Polarization of diffraction radiation of a bunch of charged particles on a metal sphere

Diffraction radiation is widely used for non-destructive diagnostics of charged particle beams. In the series of the previous works, a method was developed for describing the diffraction radiation of a non-relativistic particle on a perfectly conducting sphere, based on the method of images well-known from electrostatics. This method allows one to derive the analytic formulae for two main radiation characteristics, i.e. spectral angular density and polarization. The characteristic features of these values allow the possibility of developing, on their basis, new methods for monitoring the parameters of the trajectory of a moving particle in relation to the sphere center. In this work, formulae are obtained that describe the polarization of the coherent diffraction radiation on a metal sphere from a pancake-bunch of charged particles. It is shown that the polarization of the radiation in this case makes it possible to estimate the positions of the bunch edges relative to the center of the sphere. This can be used for the non-destructive measurement of the characteristic bunch dimensions.