Ion transport in inhomogeneous media based on the bipartition model for primary ions

The present paper is focused on the mathematical modeling of the charged particle transport in nonuniform media. We study the energy deposition of high energy protons and electrons in an energy range of ≈50–500 MeV. This work is an extension of the bipartition model; for high energy electrons studied by Luo and Brahme in [Z. Luo, A. Brahme, High energy electron transport, Phys. Rev. B 46 (1992) 739–752] [42]; and for light ions studied by Luo and Wang in [Z. Luo, S. Wang, Bipartition model of ion transport: an outline of new range theory for light ions, Phys. Rev. B 36 (1987) 1885–1893]; to the field of high energy ions in inhomogeneous media with the retained energy-loss straggling term. In the bipartition model, the transport equation is split into a coupled system of convection–diffusion equations controlled by a partition condition. A similar split is obtained in an asymptotic expansion approach applied to the linear transport equation yielding pencil beam and broad beam models, which are again convection–diffusion type equations. We shall focus on the bipartition model applied for solving three types of problems: (i) normally incident ion transport in a slab; (ii) obliquely incident ion transport in a semi-infinite medium; (iii) energy deposition of ions in a multilayer medium. The broad beam model of the proton absorbed dose was illustrated with the results of a modified Monte Carlo code: SHIELD - HIT+.