Генерация когерентного рентгеновского излучения гармоник в однопроходном лазере на свободных электронах со сдвигом фаз электронов относительно фотонов

Abstract

Theoretical study of the radiated FEL power and bunching is conducted in single-pass free electron laser (FEL) with repetitive shift of the photon pulse with respect to the electron bunch in between the sections of the undulator with field harmonics. Using the analytical calculations, the asymmetric elliptic and planar undulator fields are identified for the undulators to be able to reduce the fundamental tone and enhance the harmonic radiation. This effect is amplified by the phase shift kπ/n, k=2,4,6… of the electrons and photons between the undulator sections. This allows n-th FEL harmonic reach its peak power beyond the fundamental saturation FEL length. It is not possible to achieve in a common FEL due to fast increase of the energy spread, induced by the fundamental tone along FEL and its early saturation. The phenomenological model of the FEL is used for the analysis of the bunching coefficients and harmonic powers evolution in the FEL. The model describes the debunching between the undulator sections, where the phase shift is imposed, and accounts for the higher sensitivity to losses of the electron-photon interaction at high harmonic wavelengths. The losses are due to the beam energy spread and emittance, deviation off the axis, diffraction etc. Explicit expressions for the Bessel coefficients of the planar and elliptic undulators with field harmonics are obtained and analyzed. The combination of the undulator field harmonics is identified, which reduces the fundamental tone and enhances the 3rd and 5th UR harmonics as compared with the radiation from a planar undulator. We propose the use of these undulators in a FEL with the electron-photon phase shift, which increases high harmonic powers in X-ray band by ~100 times with respect to common FELs.