Application of the GBFP Method to Electron Partial-Wave Expansion Elastic Scattering Differential Cross Sections Within the Geant4 Toolkit - Paper 69
- University of New Mexico, Dept. of Chemical and Nuclear Engineering, Farris Engineering Center, Albuquerque, New Mexico, 87131 (United States)
- Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico, 87185-1179 (United States)
Analog Monte Carlo simulation of electrons in complex material geometries is generally impractical because the long range Coulomb interactions result in highly peaked differential cross sections (DCS) for scattering and energy-loss and extremely small collision mean free paths (mfp). The condensed history (CH) Monte Carlo method attempts to alleviate this limitation by advancing electrons in fixed steps and sampling angular deflections and energy losses from precomputed distributions obtained from approximate solutions to the underlying transport equation that are valid only for thin layers. Though CH is efficient and is widely employed in production codes (ITS, MCNP, EGS, Geant), step size restrictions and inconsistent handling of material and free surface boundaries limit the ultimate accuracy possible with this approach, especially in applications to highly heterogeneous media. Recently proposed alternatives to the CH method, such as the Generalized Boltzmann Fokker-Planck (GBFP) method, restore the correct transport mechanics by simulating single events based on a Boltzmann transport equation but with efficiency and accuracy achieved through the use of reduced-physics interaction models. Motivated by Lewis theory, various moment-preserving strategies are employed in the GBFP approach to construct DCSs that are less singular, and with mfps shorter than analog. Specifically, the approximate cross sections are constructed to rigorously preserve a finite number of angular and energy-loss moments of the analog DCSs while all higher moments are approximated in terms of the exact lower moments. By systematically increasing the number of moments retained, any desired accuracy can be obtained for integrated quantities, such as dose, reflection and transmission yields, as well as distributed quantities such as energy and angular distributions. For relativistic Rutherford cross section models, the GBFP method has been demonstrated in Monte Carlo simulation to yield accuracy comparable to analog but at a fraction of the cost. One advantage of the GBFP approach is that angular deflection and energy-loss interactions depend only on Legendre moments and energy-loss moments and not the detailed form of the analog DCSs. This feature allows moment-preservation to be enforced through DCSs expressed as a superposition of discrete (i.e., using delta-functions) angular deflections and discrete energy losses. This promotes extremely efficient computation when compared to analog and completely continuous or hybrid discrete-continuous moment-based DCS reconstructions, while yielding highly accurate results for integrated and distributed quantities. In this paper, we demonstrate that the moment-preserving algorithms central to our fully discrete GBFP method can be readily extended to apply to tabulated DCS data, specifically to the partial-wave expansion (PWE) elastic scattering DCSs. Since data libraries for the PWE DCSs for energy and material combinations of interest can be prohibitively large, the GBFP method provides a means to reduce data storage requirements. We implemented our algorithm in the Geant4 Monte Carlo code and all numerical results are obtained using this implementation. (authors)
- Research Organization:
- American Nuclear Society - ANS, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)
- OSTI ID:
- 23082906
- Resource Relation:
- Conference: RPSD 2014: 18. Topical Meeting of the Radiation Protection and Shielding Division of ANS, Knoxville, TN (United States), 14-18 Sep 2014; Other Information: Country of input: France; 12 refs.; available on CD Rom from American Nuclear Society - ANS, 555 North Kensington Avenue, La Grange Park, IL 60526 (US)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ACCURACY
ALGORITHMS
ANGULAR DISTRIBUTION
APPROXIMATIONS
BOLTZMANN EQUATION
COMPUTERIZED SIMULATION
DELTA FUNCTION
DIFFERENTIAL CROSS SECTIONS
ELASTIC SCATTERING
ENERGY LOSSES
FOKKER-PLANCK EQUATION
MONTE CARLO METHOD
NUCLEAR DATA COLLECTIONS
PARTIAL WAVES
RELATIVISTIC RANGE
THIN FILMS