Electron Beam Flattening with an Annular Scattering Foil

A narrow parallel beam of electrons from an accelerator is commonly spread over a useful area by multiple scattering in a thin foil for applications such as radiation therapy and bubble chamber experiments. If the intensity at the edge of the resulting useful field is a fraction x of that in the center, then only the fraction 1-x of the incident beam is used. A secondary scattering foil which intercepts electrons outside the useful field redirects some of these into a distribution which complements that from the primary scatterer, allowing the use of a thinner primary scatterer. The resulting distribution function is developed, in a small-angle approximation, and integrated for annular secondary scatterer elements as a double series which is evaluated by a computer program in terms of the thickness and dimensions of the annulus. Results are discussed and limits of applicability of the theory are pointed out.