  Compton scattering is the nonresonant inelastic scattering of an x-ray photon
by an electron and has been used to probe the electron momentum distribution in
gas-phase and condensed-matter samples. In the low x-ray intensity regime,
Compton scattering from atoms dominantly comes from bound electrons in neutral
atoms, neglecting contributions from bound electrons in ions and free (ionized)
electrons. In contrast, in the high x-ray intensity regime, the sample
experiences severe ionization via x-ray multiphoton multiple ionization
dynamics. Thus, it becomes necessary to take into account all the contributions
to the Compton scattering signal when atoms are exposed to high-intensity x-ray
pulses provided by x-ray free-electron lasers (XFELs). In this paper, we
investigate the Compton spectra of atoms at high x-ray intensity, using an
extension of the integrated x-ray atomic physics toolkit, \textsc{xatom}. As
the x-ray fluence increases, there is a significant contribution from ionized
electrons to the Compton spectra, which gives rise to strong deviations from
the Compton spectra of neutral atoms. The present study provides not only
understanding of the fundamental XFEL--matter interaction but also crucial
information for single-particle imaging experiments, where Compton scattering
is no longer negligible.
