Study On Compton Scattering Of X-ray Laser With Bound Electrons By Frequency Domain Theory

The birth of X-ray free electron laser has opened an era to investigate the nonlinear interaction between ultrafast and ultra-intense X-ray laser and matter.In recent years,by using X-ray free electron lasers,many nonlinear phenomena at X-ray wavelengths have been observed experimentally for the first time,including the anomalously large redshift found by Fuchs et al.in the nonlinear Compton scattering experiment of X-ray laser and solid target.However,due to the lack of theoretical research on the nonlinear Compton scattering processes of bound electrons and X-ray laser,the phenomenon has not been explained.In view of the theoretical vacancy,a non relativistic frequencydomain theory,based on the non-perturbative quantum electrodynamics,of X-ray Compton scattering by bound electrons is developed.This paper focuses on the linear and nonlinear Compton scattering of X-ray laser and bound electrons and the main results we obtained are as follows:1.Based on the nonrelativistic frequency-domain theory,we derive the expressions of transition matrix element for linear and nonlinear Compton scattering of bound electrons in high frequency laser field.According to these expressions,the Compton scattering process can occur through two transition paths: one is the electronassisted mode-mode(EMM)transition,and the other is the laser-assisted electron-mode(LEM)transition.By these formula,the differential probability of scattered light can be obtained.2.We theoretically calculate the process of X-ray linear Compton scattering by bound electrons.We find that,when the polarization direction of the scattered light is parallel to the polarization direction of the incident light,the doubly differential probability of the scattered light is dominated by the EMM transition;when the polarization direction of the scattered light is perpendicular to the polarization plane of the incident light,the double differential probability of the scattered light is determined by the LEM transition.In addition,we also found that choosing the polarization direction of scattered light parallel to the polarization direction of incident light will be more conducive to obtain the density distribution of electrons in momentum space by means of the linear Compton scattering.3.For the first time,we obtain the redshift phenomenon of the nonlinear Compton scattering spectrum in our theoretical calculation,which is consistent with the experimental observation.Through the analysis,we find the reason for the redshift of the peak position of the double-differential probability spectrum,i.e.,the bound electron provides a redshift equivalent to its ionization energy,and the inverse relationship between the momentum of the final state electron and the scattered photon energy increases the redshift of the peak position.This work makes up the deficiency of the existing theories in the study of the nonlinear X-ray Compton scattering mechanism by bound electrons.4.We calculate the high-order nonlinear Compton scattering process of bound electrons in X-ray laser field.It shows that for the two-step transition process of twophoton Compton scattering,the energy range of scattered light is always near the fundamental frequency region,and increases with the increase of the scattering angle.When the scattering angle is 0°,the two-step transition induces the elastic scattering.The characteristics of the high-order scattering process are attributed to the fact that the two-step transition is constrained not only by the energy conservation,but also by the momentum conservation in the scattering transition of the second step.We also give an energy zone map of the scattering process,which is helpful to judge which scattering process the detection results come from.In addition,we calculate the doubly differential probability of three-photon Compton scattering of X-ray laser and bound electrons.It shows that the two-step transition process of three-photon Compton scattering is difficult to be detected at current experimental level,due to the large coverage of other scattering processes.Our work will contribute to the understanding and analysis of the experimental results of nonlinear X-ray Compton scattering by bound electrons.