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.
This report describes experiences gained in performing radiation transport computations with the SCEPTRE radiation transport code for System Generated ElectroMagnetic Pulse (SGEMP) applications. SCEPTRE is a complex code requiring a fairly sophisticated user to run the code effectively, so this report provides guidance for analysts interested in performing these types of calculations. One challenge in modeling coupled photon/electron transport for SGEMP is to provide a spatial mesh that is sufficiently resolved to accurately model surface charge emission and charge deposition near material interfaces. The method that has been most commonly used to date to compute cable SGEMP typically requires a sub-micron mesh size near material interfaces, which may be difficult for meshing software to provide for complex geometries. We present here an alternative method for computing cable SGEMP that appears to substantially relax this requirement. The report also investigates the effect of refining the energy mesh and increasing the order of the angular approximation to provide some guidance on determining reasonable parameters for the energy/angular approximation needed for x-ray environments. Conclusions for γ-ray environments may be quite different and will be treated in a subsequent report. In the course of the energy-mesh refinement studies, a bug in the cross-section generation software was discovered that may cause underprediction of the result by as much as an order of magnitude for the test problem studied here, when the electron energy group widths are much smaller than those for the photons. Results will be presented and compared using cross sections generated before and after the fix. We also describe adjoint modeling, which provides sensitivity of the total charge drive to the source energy and angle of incidence, which is quite useful for comparing the effect of changing the source environment and for determining most stressing angle of incidence and source energy. This report focusses on cable SGEMP applications, but many of the conclusions will be directly applicable for box Internal ElectroMagnetic Pulse (IEMP) modeling as well.
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 Maxwell’s equations with a simple electromagnetic solver to generate self-consistent fields.
The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field.
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.