Multidimensional Electron-Photon Transport with Standard Discrete Ordinates Codes

Abstract

1do not work for charged-particle beams. It is hoped, however, that the methods presented here provide some progress toward a multidimensional, deterministic electron-transport capability.Coupled electron-photon transport capability is needed for an ever-increasing number of applications, including the response of electronics components to space and man-made radiation environments, medical radiation therapy, industrial curing, and food sterilization. Currently, powerful Monte Carlo codes are available for electron transport*. While some problems are well suited for a Monte-Carlo approach, other problems are more efficiently solved with a deterministic method, e.g. computing distributions, modeling deep penetration, and low-probability events.Deterministic electron transport capability has been available for one-dimensional geometries, with the CEPXS/ONELD code package5. Unfortunately, the CEPXS/ONELD approach is not easily extendable to multidimensional geometries. Bill Filippone and his students at the University of Arizona developed the multidimensional, deterministic charged-particle code, SMARTEPANTS'.This code is presently under active development.The work presented here combines the CEPXS/ONELD and SMARTEPANTS approaches, resulting in SMARTEPANTS-like cross sections that are compatible with production discreteordinates codes. The resulting cross sections have a number of desirable properties: 1) positivity, 2) much smaller than the true interaction cross sections, 3) low-order Legendre expansion, 4) and not tied to a particular quadrature set. These desirable properties will be further explained, with limitations given, later in this article. BOLTZMANN-FOKKER-PLANCK OPERATORThe Boltzmann operator, L, describing the distribution in space, direction, and energy of a field of either charged or neutral particles is defined by7 L@(r, 52, E) = -52 0 V@(r, 52, E ) -at(r, E)@(r, 52, E) + JJ as(r, 521 + 52, E' + E)a(r, a', E')~oz'~E'.(1)The scattering cross section, as(r,O' -+ 52, E' + E), is the probability per unit energy and solid angle that a particle of energy E' moving in direction 52' will be scattered to energy E in direction 52. The total cross section is at(r, E). For neutral-particle applications, the Boltzmann equation is normally solved by expanding the scattering cross section in a low-order Legendre polynomial expansion and the discretizing the spatial, energy, and angular dependence of the fluence.For scattering that is highly forward peaked, which is characteristic of charged-particle scattering, the Legendre polynomial angular expansion of the cross sections that is normally used in discrete ordinates codes is inadequate. The Boltzmann-Fokker-Planck (BFP) operator is an approximation to the Boltzmann-transport operator for scattering interactions that are highly forward peaked.In order to model electron transport with a BFP formulation, the scattering cross section is separated into three components, 1) the elastic-scattering part (for directional change without energy loss), 2) a soft inelastic-s...

Dosimetric comparison of Acuros XB deterministic radiation transport method with Monte Carlo and model-based convolution methods in heterogeneous media

“…The GBBS then iteratively solve the radiation transport problem within specified volumes to compute radiation doses. Historically, GBBS algorithms have been developed and used in various neutral-and charged-particle shielding calculations, [19][20][21] but they seldom have been used in external photon beam dose calculations. In 2006, Gifford et al investigated the potential of Attila, a general-purpose GBBS developed by Los Alamos National Laboratories (Los Alamos, NM) and licensed to Transpire, Inc. (Gig Harbor, WA), for low-dose-rate Cesium-137 brachytherapy sources loaded inside a shielded gynecological applicator and for 1.5 Â 1.5 cm 2 18 MV external photon beam dose calculations.…”

Monte Carlo modeling for intravascular brachytherapy sources

“…Morel, Lorence and their collegues (Morel, 1979; Morel and Wienke, 1982;Lorence, Nelson, and Morel, 1985;Lorence, Morel, and Valdez, 1989a, 1989bLorence, 1992; Lorence and Morel, 1992) developed a reasonably successful one-dimensional calculation involving complex numerical procedures using carefully prepared scattering matrices. Work on multi-dimensional treatments is reported by Fillipone et al (1990), , , Datta and Ray (1993), and Drumm (1997). These deterministic calculations have the advantage of producing results free of statistical fluctuations, but are subject to approximations used in the calculations and to some numerical artifacts.…”

Parallel FE approximation of the even/odd-parity form of the linear Boltzmann equation

“…Eq. (2.1) is applicable to neutral-particle transport and can also model the transport of electrons for many problems of interest if Goudsmit-Saunderson modified electron cross sections are used [3].…”

“…The code is designed to model the transport of neutral particles but can also model the transport of charged particles, such as electrons, by using specially modified electron cross sections [3]. The reference describes a Goudsmit-Saunderson modification to CEPXS electron cross sections [ll], resulting in electron cross sections that are compatible with neutral-particle transport codes.…”