1-D radial moment calculations of 3-D coupled electron -photon beams.

Abstract

We examine narrow pencil beams of radiation normally incident on slabs of material. As the particles in the beam penetrate the material, they, undergo scattering events, change direction and energy, and the beam broadens. A method has been developed for determining the exact radial moments of this 3-D beam of radiation as a function of depth into the slab by solving a system of 1-D transport equations. We present the derivation of these equations up to the fourth-order radial moment. We apply this method to monoenergetic beams with Fokker-PIanck, Henyey-Greenstein, and screened Rutherford scattering using a 1-D discrete ordinates code. We examine the radial distributions resulting from these scattering kernels and the use of radial moments in analytical expressions to approximate the radial distribution of the flux. We also implement the radial moment equations in the ONEBFP discrete ordinates code up to the second-order radial moment. We apply ONEBFP to energy-dependent, coupled electron-photon beams using CEPXS-generated cross sections. Thus, by solving 1-D transport equations, we obtain realistic multidimensional information concerning the broadening of 3-D electron-photon beams. This information is relevant to fields such as radiography, particle accelerators, lasers, medical imaging, and radiation oncology. We demonstrate the efficiency of the 1-D calculations and make comparisons with 3-D Monte Carlo calculations using the ITS CYLTRAN code. We employ modified P_N synthetic acceleration to speed up the iterative convergence of the 1-D charged particle calculations. For high-energy photon beams, we utilize a hybrid Monte Carlo/discrete ordinates method. Finally, we examine the radial distributions of the energy deposition resulting from electron and photon beams.