Incoherent X-ray diffraction radiation for noninvasive diagnostics of transverse size of ultrarelativistic beams

Polarization radiation, which includes diffraction radiation, transition radiation, Smith-Purcell radiation, and others, can be a good instrument for beam diagnostics. All information about the beam size is contained in the so-called form-factor of the beam. The form-factor represents the sum of two parts corresponding to the coherent and incoherent radiation. Contrary to the general opinion the incoherent part does not always equal unity. In this report we give theoretical description of the incoherent part of the form-factor both for Gaussian and uniform distribution of the ultrarelativistic particles in the bunch. We show that the incoherent form-factor depends on the transverse size of the beam, and discuss the new opportunities for non-invasive diagnostics of ultrarelativistic electron beams. (paper)