An efficient method for calculating plural scattering of relativistic electrons in thin foils and multilayers

The radiation characteristics of soft X-ray emission by relativistic electrons, which produce (resonant) transition radiation or Cherenkov radiation inside a foil or multilayer, is determined not only by the intrinsic emission process but also by the angular distribution of the electrons due to Rutherford scattering. The number of scatterings events in these micron-thick foils or multilayers is smaller than about 20, the so-called plural scattering regime. We developed a numerical method to calculate very efficiently the angular distribution of relativistic electrons while passing through a single layer of any material and arbitrary thickness in the plural and part of the multiple scattering regime. The angular scattering distribution is a truncated weighted summation of universal distribution functions, each representing a fixed number of scattering events. These universal distribution functions have to be calculated only once and can be stored in a database for later use. This method of calculating the angular scattering distributions has also been extended to deal with multilayers and to take into account incident electron beams with an arbitrary angular distribution. The calculations have been validated by comparison with Monte Carlo simulations, which require much more computing time. (C) 2004 Elsevier B.V.. All rights reserved.