Nonlinear X-ray Compton scattering: A new mathematical model for X-ray wave mixing mechanism

The present report deals with a modification of the nonlinear X-ray Compton scattering expression by introducing an index of refraction R. XFEL-based two hard X-ray photons with the energy $\omega$ around 9 keV were effectively mixed up to form a single high-energy photon (18 keV) in a prior publication (Fuchs et al., 2015). Using the Volkov correction, an alternative estimation of scattered X-ray photon energy ${\omega }^{\prime }$ via a nonlinear process was expressed. Applying this theoretical model, it was determined that an 18 keV single high-energy scattered photon can be produced by mixing two 9 keV photons with a field strength parameter $\chi$ ranging from 0.1 to 0.2.