A computationally efficient moment-preserving Monte Carlo electron transport method with implementation in Geant4

Abstract

The moment-preserving method, demonstrated as a viable alternative to condensed history for electrons, is extended to protons. Given the generality and the flexibility of the method, a discrete Coulomb scattering and discrete impact-ionization differential cross-section library for protons was readily developed and existing Geant4 electron discrete process and model classes were extended to make use of the new proton library. It is shown that levels of efficiency and accuracy similar to those demonstrated for electrons are obtainable for protons in straight-ahead, energy-loss problems. However, in problems with deflection, agreement is strongly dependent on the proton energy. That is, good agreement was observed in the few MeV range, while unsatisfactory agreement was observed in problems with proton energies above 100-MeV.

A computationally effcient moment-preserving Monte Carlo proton transport method in Geant4

“…For simplicity, we ignore delta-ray electrons, but accounting for delta-rays can be accommodated in the MP method as previously demonstrated. (8) We begin with a discussion of elastic Coulombic collisions with atoms as described by the Wentzel differential cross section. (9,10) The Wentzel cross section describes collisions with atoms where particles are deflected through some angle and impart energy to the atom depending on the angle through which the particle was deflected.…”

“…As described in Dixon et al, (8) differential cross section moments are central to the MP method so we now define the relevant DCS moments and then introduce the MP models used in this study.…”

“…In this paper, we extend the recently developed momentpreserving (MP) method demonstrated as a viable alternative to the condensed history method for electron transport, (8) to protons. Motivated by Lewis theory, analog DCSs are replaced in this approach by approximate DCSs that preserve a finite number of angular deflection and energy-loss moments of the analog DCS while approximating all remaining moments in terms of the exact lower order moments.…”

“…Motivated by Lewis theory, analog DCSs are replaced in this approach by approximate DCSs that preserve a finite number of angular deflection and energy-loss moments of the analog DCS while approximating all remaining moments in terms of the exact lower order moments. This has been shown to yield longer mean free paths and less peaked cross sections, (8) which promotes the use of single-scatter Monte Carlo simulation. Moreover, accuracy scales with the number of moments preserved, while efficiency is achieved in most applications through the need to preserve only a limited number of moments.…”

“…Moreover, accuracy scales with the number of moments preserved, while efficiency is achieved in most applications through the need to preserve only a limited number of moments. (8) Finally, the algorithms associated with the MP method are independent of the form of the underlying DCS, whether a theoretical result or tabulated data (numerical or experimental), and apply generically to all charged particle types. Therefore, significant reduction in code development and maintenance can be realized through use of a generic class that is extensible to a variety of charged particle types.…”