Incoherent form factor in diffraction and Smith–Purcell radiations

It has been shown that polarization radiation of charged particle beams generally includes an incoherent form factor caused by a finite transverse size of a beam. Consequently, a widespread opinion that the form factor characterizes only coherent radiation of charge particle bunches is generally invalid. The reason for the existence of incoherent form factor is the interaction of charged particles with the target edge in the direction perpendicular to their trajectory. The incoherent form factor exists for diffraction radiation, Smith-Purcell radiation, and other types of polarization radiation in the case of transversely limited targets: transition radiation, parametric X-ray radiation, and Cherenkov radiation. It has been shown that the difference of the incoherent form factor from unity increases with a decrease in the ratio of the impact parameter to the transverse size of the bunch. Furthermore, it has been shown that the transverse part of the coherent form factor differs from unity to the same extent as the incoherent form factor.