Vector electromagnetic theory of transition and diffraction radiation with application to the measurement of longitudinal bunch size

We have developed a novel method based on vector electromagnetic theory and Schelkunoff's principles, to calculate the spectral and angular distributions of transition radiation (TR) and diffraction radiation (DR) produced by a charged particle interacting with an arbitrary metallic target. The vector method predicts the polarization and spectral-angular distributions of the radiation at an arbitrary distance from the source, i.e., in both the near and far fields, and in any direction of observation. The radiation fields of TR and DR calculated with the commonly used scalar Huygens model are shown to be limiting forms of those predicted by the vector theory and the regime of validity of the scalar theory is explicitly shown. Calculations of TR and DR done using the vector model are compared to results available in the literature for various limiting cases and for cases of more general interest. Our theory has important applications to the design of TR and DR diagnostics, particularly those utilizing coherent TR and DR to infer the longitudinal bunch size and shape. A new technique to determine the bunch length using the angular distribution of coherent TR or DR is proposed.