Partially Coherent Crystalline Undulator Radiation from a Positron Bunch Modulated via the SASE XFEL Process

Abstract: Crystalline undulator (CU), where the positrons of a bunch are channeled planarly, is considered. In contrast to channeling radiation, CU radiation (CUR) occurs due to the average sinusoidal motion of positrons. Taking into account the medium polarization, besides hard photons, soft photons are also generated. In the SASE XFEL process, microbunching occurs with a longitudinal size on the order of the wavelength of the stimulated radiation due to the interaction between positrons and generated photons at zero angle. These microbunches in CU will radiate coherently, and the radiation of the bunch will be partially coherent. Charged particles organized into a microbunch with a well-defined spatial phase distribution can emit coherent (synergistic or collective) radiation when the wavelength of the emitted radiation is comparable to or longer than the longitudinal size of the microbunch. The CU parameters, the spatial period and the amplitude, are selected to preserve both the channeling phenomenon of positrons and the coherence of CUR from positron microbunches. The gain of spontaneous radiation depends on the modulation depth of the microbunch, which is a critical parameter of the bunch and can also be determined through the proposed experiment. A numerical analysis has been conducted for a specific case involving CUR generated by a positron bunch modulated during the SASE XFEL, at a corresponding wavelength of the process.