The generation of harmonics in two-frequency undulator in a self-amplified spontaneous emission free electron laser (SASE FEL) is studied in order to produce Roentgen radiation in a relatively compact sized installation. The dynamics of SASE FEL is analyzed with the help of the phenomenological model to obtain the maximum of the X-ray high-harmonic power. The model accounts for the properties of the undulator magnetic field and of the electron beam and includes the major sources of losses, such as the electron energy spread, etc. It is compared and calibrated with the existing data on a FEL experiment. The advantages of the two-frequency undulator for Roentgen SASE FEL are demonstrated and the possibility to generate powerful mild Roentgen radiation at already ~25 m length is shown. The evolution of the bunching coefficients for high harmonics is studied together with the evolution of the FEL-induced energy spread. The linear and non-linear regimes are explored for common and for two-frequency undulators The usage of the two-frequency undulator for cascade SASE FEL with high X-ray harmonic power and high-harmonic bunching coefficients with low-induced energy spread is proposed.

We analyze the undulator radiation from planar bi-harmonic undulators with account for all principle losses in real devices. The exact analytical expressions for the UR spectrum, intensity, and the line shape are obtained in terms of special functions. The interplay of various broadening contribution is elucidated and their role is explored. Suspension and boost of certain harmonics by fine tuning the undulator parameters is demonstrated. The constant non-periodic magnetic constituents are studied to compensate the divergency of the electronic beam. The examples of harmonic generation in various undulator schemes with single and double period magnetic field are explored. Influence of inhomogeneous and homogeneous broadening on these harmonics is demonstrated. The analysis is applied to evaluate the harmonics in self-amplified spontaneous emission free electron laser.

For a real, meaningful pump-probe experiment with attosecond temporal resolution, an intense isolated attosecond pulse is in demand. For that purpose we report the generation of an intense isolated attosecond pulse, especially in X-ray region using a current-enhanced self-amplified spontaneous emission in a free electron laser (FEL). We use a few cycle laser pulse to manipulate the electron-bunch inside a two-period planar wiggler. In our study, we employ the electron beam parameters of Pohang Accelerator Laboratory (PAL)-XFEL. The RF phase effect of accelerator columns on the longitudinal energy distribution profile and current profile of electron-bunch is also studied, aiming that these results can be experimentally realized in PAL-XFEL. We show indeed that the manipulation of electron-energy bunch profile may lead to the generation of an isolated attosecond hard X-ray pulse: 150 attosecond radiation pulse at 0.1 nm wavelength can be generated.

In this article, we discuss the modifications that occur in the brightness and gain of a longitudinal wiggler-free electron laser with the aid of induced betatron oscillation. Two novel approaches have been discussed to improve the gain of the system. In the first scheme, an auxiliary undulator field with betatron oscillations brings in additional bunching and results in enhanced gain. In the second scheme, an axial magnetic field is tuned to provide additional bunching for gain enhancement.