Incoherent Form Factor in Diffraction and Smith—Purcell Radiations

Abstract

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.

Non-linear quantum effects in electromagnetic radiation of a vortex electron

“…which reflects the well-known fact that an incoherent form-factor for a beam equals unity [29,30]. As has been recently shown in Ref.…”

“…As has been recently shown in Ref. [30], the incoherent form-factor can differ from unity when the grating in Smith-Purcell radiation or a target in transition and diffraction radiation is spatially limited -say, when the grating has a width smaller than the transverse coherence length of the virtual photon βγλ, so the radiation formation width is defined by the geometrical sizes of the target.…”

Does a Form Factor in Smith–Purcell Radiation Exist Always?

“…In particular, it was shown that the incoherent form factor also contains information about the transverse dimensions of the bunch, and the coherent term is not simply the Fourier transform of the distribution function. It is essential that, as we pointed out in [6], these conclusions are valid for targets homogeneous along the surface in the direction transverse to the motion of the electron bunch.…”

“…The generally accepted theoretical approach taking into account the coherence effects involves calculating the angular and frequency distributions of the intensity for a single electron and then multiplying the single-particle intensity by the form factor of the bunch. The latter is the sum of two terms, coherent and incoherent [6], and contains all information about the shape and size of the bunch. Usually, the incoherent term is assumed to be equal to the number of electrons in the bunch, and the coherent term is equal to the square of the number of electrons multiplied by the squared absolute value of the Fourier transform of the electron distribution function in the bunch.…”

“…Usually, the incoherent term is assumed to be equal to the number of electrons in the bunch, and the coherent term is equal to the square of the number of electrons multiplied by the squared absolute value of the Fourier transform of the electron distribution function in the bunch. It was shown in [6] that, for edge types of radiation, such as Smith-Purcell, diffraction Cherenkov, or diffraction radiation, the coherent and incoherent terms in the form factor are different. In particular, it was shown that the incoherent form factor also contains information about the transverse dimensions of the bunch, and the coherent term is not simply the Fourier transform of the distribution function.…”