Clifton Russell Drumm

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

A novel solution method has been developed to solve the linear Boltzmann equation on an unstructured triangular mesh. Instead of tackling the first-order form of the equation, this approach is based on the even/odd-parity form in conjunction with the conventional multigroup discrete-ordinates approximation. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, and the method is well suited for massively parallel computers.

An Analysis of the Extended-Transport Correction with Application to Electron Beam Transport

Abstract Charged-particle transport is characterized by scattering cross sections that are extremely large and forward-peaked, requiring specialized treatment as compared with neutral-particle transport. The extended-transport correction (ETC) is known to be an effective method to treat elastic scattering of electrons. We apply the ETC to inelastic downscattering of electrons, and evaluate the effectiveness of the method by comparing the scattering moments for the screened Rutherford scattering kernel and for scattering with a deterministic cosine. The ETC approximation results in a δ-function in angle downscatter source term, for energy loss without direction change, which has been incorporated into the CEPTRE discrete ordinates code in a manner that is compatible with general quadrature sets, not requiring a specialized Galerkin quadrature. The ETC approximation also makes it possible to develop a first-collision source technique that is effective for charged-particle transport, by including particles that have downscattered in energy without direction change in the uncollided-flux solution. We demonstrate the effectiveness of these techniques for problems involving electron beam sources incident on infinite and finite water cylinders and compare the energy- and charge-deposition distributions with ITS Monte Carlo results with good agreement.

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

A Discontinuous Phase-Space Finite Element Discretization of the Linear Boltzmann-Vlasov Equation for Charged Particle Transport

We examine the modeling of charged-particle transport when both collision processes with background media and electromagnetic effects are important using the Boltzmann-Vlasov equation. We derive and transform the Boltzmann-Vlasov equation into a form very similar to the standard linear Boltzmann equation with additional operators. We apply the discontinuous finite element methods for discretization in the spatial, energy, and angular variables. An implementation of these methods demonstrates correct transport behavior for fixed electric and magnetic fields. We also demonstrate coupling to Maxwells equations with a simple electromagnetic solver to generate self-consistent fields.

SCEPTRE 1.4 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general purpose C++ code for solving the Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates. Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Party Libraries (TPL) to be available, and example scripts for building these TPL’s are provided. The TPL’s needed by SCEPTRE are Trilinos, boost, and netcdf. SCEPTRE uses an autoconf build system, and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

Modeling Electron Transport in the Presence of Electric and Magnetic Fields

This report describes the theoretical background on modeling electron transport in the presence of electric and magnetic fields by incorporating the effects of the Lorentz force on electron motion into the Boltzmann transport equation. Electromagnetic fields alter the electron energy and trajectory continuously, and these effects can be characterized mathematically by differential operators in terms of electron energy and direction. Numerical solution techniques, based on the discrete-ordinates and finite-element methods, are developed and implemented in an existing radiation transport code, SCEPTRE.