Numerical simulations of X-rays Free Electron Lasers (XFEL)

We study a nonlinear Schr\"odinger equation which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation appears as a first-principles model for the beam-matter interactions that would take place in an XFEL molecular imaging experiment in \cite{frat1}. Since XFEL is more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective time-averaged one is examined. We use an operator splitting pseudo-spectral method to investigate numerically the behaviour of the model versus its time-averaged version in complex situations, namely the energy subcritical/mass supercritical case, and in the presence of a periodic lattice. We find the time averaged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases \cite{xfel1}.Comment: 14 page

Stochastic stimulated electronic x-ray Raman spectroscopy

Resonant inelastic x-ray scattering (RIXS) is a well-established tool for studying electronic, nuclear and collective dynamics of excited atoms, molecules and solids. An extension of this powerful method to a time-resolved probe technique at x-ray free electron lasers (XFELs) to ultimately unravel ultrafast chemical and structural changes on a femtosecond time scale is often challenging, due to the small signal rate in conventional implementations at XFELs that rely on the usage of a monochromator set up to select a small frequency band of the broadband, spectrally incoherent XFEL radiation. Here, we suggest an alternative approach, based on stochastic spectroscopy, that uses the full bandwidth of the incoming XFEL pulses. Our proposed method is relying on stimulated resonant inelastic x-ray scattering, where in addition to a pump pulse that resonantly excites the system a probe pulse on a specific electronic inelastic transition is provided, that serves as seed in the stimulated scattering process. The limited spectral coherence of the XFEL radiation defines the energy resolution in this process and stimulated RIXS spectra of high resolution can be obtained by covariance analysis of the transmitted spectra. We present a detailed feasibility study and predict signal strengths for realistic XFEL parameters for the CO molecule resonantly pumped at the O1s-{\pi}* transition. Our theoretical model describes the evolution of the spectral and temporal characteristics of the transmitted x-ray radiation, by solving the equation of motion for the electronic and vibrational degrees of freedom of the system self consistently with the propagation by Maxwell's equations

Corrugated structure insertion for extending the SASE bandwidth up to 3% at the European XFEL

The usage of x-ray free electron laser (XFEL) in femtosecond nanocrystallography involves sequential illumination of many small crystals of arbitrary orientation. Hence a wide radiation bandwidth will be useful in order to obtain and to index a larger number of Bragg peaks used for determination of the crystal orientation. Considering the baseline configuration of the European XFEL in Hamburg, and based on beam dynamics simulations, we demonstrate here that the usage of corrugated structures allows for a considerable increase in radiation bandwidth. Data collection with a 3% bandwidth, a few microjoule radiation pulse energy, a few femtosecond pulse duration, and a photon energy of 5.4 keV is possible. For this study we have developed an analytical modal representation of the short-range wake function of the flat corrugated structures for arbitrary offsets of the source and the witness particles.Comment: 29 pages, 17 figure

Superradiant Undulator Radiation for Selective THz Control Experiments at XFELs

The generation of frequency-tunable, narrow-bandwidth and carrier-envelope-phase stable THz pulses with fields in the MV/cm regime that can be appropriately timed to the femtosecond X-ray pulses from free-electron-lasers is of highest scientific interest. It will enable to follow the electronic and structural dynamics stimulated by (non)linear selective excitations of matter on few femtosecond time and {\AA}ngstrom length scales. In this article, a scheme based on superradiant undulator radiation generated just after the XFEL is proposed. The concept utilizes cutting edge superconducting undulator technology and provides THz pulses in a frequency range between 3 and 30 THz with exceptional THz pulse energies. Relevant aspects for realization and operation are discussed point by point on the example of the European XFEL

Efficient electronic structure calculation for molecular ionization dynamics at high x-ray intensity

We present the implementation of an electronic-structure approach dedicated to ionization dynamics of molecules interacting with x-ray free-electron laser (XFEL) pulses. In our scheme, molecular orbitals for molecular core-hole states are represented by linear combination of numerical atomic orbitals that are solutions of corresponding atomic core-hole states. We demonstrate that our scheme efficiently calculates all possible multiple-hole configurations of molecules formed during XFEL pulses. The present method is suitable to investigate x-ray multiphoton multiple ionization dynamics and accompanying nuclear dynamics, providing essential information on the chemical dynamics relevant for high-intensity x-ray imaging.Comment: 28 pages, 6 figure

A split-beam probe-pump-probe scheme for femtosecond time resolved protein X-ray crystallography

In order to exploit the femtosecond pulse duration of X-ray Free-Electron Lasers (XFEL) operating in the hard X-ray regime for ultrafast time-resolved protein crystallography experiments, critical parameters that determine the crystallographic signal-to-noise (I/σI) must be addressed. For single-crystal studies under low absorbed dose conditions, it has been shown that the intrinsic pulse intensity stability as well as mode structure and jitter of this structure, significantly affect the crystallographic signal-to-noise. Here, geometrical parameters are theoretically explored for a three-beam scheme: X-ray probe, optical pump, X-ray probe (or “probe-pump-probe”) which will allow experimental determination of the photo-induced structure factor amplitude differences, ΔF, in a ratiometric manner, thereby internally referencing the intensity noise of the XFEL source. In addition to a non-collinear split-beam geometry which separates un-pumped and pumped diffraction patterns on an area detector, applying an additional convergence angle to both beams by focusing leads to integration over mosaic blocks in the case of well-ordered stationary protein crystals. Ray-tracing X-ray diffraction simulations are performed for an example using photoactive yellow protein crystals in order to explore the geometrical design parameters which would be needed. The specifications for an X-ray split and delay instrument that implements both an offset angle and focused beams are discussed, for implementation of a probe-pump-probe scheme at the European XFEL. We discuss possible extension of single crystal studies to serial femtosecond crystallography, particularly in view of the expected X-ray damage and ablation due to the first probe pulse