Scattering of light on relativistic heavy ion beams is widely used for characterizing and tuning the properties of both the light and the ion beam. Its elastic component—Rayleigh scattering—is investigated in this work for photon energies close to certain electronic transitions because of its potential usage in the Gamma Factory initiative at CERN. The angle-differential cross-section, as well as the degree of polarization of the scattered light are investigated for the cases of 1 s − 2 p 1 / 2 and 1 s − 2 p 3 / 2 resonance transitions in H-like lead ions. In order to gauge the validity and uncertainty of frequently used approximations, we compare different methods. In particular, rigorous quantum electrodynamics calculations are compared with the resonant electric-dipole approximation evaluated within the relativistic and nonrelativistic formalisms. For better understanding of the origin of the approximation, the commonly used theoretical approach is explained here in detail. We find that in most cases, the nonrelativistic resonant electric-dipole approximation fails to describe the properties of the scattered light. At the same time, its relativistic variant agrees with the rigorous treatment within a level of 10% to 20%. These findings are essential for the design of an experimental setup exploiting the scattering process, as well as for the determination of the scattered light properties.

The successful realization of high gain free-electron lasers has opened new possibilities to X-ray scientists for investigating matter in different states. The availability of unprecedented photon properties stimulated the development of new experimental techniques capable of taking full advantage of these options and has started a virtuous collaboration between machine experts and photon users to improve further and optimize the generated X-ray pulses. Over the recent years, this has led to the development of several advanced free-electron laser (FEL) schemes to tailor the photon properties to specific experimental demands. Presently, tunable wavelength X-ray pulses with extremely high brilliance and short pulse characteristics are a few of the many options available at FELs. Few facilities can offer options such as narrowband or extremely short pulses below one fs duration and simultaneous pulses of multiple colors enabling resonant X-ray pump—X-ray probe experiments with sub fs resolution. Fully coherent X-ray radiation (both spatial and temporal) can also be provided. This new option has stimulated the application of coherent control techniques to the X-ray world, allowing for experiments with few attoseconds resolution. FELs often operate at a relatively low repetition rate, typically on the order of tens of Hz. At FLASH and the European XFEL, however, the superconducting accelerators allow generating thousands of pulses per second. With the implementation of a new seeded FEL line and with an upgrade at FLASH linac, all the new features will become available in the soft X-ray spectral range down to the oxygen K edge with unprecedented average photon flux due to the high repetition rate of pulses.

Currently, the Free electron laser user facility FLASH at DESY is undergoing a significant upgrade involving the complete transformation of one of its beamlines to allow external seeding. With the Echo-Enabled Harmonic Generation (EEHG) seeding method, we aim for the generation of fully coherent XUV and soft X-ray pulses at wavelengths down to 4 nm. The generated FEL radiation is sensitive to various electron beam properties, e.g., its energy profile imprinted either deliberately or by collective effects such as Coherent Synchrotron Radiation (CSR). In dedicated particle tracking simulations, one usually makes certain assumptions concerning the beam properties and the collective effects to simplify implementation and analysis. Here, we estimate the influence of some of the common assumptions made in EEHG simulations on the properties of the output FEL radiation, using the example of FLASH and its proposed seeding beamline. We conclude that the inherent properties of the FLASH1 beam, namely the negatively chirped energy profile, has dominant effect on the spectral intensity profile of the radiators output compare to that of the CSR induced chirp.