Nonlinear Mechanisms of Free Electron Laser

Abstract

The problem of creation of shortwave coherent EM radiation sources in general aspects reduces to the implementation of free electron lasers (FEL). The principal advantage of a FEL with respect to traditional quantum generators operating on discrete transitions in atomic/molecular systems is that the radiation frequency is continuously Doppler upshifted due to high relativism of electron beams, providing rapid tunability over a broad range of frequencies up to $\gamma$-ray. Among the diverse versions of FEL at present the undulator scheme is being actively developed. Although the amplifying frequencies are still far from X-ray, the main hopes for an efficient X-ray FEL remain associated with the undulator scheme based on the accumulation of coherent radiation of ultrarelativistic electron beams in the Self-Amplified Spontaneous Emission (SASE) regime, in which the initial shot noise on the electron beam is amplified over the course of propagation through a long wiggler. For that it is required that the lengths are on the order of several ten to hundred meters. The recent experimental success shows the feasibility of construction of such facilities. Nevertheless, because there are no drivers or mirrors operable at X-ray wavelengths the problem reduces to amplification/generation of coherent radiation in the single-pass regime. It is clear that the latter can be achieved with more efficiency via the nonlinear schemes of FEL induced by strong pump EM fields. The latter will considerably abbreviate the amplification length as well and one can expect small setup FEL devices. On the other hand, as the photon wavelength moves into the deep UV and X-ray regions the interaction becomes quantum mechanical, i.e., quantum recoil becomes comparable to or larger than the gain bandwidth and quantum effects play an essential role. The quantum effects are also essential if one considers the FEL versions where one or two degrees of freedom of the charged particles are quantized and the resonant enhancement of electron–photon interaction cross section holds. This takes place for the X-ray laser schemes based on the electron/positron beam channeling radiation in crystals. The smallness of the electron–photon interaction cross section can also be compensated and the quality of the output X-ray radiation can be enhanced in the hybrid schemes of FEL and atomic laser. It can be achieved by means of fast high-density ion beam interaction with a strong counterpropagating pump laser field or with a crystal periodic electrostatic potential. Investigation of the nonlinear schemes and quantum aspects of FEL on the basis of a self-consistent set of Maxwell and quantum kinetic equations is the subject of the present chapter.