X-ray Emission Spectroscopy at X-ray Free Electron Lasers: Limits to Observation of the Classical Spectroscopic Response for Electronic Structure Analysis

X-ray free electron lasers (XFELs) provide ultrashort intense X-ray pulses suitable to probe electron dynamics but can also induce a multitude of nonlinear excitation processes. These affect spectroscopic measurements and interpretation, particularly for upcoming brighter XFELs. Here we identify and discuss the limits to observing classical spectroscopy, where only one photon is absorbed per atom for a Mn²⁺ in a light element (O, C, H) environment. X-ray emission spectroscopy (XES) with different incident photon energies, pulse intensities, and pulse durations is presented. A rate equation model based on sequential ionization and relaxation events is used to calculate populations of multiply ionized states during a single pulse and to explain the observed X-ray induced spectral lines shifts. This model provides easy estimation of spectral shifts, which is essential for experimental designs at XFELs and illustrates that shorter X-ray pulses will not overcome sequential ionization but can reduce electron cascade effects.