Brian Claude Franke

ITS Version 3.0: The Integrated TIGER Series of Coupled Electron/Photon Monte Carlo Transport Codes

ITS is a powerful and user-friendly software package permitting state-of-the-art Monte Carlo solution of lineartime-independent coupled electron/photon radiation transport problems, with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. Our goal has been to simultaneously maximize operational simplicity and physical accuracy. Through a set of preprocessor directives, the user selects one of the many ITS codes. The ease with which the makefile system is applied combines with an input scheme based on order-independent descriptive keywords that makes maximum use of defaults and internal error checking to provide experimentalists and theorists alike with a method for the routine but rigorous solution of sophisticated radiation transport problems. Physical rigor is provided by employing accurate cross sections, sampling distributions, and physical models for describing the production and transport of the electron/photon cascade from 1.0 GeV down to 1.0 keV. The availability of source code permits the more sophisticated user to tailor the codes to specific applications and to extend the capabilities of the codes to more complex applications. Version 6, the latest version of ITS, contains (1) improvements to the ITS 5.0 codes, and (2) conversion to Fortran 90. The general user friendliness of the software has been enhanced through memory allocation to reduce the need for users to modify and recompile the code.

MONTE CARLO ELECTRON DOSE CALCULATIONS USING DISCRETE SCATTERING ANGLES AND DISCRETE ENERGY LOSSES

Abstract We present a computationally efficient single event Monte Carlo approach for calculating dose from electrons. Analog elastic scattering and inelastic energy-loss differential cross sections for electrons are converted into corresponding discrete cross sections that are constrained to exactly preserve low-order moments of the analog cross sections. While the method has been implemented and tested for the Rutherford model for scattering and energy loss, its dependence solely on cross-section moments makes our approach arbitrarily general. By comparison with analog Monte Carlo calculations, we demonstrate that few discrete angles and energies are required to achieve accurate dose distributions, and the calculations are fast. The method is capable of yielding accurate results across the entire spatial extent of the transport problem, from relatively isotropic scattering to highly forward-peaked scattering. We compare the accuracy of the angular approximation with the Goudsmit-Saunderson angular approximation commonly used by condensed history methods and similarly analyze the energy approximation. Finally, we present an investigation of the combined approximations and illustrate the accuracy of this method in the presence of a material interface. The computational efficiency of each method is explicitly compared using timing studies.

ITS5 theory manual.

This document describes the modeling of the physics (and eventually features) in the Integrated TIGER Series (ITS) codes [Franke 04] which is largely pulled from various sources in the open literature (especially [Seltzer 88], [Seltzer 91], [Lorence 89], [Halbleib 92]), although those sources often describe the ETRAN Code from which the physics engine of ITS is derived, not necessarily identical. This is meant to be an evolving document, with more coverage and detail as time goes on. As such, entire sections are still incomplete. Presently, this document covers the continuous-energy ITS codes with more completeness on photon transport (though electron transport will not be completely ignored). In particular, this document does not cover the Multigroup code, MCODES (externally applied electromagnetic fields), or high-energy phenomena (photon pair-production). In this version, equations are largely left to the references though they may be pulled in over time.

Radial Moment Calculations of Coupled Electron-Photon Beams

Abstract We consider the steady-state transport of normally incident pencil beams of radiation in slabs of material. A method has been developed for determining the exact radial moments of three-dimensional (3-D) beams of radiation as a function of depth into the slab, by solving systems of one-dimensional (1-D) transport equations. We implement these radial-moment equations in the ONEBFP discrete ordinates code and simulate energy-dependent, coupled electron-photon beams using CEPXS-generated cross sections. Modified PN synthetic acceleration is employed to speed up the iterative convergence of the 1-D charged-particle calculations. For high-energy photon beams, a hybrid Monte Carlo/discrete ordinates method is examined. We demonstrate the efficiency of the calculations and make comparisons with 3-D Monte Carlo calculations. Thus, by solving 1-D transport equations, we obtain realistic multidimensional information concerning the broadening of electron-photon beams. This information is relevant to fields such as industrial radiography, medical imaging, radiation oncology, particle accelerators, and lasers.

Supercomputer and Cluster Performance Modeling and Analysis Efforts: 2004-2006

This report describes efforts by the Performance Modeling and Analysis Team to investigate performance characteristics of Sandias engineering and scientific applications on the ASC capability and advanced architecture supercomputers, and Sandias capacity Linux clusters. Efforts to model various aspects of these computers are also discussed. The goals of these efforts are to quantify and compare Sandias supercomputer and cluster performance characteristics; to reveal strengths and weaknesses in such systems; and to predict performance characteristics of, and provide guidelines for, future acquisitions and follow-on systems. Described herein are the results obtained from running benchmarks and applications to extract performance characteristics and comparisons, as well as modeling efforts, obtained during the time period 2004-2006. The format of the report, with hypertext links to numerous additional documents, purposefully minimizes the document size needed to disseminate the extensive results from our research.

Comparison of Two Galerkin Quadrature Methods.

We compare two methods for generating Galerkin quadratures. In method 1, the standard SN method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard SN method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwise sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding SN equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.

A discretization scheme for the three-dimensional angular Fokker-Planck operator

Abstract A new Sn discretization of the angular Fokker-Planck operator used in three-dimensional calculations is derived for product quadrature sets. It is straightforward to define discretizations that preserve the null space and zeroth angular moment of the analytic operator and are self-adjoint, monotone, and nonpositive-definite. Our new discretization differs from more straightforward discretizations in that it also preserves the three first angular moments of the analytic operator when applied in conjunction with product quadrature sets constructed with Chebychev azimuthal quadrature. Otherwise, it preserves only two of the three first angular moments. Computational results are presented that demonstrate the superiority of this new discretization relative to a straightforward discretization. Two-dimensional versions of the new discretization are also given for x-y and r-z geometries.

Adaptive Three-Dimensional Monte Carlo Functional-Expansion Tallies

Abstract We describe a method that enables Monte Carlo calculations to automatically achieve a user-prescribed error of representation for numerical results. Our approach is to iteratively adapt Monte Carlo functional-expansion tallies (FETs). The adaptivity is based on assessing the cellwise 2-norm of error due to both functional-expansion truncation and statistical uncertainty. These error metrics have been detailed by others for one-dimensional distributions. We extend their previous work to three-dimensional distributions and demonstrate the use of these error metrics for adaptivity. The method examines Monte Carlo FET results, estimates truncation and uncertainty error, and suggests a minimum-required expansion order and run time to achieve the desired level of error. Iteration is required for results to converge to the desired error. Our implementation of adaptive FETs is observed to converge to reasonable levels of desired error for the representation of four distributions. In practice, some distributions and desired error levels may require prohibitively large expansion orders and/or Monte Carlo run times.

Automated Monte Carlo biasing for photon-generated electrons near surfaces.

This report describes efforts to automate the biasing of coupled electron-photon Monte Carlo particle transport calculations. The approach was based on weight-windows biasing. Weight-window settings were determined using adjoint-flux Monte Carlo calculations. A variety of algorithms were investigated for adaptivity of the Monte Carlo tallies. Tree data structures were used to investigate spatial partitioning. Functional-expansion tallies were used to investigate higher-order spatial representations.

Verification and Preliminary Results of the Generalized Boltzmann Fokker-Planck Method for Charged Particle Radiation Transport

The short mean free paths and zero/low energy transfers associated with charged particle interactions create a computationally intensive problem to model. This paper suggests an accurate and efficient momentpreserving alternative to traditional Monte Carlo transport methods. The Generalized Boltzmann Fokker- Planck Method is an approximation of the scattering cross sections used in the linear transport equation which exactly preserves a finite number of scattering moments using a discrete angle representation. Unlike condensed history, this method preserves exponentially distributed interaction sites, simplifies pre-computation and ultimately leads to simplified boundary crossing algorithms. While this method was developed using the screened Rutherford differential cross section, it has recently been updated with improved interaction physics. Transmission/reflection spectra and dose-depth profiles generated using this method has been benchmarked against both analog and condensed history calculations, and have shown an increase in computational efficiency. Moreover, this method may prove broadly applicable to any Monte Carlo simulation involving sufficiently forward-peaked probability distributions. Future work will integrate these methods into the Integrated TIGER Series (ITS) suite to analyze accuracy and performance enhancement in fully coupled photon-electron transport in realistic three dimensional (3-D) geometries.