Abstract
In this paper, we investigate photon-photon scattering in vacuum in the head-on collision of an optical laser and an x-ray free-electron laser (XFEL) of multiple modes. For the XFEL as probe light with focus waist larger than the optical laser, the scattering photons with the same energy of the initial probe XFEL can be separated from the XFEL background due to the different scattering angle at far field. Here, we study the effect of XFEL's transverse profile, due to superposition of modes, in this vacuum diffraction process. Based on the parameters of upcoming facilities with 100-PW optical lasers and intense XFEL, we show that for a given photon number of the probe XFEL, the separable scattering photon number can be greatly enhanced when the XFEL is composed of different Laguerre-Gaussian modes. As an example, with SHINE's setup there will be 185 photons separable from the XFEL background for each shot, which is 2.5 times that of the case with the usual Gaussian profile.
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