fields. The wiggler field itself may be either magnetostatic or electromagnetic in nature. Although the bulk of experiments as of this time have relied upon magnetostatic wigglers with either helical or planar polarizations, the fundamental principle has also been demonstrated in the laboratory using a large-amplitude electromagnetic wave to induce the requisite undulatory motion in the electron beam. The basic difference between magnetostatic and electromagnetic-wave wigglers lies in the frequency of the output radiation, which depends upon both the wiggler period and the beam energy in both cases. In the case of a magnetostatic wiggler, the wavelength of the output radiation scales as λ ≈ λw/2γb2 where λw denotes the wiggler period and γb is the bulk relativistic factor of the beam. In contrast, the wavelength of the output radiation for an electromagnetic-wave wiggler scales as λ ≈ λw/4γb2. As a result, for fixed wiggler periods and beam energies, the electromagnetic-wave wiggler will produce shorter output wavelengths. As a consequence, electromagnetic-wave wigglers become attractive alternatives to magnetostatic wigglers the production of short wavelengths when the electron beam energy is constrained. In this chapter, the theory of single-particle trajectories and small-signal gain in an electromagnetic-wave wiggler is developed. This is followed by a discussion of efficiency enhancement. Since it is difficult to taper an electromagnetic-wave wiggler, we consider the interaction when an axial magnetic field is present and consider the efficiency enhancement that results when the axial magnetic field is tapered.