Charged-Particle Transport in One-Dimensional Systems

Abstract

A semianalytical technique to study the charged-particle transport in one-dimensional finite media is developed. For this purpose, the transport equation is written in the form of coupled integral equations, separating the spatial and energy-angle transmissions. Legendre polynomial representation for the source, flux, and scattering kernel are used to solve the equations. For evaluation of the spatial transmission, discrete ordinate representation in space, energy, and direction cosine is used for the particle and source flux. The integral equations are then solved by the fast iteration technique. The computer code CHASFIT, written on the basis of the above formulation, is described. The fast convergence of the iteration process which is characteristic of charged-particle transport is demonstrated. Convergence studies are carried out with a number of mesh points and polynomial approximations. The method is applied to study the depth-dose distributions due to 140-, 200-, 300-, 400-, 600-, and 740-MeV protons incident normally on a 30-cm-thick tissue slab. The values of the quality factor at the surface and at 5 cm depth, as well as the total average quality factor, are calculated. The results thus obtained are compared with those predicted by the Monte Carlo method. This method can also be applied to multienergy, multiregion systems with arbitrary degree of anisotropy.

Pion transport studies

“…Initially there is a rapid build up of the dose and thereafter the dose remains constant. It is also found that the secondary pion dose is about one tenth of the secondary proton dose as indicated in the case of 600 MeV protons (Muthukrishnan and Gopinath 1983). The depth-dose distributions are compared with the Monte Carlo values (Wright et a1 1969) in this figure and the values vary within a factor of five.…”

“…The transport equation is written in the form of coupled integral equations, separating the spatial and energy-angle transmission (Muthukrishnan and Gopinath 1983) , E', p ' ) G ( x , E ' + E,, a'+ a ) dE' dQ'+ S'(xj, E,, pi). (2)…”

“…T and G represent the transmission and the scattering kernels respectively. The method of solving the transport equation is described elsewhere (Muthukrishnan and Gopinath 1983). We therefore describe here only the transmission and the scattering kernels for pions and the changes that are incorporated.…”

“…In our earlier work on proton transport (Muthukrishnan and Gopinath 1983), we did not consider the production and transport of pions through matter. This is justified because, above the threshold energy of 280 MeV for pion production and up to 400 MeV, the cross section is so small that one can ignore its production.…”