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The previous theory of high-gain free-electron laser (FEL) operating in the quantum regime is semiclassical because the electron dynamic is quantized but the radiation field is classically described. Here, we present for the first time a fully quantum mechanical theory where also the field is quantized. We shall restrict to the FEL operation in the steady state regime where the slippage length is much smaller than the bunch length. The results predicted by this theory are quite different from those of the semiclassical theory.

A unified analysis is presented to calculate the incoherent spontaneous power of cooperative radiations based on self-amplified spontaneous emission. Using quantum mechanical tools, we derive analytical expressions for the incoherent spontaneous power of undulator and Cherenkov free-electron lasers (FELs). The undulator and Cherenkov FELs are considered as two different examples for the radiation that accumulate cooperatively. In the case of the undulator FEL, we show an excellent agreement between an expression for the incoherent radiation power derived in the present work and that obtained using a completely different approach [Phys. Rev. E 65 (2002) 026501]. For the Cherenkov radiation, we demonstrate a satisfactory agreement between the incoherent power predicted in our analysis and previous experimental results.

In this work we use the one-dimensional free electron laser (FEL) model to define necessary parameters of an electron beam to produce self amplified spontaneous emission (SASE) in an ion channel laser (ICL) undulator. Limits and constraints on beam parameters are given, based on theoretical argument and numerical simulations results using the Architect hybrid code.

In this paper, we propose for first time practical parameters to construct a compact sub-Angstrom Free Electron Laser (FEL) based on Compton backscattering. Our recipe is based on using picocoulomb electron bunch, enabling very low emittance and ultracold electron beam. We assume the FEL is operating in a quantum regime of Self Amplified Spontaneous Emission (SASE). The fundamental quantum feature is a significantly narrower spectrum of the emitted radiation relative to classical SASE. The quantum regime of the SASE FEL is reached when the momentum spread of the electron beam is smaller than the photon recoil momentum. Following the formulae describing SASE FEL operation, realistic designs for quantum FEL experiments are proposed. We discuss the practical constraints that influence the experimental parameters. Numerical simulations of power spectra and intensities are presented and attractive radiation characteristics such as high flux, narrow linewidth, and short pulse structure are demonstrated.

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